When using some wired earbuds, one of the annoying problems you face is the tangling of the wires. That's where tangle-free earbuds come into play.
Zipbuds SLIDE Sport Earbuds if you are a fitness freak. Klipsch Image S4i-II is best suited for outdoor use.
The earbuds which do not have flat cables, tend to tangle a bit quickly when you put them up in your pocket or even when you put it on your couch.
If you are a curious human (I guess you are!), you may have sometimes wondered why the cables of earbuds tangle all by themselves. Finally, scientists are now able to explain why wires tangle itself.
In the study, they found that almost 50% of the time, the string would form a knot by itself.
How strange? Added to that, the strings that are less than 46cms do not get tangled at all. The cable of earbuds is obviously above 46cms, so they tangle a lot.
The earbuds I mention, do also come with the inline mic so that you find these tangle-free earbuds to be used easily with your smartphones or iPhones on the go.
After some research, scientists found out that flat-cable earbuds do not tangle easily. So, if you want tangle-free earbuds, flat-cable earbuds are the way to go.
The ACIL Bluetooth Noise-cancelling Earbuds are equipped with a unique tangle free flat cable. If you're a music lover, you probably understand how frustrating it is when your earphones get tangled up. It often forces you to spend considerable time untangling the headphones.
Purchasing tangle-free cable earphones such as ACIL Bluetooth Earbuds eliminates the inconveniences brought about by tangled earphones.
Since they're wireless, you don't need to directly connect them with your smart device. Simply switch on the Bluetooth functionality and wear these in-ear headphones as you work out or stroll around the block.
If you prefer earphones with mic, you'll love the ACIL Bluetooth Earbuds. These exquisite earphones come with an in-line microphone that can be regulated using button control.
The sound accuracy of this tangle free headset makes it one of the best tangle free earphones in the market.
These tangle free cable headphones are designed by highly trained audio engineers. They feature authentic, wide-ranging sound consisting of powerful lows and exquisite highs. You will enjoy the crisp sound quality delivered by these in-ear headphones – users describe this sound as "deep and full".
Considering the budget-friendly price of these tangle-free earphones with a flat cable, there's all the reason to purchase them. These ACIL Bluetooth headphones are equipped with two distinct drivers: the Knowles balanced armature driver and the 10.8mm dynamic driver.
As a result, you get lively treble audiophiles that merge perfectly with the deep, dynamic bass.
It's important to purchase a tangle free headset that's comfortable to wear. The ACIL Earbuds are intricately designed to provide the perfect fit. These in ear headphones utilize an ergonomic, asymmetrical design to offer a comfortable fit.
The distinct ear-tips of the ACIL Bluetooth Earbuds are constructed using soft liquid silicone material that acts as a soft seal. There's an assortment of ear-tips that are included within the package to cater for the dissimilar ears of different users (these are the S/XS/M/L ear tips).
Apart from ear-tips, these Bluetooth earphones are equipped with a magnetic clasp that fits securely onto any outfit, optimizing comfort even when you're on the move.
The Pioneer Hi-Res in ear headphones are equipped with a tangle free cable that offers immense convenience to users. The cable is braided and fitted with a gold-plated jack. Pioneer provides one of the best tangle free earphones in the industry, and they've certainly outdone themselves here.
The braided cable is black in color and features an inline mic and control feature. These earphones with mic allow you to pick up calls without having to grab your phone. You can also control your music selection by manipulating the remote control.
Using the Pioneer Hi-Res tangle free earphones offers users lots of freedom and convenience. You won't have to spend hours untangling these in-ear headphones, owing to the braided cable. It's a great idea to invest in such impressive earphones.
These pioneer headphones provide a surreal listening experience. They are accurately tuned to provide a clear sound that is not only accurate but also enjoyable to listen to.
Pioneer SE-CH5T-K is specially developed to reproduce high-resolution audio formats accurately. It possesses powerful drivers that are capable of delivering 40 kHz sounds. You can comfortably listen to jazz, rock and other instrumental music genres with intriguing clarity.
Music lovers are always keen to find tangle free earphones that deliver detailed vocals consistently. In this regard, these Pioneer Hi-Res headphones don't disappoint. The bass quality is simply to die for.
A concise review of the best tangle free earphones wouldn't be complete without a deep look into the comfort level of Pioneer Hi-Res headphones. This unique earpiece sport an ergonomic design that's perfect for in-ear listening.
Weighing at 2.72 ounces, these headphones are lightweight and convenient to wear – you'll barely notice wearing them. In addition, they boast of having Airflow Control Port.
This is a cutting-edge technology that enhances the mid-range bandwidth and also highlights the bass frequencies. As a result, audio is delivered with an exquisite depth of clarity.
In conclusion, the Pioneer Hi-Res headphones fasten securely over users' ears to provide a comfortable fit. The cable deliver less bumps during movement, ensuring that you listen to less noise and more music.
If you are looking for a completely tangle-free, and durable earbuds for working out, these work like a charm. Most of the zipper earbuds come with a zipper.
However, these earbuds come with a Zipperless Zipper Cabling, which lets you use the earbuds without worrying about tangling.
The lack of the actual zipper is a significant upgrade over the previous version of ZipBuds and makes the earbuds very lightweight for everyday use.
The zipper starts from the remote pad and does an excellent job of holding the two wires together and prevent them from tangling.
The bass is balanced and punchy. It does not sacrifice mids and highs due to the strong bass. These earbuds can even satisfy the needs of a bass-head to some extent.
For the price, the audio quality is excellent. The mids are clear and highs are very crisp. You won't be noticing any muddiness and distortion in your sound at all.
There is an inline mic that is sweat proof and gets you rid background noise effectively. The voice turns out to be very clear, and I personally thought that the mic could be much better in terms of sound quality.
These Zipbuds SLIDE Sport earbuds come with multiple sizes of Dual-Composite Silicone Ear Tips. These ear tips, when combined with the Sport Fit Mold gives you the utmost comfort and great fit for even intense workouts.
They are very comfortable for long use, and never fall off your ears with a secure fit. As they are meant for the active lifestyle, they are designed so that the earbuds won't irritate your ears due to the sweat while working out.
This Klipsch Image S4i-II is one of the good flat cable in-ear headphones under $50. Like that of the majority of the Klipsch earbuds, these also do come with a tangle-free flat cable.
With this flat cable, you do not have to worry about untangling your earbud cables repeatedly.
The cables are bit heavier and thick, and they bounce out a little when running or jogging. Nevertheless, this design makes the earbuds very resistant to tangling.
Bass is balanced and not overpowering. The bass is pleasant to hear.
The mids and highs are pronounced accurately with no distortion at all. The earbuds add some warmth effect to the songs which is great to hear and relax.
The major downside of this earbud is microphonics. With the flat cords, these earbuds produce some cord noise when in movement and rubbing against your cloth fabrics.
The earbuds are not suitable for working out due to this.
As I said earlier, the cord is little heavy causing the buds to fall out for some people while running.
The earbuds come with the three-button remote control and also an inline mic for voice calls. The clarity of the voice in mic is decent and serves its purpose.
These Klipsch S4i-II earbuds come with multiple ear tips. The patent-pending oval ear tips provide great comfort for extended hours of listening.
They fit in perfectly. However, in case if you didn't find the perfect fit, you may find the earbuds fall out of your ears in case of very intense workouts due to the slightly heavy cords bouncing while you are running on the treadmill.
However, if you got a spare short clip-on, this can be prevented.
Apart from falling out sometimes, these offer great comfort without causing any discomfort in your ears.
Although these Sennheiser CX 300 earbuds don't come with inline mic, these are worth mentioning as they are best tangle-free earbuds under $50.
Below $50 this is the best bet if you want tangle-free earbuds with a strong bass. The earbuds come with 1.2m tangle-free cable that's of high quality.
It also comes with 3.5mm right-angled connector to prevent the wear and tear of the connection between the cable and the earbuds.
If you've ever used the previous version of these earbuds the CX300II, they tend to tangle. But these earbuds are a great upgrade to the previous one as this never tangle in your pocket.
The bass in these earbuds are strong. But the bass of these can't be compared to the Sennheiser CX 300 II earbuds – the bass monsters. The bass is well balanced and certainly don't overpower the other sound ranges.
The mids are where these earbuds are great. The vocals sound clear, and you love it. The highs are not harsh but pleasant to hear. It is a pleasant surprise to see these earbuds performing great in all the frequency ranges.
The earbuds do a great job of blocking out an ample of ambient noise; they are good at isolation.
They are very comfortable to wear for extended periods of time. You can expect these earbuds to serve you well in the gym while working out.
The earbuds stay fit in your ears even while moving. The earbuds come with four rubber ear tips but don't come with Comply foam ear tips. The ear tips offer great seal and comfort.
If you want more features in your earbuds out of the money you spent, these earbuds won't disappoint you.
The tangle-free flat cable enables the earbuds to get rid of any natural tangles. This lets you use these earbuds without any hassle. The connectors are of the right angle and it ensures that the connection won't get broke.
These NoiseHush NX80 earbuds are comfortable to carry and fold without worrying about those knots. The cable has a unique feel, with a nice blue or red color based on the color of the earbuds you buy.
NoiseHush NX80 earbuds do come with an inline mic. That's fairly good at getting rid of the noise. The sound quality is good and more than enough for voice calls.
Although there's an inline control there's no option to change the volume. But that would not be a serious downside for most of them.
The sound quality is great for the price below $20. These are bass-heavy earbuds. These earbuds deliver that thumping effect for rock and rap genres kind of music.
The bass overpowers the mids to a certain range. Although the bass does not sacrifice the mids entirely but it affects it a little. But with some slight EQ changes, this can be fixed, though. The mids are clear.
The highs are not too high. But are not too harsh.
The mic quality is great and conversations turn out very clear.
For the price, these offer good value.
These NoiseHush NX80 earbuds are comfortable. These come in with three various sizes of ear tips. For most of the people with medium sized ears, the small ear tips are very comfortable.
You can easily wear these on for hours without getting hurt.
These Philips In-ear High Precision Tx2 Earbuds are the best tangle free earbuds with mic below $50. This earbud comes with a tangle-free flat cord with slider technology.
This enables you to get rid of any slight tangles that may occur easily.
You can easily pull them out from your pocket and use them on the go, without worrying them to untangle them.
The cable also includes an inline mic and remote control. The mic does an excellent job of getting rid of background noise, so you'll have clear conversations with these on.
If you've ever used earbuds from Jlabs or Panasonic in this range, Philips clearly beats them regarding sound quality.
As they fit nicely into your ears, the extended bass can be felt strongly in your ears. The bass is tight and extended.
The mids are very clear; you often notice the details of the songs you've never noticed before. The highs are crystal clear, and there is no distortion whatsoever.
To get a awesome sound quality, you can go with dual driver earbuds.
These Philips In-ear earbuds come with three sets of ear tips. These ensure that you find the perfect pair that fits in your ears snugly.
If you have tiny ears, you may find it difficult to find a good ear tip pair out of these.
So, you may need to get another set ear tips preferably Comply Foam Eartips that suits your ear size and fits in perfectly.
Once you find the perfect fit, the sound isolation is excellent.
Untangling wires of the earbuds especially in a crowded place may seem a little embarrassing. So, these tangle-free earbuds come handy at those times.
Wireless earbuds are also good choice.
I hope you found these best tangle-free earbuds helpful. Most of the best tangle-free earbuds come with a flat cable, although zipper earbuds I mentioned is the exception.
Before picking up a good earbud, make sure it also has an inline mic. Don't preassume anything.


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Eduardo David Leonardo, MD, PHD
Specialties: PsychiatryMore specialties
Eduardo David Leonardo, MD, PHDBook an Appointment
1051 Riverside Drive
Additional Locations for Eduardo David Leonardo, MD, PHD
ColumbiaDoctors - 119 West 57th Street
About Eduardo David Leonardo, MD, PHD
Dr. Leonardo graduated from Yale University and received his M.D. and Ph.D. from the University of California at San Francisco.
He completed residency training at NYSPI/Columbia University, College of Physicians & Surgeons. He completed a Research Fellowship in Anxiety, Mood and related disorders in 2006 and has been on the faculty since then. He is currently an Associate Residency training director and director of Neuroscience Education and Research training for the Department of Psychiatry residency program at Columbia.
Adult Psychopharmacology
Psychopharmacology of Anxiety and Depression
Medical School: University of California San Francisco School of Medicine
Internship: New York State Psychiatric Institute
Residency: NewYork-Presbyterian Hospital/Columbia University Medical Center
Assistant Professor of Psychiatry at CUMC
Associate Director, Residency Training Department of Psychiatry

redpajama_set_name: RedPajamaCommonCrawl


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WONDER- Martha's Vineyard African American Film Festival
May 06, 2019 by Jamyl Dobson
So, late last year I had the pleasure of filming a short film called, Wonder! I just learned that the film has now got into its first film festival. The film is now apart of the Martha's Vineyard African American Film Festival which is a huge deal because the festival is also an Oscars Qualifier! The producers of the film are still waiting to hear back from a few other festivals in which it was submitted.
What is the film about you may ask? Well, first I should mention that this short film is intended to be a TV short which the producers hope to turn into a series. It is a wonderful coming of age story that revolves around young people of color and the LGBTQ+ community. In the film I play a small but pivotal role of the drag queen! I can't really give out too many other details about the film but just know that I can't wait for people to see this! If you happen to be in the Martha's Vineyard area this summer, the festival is from August 5-10th! And to learn more about Wonder and some of the other film project that the producers of Real Talk Film is working on, check out their website at the link HERE.
Stay tuned for more news on this short film!
May 06, 2019 /Jamyl Dobson
WONDER, JAMYL DOBSON, NYC ACTOR, FILM, TV
GOTHAM, Season 4!!
December 06, 2017 by Jamyl Dobson
So, almost 2 moths ago, I had the great fortune of getting cast in a small part on Episode 411 of Gotham! It was my very first network TV appearance and I was a fan of the show so to say that I was excited would be an understatement. Everyone on set was so friendly and it was just cool to play around this Gotham world even if it was just for a day. This is also my very first booking through my new manager, King N Queen Management. They have been an absolute God-send to me and I can't thank them and Bowling Miscia Casting for the opportunity!
So be sure to catch the episode of Gotham airing this Thursday at 8pm! You can also find it online on Hulu and fox.com the following day! Here's a snap of me in my dressing room preparing for show. Great way to close out 2017!
December 06, 2017 /Jamyl Dobson
GOTHAM, jamyl dobson, TV, FILM, FOX, NYC ACTOR
The Path Season 2!!
January 25, 2017 by Jamyl Dobson
So last summer I had the great fortune of being cast in a small part for the season premiere of the 2nd season of "The Path" on Hulu! Even though it was a small part, it was the highest profile gig that I've EVER booked! As if that weren't enough, I had the great honor to film 2 scenes with the show's lead, Aaron Paul (Emmy winner- Breaking Bad)!! He couldn't have been nicer and the entire process felt like a dream. I learned so much simply by watching him work and how he conducted himself on set.
I don't want to give away too many details as you have to watch the episode. I also had the opportunity to play a role that I don't normally get to play: a regular construction guy. It may seem odd but in the past, I've played roles that are more flashy as I am a character actor. But this was a welcome treat and a role I was excited to take on. Another added bonus was that I got to work with a great actor from Philadelphia named Ian Bedford! Ian and I both worked at the Pennsylvania Shakespeare Festival YEARS ago. Back then, I was an acting intern and he was playing Henry V, I believe. It's always surreal to cross path with actors that you hadn't seen in years and then have the great fortune of working together, especially on a project like this!
A HUGE thank you must go out to Calleri Casting for the incredible opportunity! Here's hoping the rest of the New Year brings on more TV and film bookings! And don't forget to check me out on the the Path streaming now on Hulu!
January 25, 2017 /Jamyl Dobson
The Path, Hulu, TV, FILM, NEW YORK ACTOR
Hack My Life on TruTV!
August 18, 2015 by Jamyl Dobson
So about two months ago, I had the pleasure of shooting a little skit for the television show, Hack My Life for TruTV that filmed here in New York City. It was a very fun shoot in which I play a regular pedestrian opposite a Criss Angel-type of magician as he performs a trick or a "Hack" on me. It was just a featured role but it was so much fun to be on set and everyone was so nice! I could get used to this set life! I don't have an exact date on when my particular episode airs but keep your eyes peeled as the new season of Hack My Life premieres tonight, August 18th at 9pm/8C!!
Below are some behind the scenes snapshots from my episode.
Here's hoping for more TV and Film gigs this upcoming season!
August 18, 2015 /Jamyl Dobson
HACK MY LIFE, TV, FILM, ACTOR, NYC, Jamyl Dobson
New Representation and New Opportunities
June 15, 2015 by Jamyl Dobson
I am very happy to announce that I will now be working with Emerging Talent, LLC. They will be representing me for their theatrical division so I am very excited about that! Also, I just finished work on my first voice-over gig. I was contacted out of the blue by film director, Gustavius Smith to portray the voice of Langston Hughes in his upcoming documentary called, Playing the Numbers. This film focuses on the numbers game that begin during the Harlem Renaissance era. It is a pre-cursor to the lottery system that we all know today but it goes in depth to the individuals who started this system and the effects that it had on the community in Harlem at the time.
It was such a pleasure working on this film and to do my first voice-over gig for such an important subject matter. No word yet on when this documentary will be released. But as soon as I know I will certainly post that information here.
June 15, 2015 /Jamyl Dobson
FILM, DOCUMENTARY, AGENT, VOICE-OVER
On Camera Classes @ The Acting Studio
April 21, 2015 by Jamyl Dobson
Lately, I have been learning more about acting in front of the camera. I recently started taking acting classes at the Acting Studio. The class is taught by Victor Verhaeghe, an accomplished actor who has appeared on such shows as Boardwalk Empire, Blue bloods, Person of Interest, and Allegiance, just to name a few. I'm learning a great deal and am learning more and more that less is more. It is, at first, weird seeing yourself on camera, hearing how your voice sounds, see all the weird things that you naturally do (Tame the eyebrows, Jamyl). But it's also so great to feel the progression and to learn more of the differences between acting on camera vs. acting on stage.
The class is taught with a Meisner perspective, so it is very much about listening and responding truthfully in the moment. The class meets over the course of 8 weeks and we go through TV and film Sides, commercial auditions, learning about what our character types are and how to best sell that product to the appropriate markets, and then we get to show our work in front a casting director. Needless to say, it is invaluable. It is such a treat and I recommend anyone interested in a career in TV and Film to take this class at the Acting Studio on 54th!
April 21, 2015 /Jamyl Dobson
ACTING STUDIO, TV, FILM, CLASS


Place the chicken in a gallon sized resealable bag. Add the marinade and turn to coat. Refrigerate for 1 hour or overnight, flipping the bag several times. Or place in the freezer and use within 1 month, the chicken will marinate as it thaws.
I'm picky about lemon chicken myself-yours looks perfect, though!
Ooh yum, sounds delicious! Thanks for sharing at The Fun In Functional!
Your lemon and herb chicken looks fantastic! I'm glad to hear there's hope for lemon and herb marinades. I've only had the pre-packaged kind, but am willing to give it another shot!
I am your newest follower! Found you on the blog hop! Your dishes look fantastic, will try some this weekend!
I'm so jealous of your herb garden! I really want to give one a try. This looks great! Thanks for sharing at Must Try Monday.
This is dinner tomorrow. I have everything I need to make it. I have some Thai Basil--can't wait to add that to the mix.
Looks great, I love lemon and chicken together!
This makes me hungry just looking at it! Pinning! Thanks so much for sharing this at our Weekend Wonders party :) Hope to see you back on Thursday. Have a great week!
Hello, me again.. I just wanted to let you know that I've featured this fabulous chicken :) Come by and grab a feature button if you'd like. Have a great day!
This looks and sounds wonderful:) I love the idea of freezing the marinade and chicken, great plan! Thank you for sharing at Freedom Fridays.
Lemon has quickly become my favorite thing to pair with anything - I actually used to hate lemon-flavored things! This looks delish!
WOW! This is awesome! Thanks for sharing your recipe on our Blog Hop Recipe Swap!
I love lemon herb chicken! Thanks for sharing on our Blog Hop Recipe Swap! This would be so easy for Back to School, especially since you can let marinate over night!
LOVE your blog great ideas and yummy treats! Glad I found you via Blog Hop!


In this area of law, for instance, we advise our clients on launching a company and on choosing the right company form. We also help when conflicts exists and give advice when questions arise regarding the legal framework for shareholders and for the management body of a company.
We also advise on business association formation (corporation/group structures), transforming and reframing companies, in matters of company succession and in terms of business crises.
In most cases we accompany the whole process of transforming and reframing the company in the matter of corporate law and mostly we also design the necessary contracts, for instance, we draw the articles of association or the managing director's agreements. What matters in this context is that not only the legal aspects are considered but also the economic and fiscal components.


Not only do balance bikes come in all shapes, colours, materials and sizes – so do the seats on the bikes so we thought it would be useful to prepare some information on balance bike seats to help you in your search for the best balance bike.
Most balance bikes will have a triangular shaped seat, and the material of the seat and the amount of padding provided will often depend on the cost and overall quality of the bike.
Many bikes towards the lower end of the price range will have a hard plastic seat, so although these types of seats are very durable they don't provide much comfort for the rider.
A good example of this is the Chicco Red Bullet Balance Bike, which is one of the best value balance bikes available at around £30.
Although it does not have a huge range of features, it is great for younger children just learning to ride and it is one of the smaller balance bikes available.
Some of the more expensive bikes towards the higher end of the market will offer various layers of foam padding, which does make the ride more comfortable although will usually increase the cost of the bike.
The Specialized Hotwalk Balance bike includes a padded seat, and although it is much more expensive at around £130 it has a high specification and a great range of features.
We must not forget wooden balance bikes, which will usually come with a wooden seat! One of the main disadvantages of wooden balance bikes is that the seat does not usually have as large a range of heights as metal bikes, although they are more environmentally friendly and look great as well. You can read our full guide to the best wooden balance bikes elsewhere on this website.
Some balance bikes now also offer U-shaped seats, which will help the rider to stay on the bike - especially if they are freewheeling downhill when they might be likely to slide off a plastic seat.
The material and shape of the seat is just one aspect to consider when you are buying a balance bike, and perhaps a more important factor is the actual height of the seat and the range of heights available. Check out our Balance Bike Seat Height Guide here!


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Research Your Home
Postcards and Greeting Cards
Route 9: A Journey through Time
A Child's Life in Wellesley During the 1880s Activity Toolkit
Craft Beer Event
History in Bloom: A Spring Gala
Tollhouse Shop
Irving Taylor Barnes Maritime Journals
Introducing Eleanor Early
One Hundred Years On, Wellesley Observes Veterans Day
Wellesley's Spiritualist Past: One Family's Travel Through Space and Time
The Other Emma Stone
Mary Brewster Hazelton Painting Returns Home
High School Students Complete Senior Project
Art in Bloom!
Preservation of WWI Collection
Blizzard of 1978 Scrapbook
Art in Bloom (1)
Denton (5)
History Mysteries (33)
Alden Ludlow, contract archivist
In celebrating Women's History Month, the Wellesley Historical Society acknowledges the contributions of generations of extraordinary women who have made Wellesley the town it is today. Their unparalleled community engagement resulted in a proliferation of social, civic, and arts organizations over the last century and a half which continue to be the lifeblood of the town.
This month we would like to highlight the life of Eleanor Mary Early (1895-1969), a noteworthy and independent Wellesleyite who, in her time, was an accomplished journalist, travel writer, and novelist. Though her brother James "Jack" Early is better known, Eleanor's life was far more compelling.
Eleanor's parents, James A. Early and Sarah Jane Dolan, were married at St. John's Church, Wellesley, in 1891. They had seven children, six of whom survived until adulthood. Eleanor was the oldest. The family moved to the Wellesley area, buying a plot of land in Wellesley Hills in October 1904; they built the family home, which was at 93 Washington Street, and had a grocery business in Newton Lower Falls. All of the children attended Wellesley public schools.
Eleanor Mary Early born in Newton in 1895, and grew up in the family home in Wellesley. She attended Wellesley schools, and graduated from Wellesley High School; her notebooks and school papers reveal a thorough and diligent student who loved to write. When her brother, Jack, went off to fight in World War I, the two carried on an extensive correspondence that reveals her love and wit.
After graduating from Wellesley High School, she attended Wheelock College (then Miss Wheelock's College), and graduated in 1917, certified to be a teacher. But she enjoyed writing above all, and almost immediately pursued a career as a writer and journalist in Boston. She wrote for the Boston Herald-Traveler, the Boston Post, the Record American, and the Boston Globe. In the late 1930s she left Boston to join the staff of the New York Times. She also lived for a time in Washington, D.C. She traveled extensively, and those experiences informed her writing, which extended beyond newspaper reporting; she also was a radio commentator and magazine columnist.
She wrote books on travel, cooking, and history, as well as novels. Some of her lauded works at the time include Adirondack Tales (1939), New England Cookbook(1954), Washington Holiday (1955), Behold the White Mountains (1935), and Boston Yesterday and Today (1939). Early in career she wrote a series of travel books, which included And this is Boston! (1930) as well as And this is Washington! (1934), among others. Most of her books were published by Houghton Mifflin Company.
Throughout her life Eleanor travelled the globe, reporting as a journalist, writing travel pieces, and working on her novels. Independent and adventurous, she never married; she returned to Boston just a few years before her death in 1969. Eleanor Early's papers form a significant part of the Wellesley Historical Society's Early Family Papers.
— Alden R. Ludlow, WHS archivist
The Early Family Papers were processed in March 2018 with generous grant support from the Wellesley Community Preservation Commission (CPC) and the Massachusetts's State Historical Records Advisory Board (SHRAB).
Wellesley Historical Society
229 Washington Street Wellesley, MA 02481
(781) 235.6690 info@wellesleyhistoricalsociety.org
Follow the Society on Facebook and Instagram to receive regular updates regarding events and programing.
Tollhouse Shop Hours
In order to give our staff and volunteers a break for the holidays, we will be closed the last week of December. The Tollhouse Shop will be CLOSED on the following dates:
Saturday, December 24th
Wednesday, December 28th
Saturday, December 31st
We will resume normal hours [Wednesday & Saturday from 10am-12pm] on Wednesday, January 4th.
Wednesdays & Saturdays
*If you would like to make a donation, please contact the society at info@wellesleyhistoricalsociety.org and someone will reach out to you to make an appointment.
© 2023 Wellesley Historical Society
Website designed and produced by J Sherman Studio and Agency 3.0


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Parents Exposed to COVID-19 Can Now Choose Standby Guardians for Their Kids
(NEW YORK, NY) April 9, 2020: Health care workers and volunteers in New York State exposed to the novel Coronavirus (COVID-19) can now designate a standby guardian for their children according to an Executive Order signed by New York Governor Andrew Cuomo. A team from the Albany office of Greenberg Traurig, LLP, working pro bono with the New York Legal Assistance Group (NYLAG), helped draft language for the order. The order would also allow others exposed to COVID-19 to designate a standby guardian.
Executive Order No. 202.14, in part, expands the scope of the New York Surrogate's Court Procedure Act (S.C.P.A.) § 1726. Signed by Cuomo on April 7, the order modifies sections of the Act to provide that any parent, a legal guardian, a legal custodian, or primary caretaker who works or volunteers in a health care facility or who reasonably believes that they may otherwise be exposed to COVID-19, may designate a standby guardian by means of a written designation.
"The well- being of healthcare workers and anyone exposed to COVID-19 is paramount right now. We hope this change will give them some peace of mind when it comes to the care of their children. We are very grateful to Governor Cuomo for issuing this Executive Order and to everyone who played a role in extending the act to cover those most at risk in our state," said Randye Retkin, Director of NYLAG's LegalHealth Division. "This is an unprecedented time and we were able to move swiftly to do the right thing. We also thank Greenberg Traurig's team in Albany for understanding how important this is for New York's frontline healthcare workers and other New Yorkers exposed to the virus, and for making this a priority."
"We applaud Governor Cuomo for providing New York's health care workers with a critical tool to plan for their families. We hope this gives those who are on the front lines of the State's COVID-19 response some peace of mind," said Lynelle K. Bosworth, a shareholder in Greenberg Traurig's Albany office.
"The extension of the protections under S.C.P.A. § 1726 was critical, particularly given that courts are closed. Greenberg Traurig has a long tradition of stepping up to help communities in need, and we were honored to continue our pro bono work with NYLAG to accomplish this," said Mark F. Glaser, a shareholder in Greenberg Traurig's Albany office.
The act was first passed in 1992 at the height of the AIDS crisis to help sick parents plan for their children's futures and initiate the immediate transfer of temporary guardianship powers to someone the parent trusts, until a more permanent arrangement and hearing could be put in place, according to NYLAG. In 2018, Greenberg Traurig worked with NYLAG to help pass the legislation that would allow parents who are at risk of detainment or deportation based on immigration status to designate a standby guardian to care for their children in the event the parent is detained or deported. Until then, the Act limited the ability of parents to appoint or designate a Standby Guardian to seriously ill individuals. This Executive Order is an important extension of these protections.
"GT attorneys are rising to the occasion to serve their communities during this crisis," said Caroline J. Heller, Greenberg Traurig Litigation Shareholder and Chair of the firm's global Pro Bono Program. "We are proud of our continued pro bono work with NYLAG in support of its mission to provide legal services to low-income New Yorkers and of the impact our combined teams are making."
Founded in 1990, NYLAG provides free legal services, financial counseling, and engages in policy advocacy to help people experiencing poverty or those with low-income. NYLAG assists immigrants, victims of domestic violence, children, seniors, and chronically ill and disabled patients with a wide range of legal issues. NYLAG's LegalHealth division focuses its practice mainly on assisting ill and disabled patients through its legal clinics in more than 25 hospitals across the city. LegalHealth frequently assists parents in naming Standby Guardians for their children.
About Greenberg Traurig's Pro Bono Program
Greenberg Traurig lawyers across the firm provide pro bono legal services to the indigent and working poor, as well as to numerous civic and charitable organizations dedicated to assisting them. The firm focuses its resources on specialized and interrelated issues including civil rights and affirmative action, anti-human trafficking, family law matters, criminal appeals, immigration and political asylum, housing, and homelessness.
About Greenberg Traurig, LLP
Greenberg Traurig, LLP (GT) has approximately 2200 attorneys in 41 locations in the United States, Latin America, Europe, Asia, and the Middle East. GT has been recognized for its philanthropic giving, diversity, and innovation, and is consistently among the largest firms in the U.S. on the Law360 400 and among the Top 20 on the Am Law Global 100. Web: www.gtlaw.com Twitter: @GT_Law.
For NYC migrants, just getting inside immigration courthouse is a feat
NYLAG's Melissa Chua spoke with Gothamist about New York City's backlogged immigration system and the enduring difficulties that newly-arrived immigrants face in accessing resources. "There's nowhere to refer clients. There's no place to send them because we know that everyone is working at capacity."


Anticipated ship dates are listed below by state. We will ship your wine on this date unless the weather is too hot or too cold. If we need to hold your shipment due to weather, we will be in touch with you directly. Once we deem temperatures are safe to ship Ground, we will confirm a ship date with you and you will receive an e-mail from your shipping carrier with an expected delivery date and tracking number. If the weather in your region is too hot, we may elect to ship your wine in November if that is the only safe option for their area. We will contact you directly if any changes need to be made.
AL, AZ, southern CA, FL, GA, TX: Your wine will ship on Wednesday, May 15th. To preserve the integrity of your wine, we will be shipping via temperature-controlled or Express Air methods to these states. We will offer a flat rate cost for these services. Please contact us if you have any questions or would prefer we hold your wine in our cellar until the cooler temperatures of fall allow us ship your wine safely via Ground.
AK, northern CA, CO, HI, ID, IL, IA, KS, MI, MN, MO, MT, NE, NM, NV, ND, OH, SD, TN, WI, WY: Your wine will ship on Tuesday, May 21st.
Please review our shipping policies.
Join us at our wine club pick-up parties on Saturday and Sunday, May 18th and 19th from 11 a.m.- 4 p.m. Each club membership is allotted four (4) complimentary admissions to this event. Additional guests are welcome at $30 per guest. Each admission fee is waived with the purchase of a bottle of equal or greater value. This is an open-house style party but kindly RSVP.
For our "pick-up" Wine Club Members:We ask that you please pick-up your wine within six (6) months of its release. Soter Vineyards is unable to hold your wine shipments past this time. If after six (6) months, you have not picked-up your wine or made other arrangements with us to receive your wine, we will consider your wine abandoned and it will be returned to inventory. We are unable to process any returns/exchanges after 180 days. Please contact us at 503-662-5600 if you need to make other arrangements.
Please review our wine club terms and conditions.


ProList: Fashion is a set of 30 trendy self-animating bullet point list tools created for use exclusively within Final Cut Pro X. With ProList: Fashion, editors can easily create lists for presentations, youtube productions, and more. Simply choose from ProList: Fashion's fashionable designs and stack presets on the Final Cut Pro X timeline to create multiple bullet points. ProList: Fashion is the perfect complement for any and all presentation media.
ProList: Fashion is a package of 30 self-animating trend-setting bullet point designs, that contains simple to use backgrounds, and a grid tool that will assist with precise alignment. Choose from a large selection presets with different fashion related styles and fluid animations. ProList: Fashion's elegant style makes it the perfect complement to almost any video production.
Each preset features elegant intro and outro animations, use each preset by simply dragging and dropping it above any media or a background in the Final Cut Pro X timeline. Create personalized looks by adjusting each preset's specific customization options and inserting new text. Expand the length of the preset to extend the amount of time the bullet point stays on screen.
ProList: Fashion contains a number of control design elements such as: colors, length, width, opacity, and scale with intuitive slider control options. Utilize on-screen controls to manipulate orientation with drag and drop ease by controlling position, rotation, and scale of presets. This plugin is built efficiently for Final Cut Pro X users.
ProList: Fashion is the perfect tool for presentation style videos. Adjust the controls provided to achieve the desired look. Construct a complete bullet-point list by easily stacking multiple presets on top of one another over the desired media background. Mix and match different presets and add a background to create a unique look.
Where do I find ProList: Fashion Presets?
Once the installation is complete, you can find ProList: Fashion Presets in the FCPX Generators library.
Once the installation is complete, you can find ProLost: Fashion Presets in the FCPX Generators library.


By donating to the Adelaide Hills Hockey Club, you can make a difference. Sport brings communities together, supports physical and mental health and brings dreams to life! Donations of $2 or more to any of the projects listed below are tax deductible. Know that every bit HELPS!
This Easter we have teamed up with Kytons to raise funds for a security fence to help protect our new pitch.
Simply fill in the form, EFT to the club, and collect your order in time for Easter. It's that easy!
Please feel free to order for people outside the club on your form, just make sure that there is one electronic payment made per order form into the club account.
Payments will need to be made electronically by Monday 1st April, and all order forms given to your coach or manager that week during training.
Your orders can then be collected on Monday the 15th April from 10 Sandford Avenue, Mount Barker, between 3pm and 6pm.
Write the name of the people making orders in the left hand column of your order form (name & details).
Fill in the quantities of the desired items and the total cost of each.
Tally your total amount to pay in the right hand column.
Fill in the totals at the bottom of your order form.
To keep up to date with the Hills Hornets latest news and the hockey pitch upgrades at Anembo Park, sign-up for the Adelaide Hill's Hockey Club's newsletter.
Head to our Facebook and Instagram pages for news from the source!


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Signature Shoes Sales Numbers For 2014 Are In, And LeBron James Is The Big Winner Again
Sneaker sales are doing better than ever, and the reported U.S. sales numbers from 2014 prove that there's no slowing down. The big winner is Nike, the big loser is adidas, and Jordan Brand, again, is in the middle of the pack. Jordan Brand's signature shoe sales don't include any figures for Air Jordans or Jordan Retros, because they aren't signature shoes for active NBA players. In addition, Steph Curry's incredibly popular UA Curry One is not included in this list because the shoes only dropped five weeks ago, and Wade's Li-Nings are not readily available in the States. But with so many new signature sneaker lines debuting in recent months, the reported numbers at the end of this year could be key in projecting brand success over the next few years.
Here, we break down in order (from top the bottom) the signature athletes in the NBA that have pulled in the most dollars in the U.S. market, the reported amount, and the change from 2013. Generally speaking, it appears that sneaker sales continue to grow, with only the Melo line reporting no growth and two adidas signature guys reporting decreases. The biggest jump by number and percentage is Kobe Bryant, whose signature shoes were incredibly popular in 2014 thanks to the Flyknit-based Elite model. The biggest tumble goes to Dwight Howard, but that news isn't even the worst for adidas this week. In any case, check out the list below (info via Forbes) and let us know what numbers surprise you the most.
1. LeBron James | Nike | $340 million | +$40 million
LeBron is King of sneakers once again. He earned an estimated $340 million in shoe sales last year, which is about a $40 million jump from 2013 (an increase of 13%). There were some actual concerns regarding LeBron not wearing the 11 last season as well as the smaller, less glitzy market in Cleveland affecting the sales of the LeBron 12, but it appears that those events have not affected sales.
2. Kevin Durant | Nike | $195 million | +$20 million
Durant comes in at number 2 in this list of signature athlete cash cows. This figure is only about a $20 million jump from 2013, which is rather small compared to the massive $35 million to $175 million leap that we saw in 2012 (but that has more to do with the sheer availability of the KD 5 and KD 6). The $20 bump in the slight price bump as well as the popularity of the KD line to the kids is what caused the increase, but could the numbers be hired if KD wasn't injured and he actually wore the shoes?
3. Kobe Bryant | Nike | $105 million | +$55 million
The Black Mamba made a pretty huge leap, and all credit goes to Flyknit. In 2013, Kobe shoes reportedly sold around $50 million, but the massive popularity of the Kobe 9 Elite was a surefire sign that sales numbers would go up. Did we expect it to more than double itself?
4. Chris Paul | Jordan Brand | $35 million | +$5 million
The CP3 line is tops when it comes to Jordan Brand signature shoes. The popular guard in Los Angeles managed to pull in $35 million, which isn't too much of a surprise given the shoe's popularity among kids. Russell Westbrook isn't technically a signature athlete just yet, but if he was, would Chris be the main man for JB?
5. Derrick Rose | adidas | $35 million | -$4 million
Rose was back in action for half of 2014. Would that mean a boost in sales? Unfortunately, adidas' biggest financial commitment continues to go south because the the D Rose line actually reports a decrease from 2013. This has much to do with the fact that the D Rose 5 was actually $20 cheaper than its predecessor.
6. Carmelo Anthony | Jordan Brand | $30 million | even
The Melo line continues its mediocre existence with a second straight year of a reported $30 million in U.S. sales. The M10 was actually a great performance shoe, but even the awesome Flight Plate and Tinker-penned design wasn't enough to elevate the Melo line.
7. John Wall | adidas | $8 million | +$3 million
Just $8 million? Don't be deceived. Wall shoe sales in 2013 were reported to be around $5 million, but that was under the Reebok label. In just a few short months, the J Wall 1 by adidas as well as other hoops shoes under his name sold about $8 million, and given the Wizards star guard's rise and the generous pricepoint, expect those numbers to grow.
8. Kyrie Irving | Nike | $7 million | n/a
The Kyrie 1 dropped in late December and so far, he's garnered $7 million in sales. Expect Uncle Drew to be much higher on this list, potentially above Kobe, when we report on 2015 numbers. Outlook? $70 million.
9. Damian Lillard | adidas | $1.8 million | n/a
Lillard's another new sig-shoe guy, and in just a short while the D Lillard 1 has pulled in $1.8 million since the sneaker debuted in January. Lillard's another name that can rise the ranks, but we project it to be in the $15-19 million range.
10. Dwight Howard | adidas | $1.5 million | -$3.5 million
Big men don't sell shoes. Big men who seem to be disliked by half of the NBA and its fans definitely don't sell shoes. Who knew that Howard still had a signature line? Still, the D Howard signature pulled in $1.5 million in the United States.
Editor's PicksFeatured StoriesSteph Curry


There is a twelve-digit reference number in the notification that is provided to you. Enter it in the relevant box by choosing the state body which you have addressed your application to so that you can track the status of your application.
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June 1, 2019 | Sensors/Data Acquisition | AR/AI	| Data Acquisition	| Wearables
High Tech Comes to Fitness Monitoring
Neural networks are set to transform the future of fitness wearables.
Early wearable fitness monitoring devices were designed to perform a set of valuable but straightforward activities: tallying the number of steps we take daily, recording the number of hours we sleep, and monitoring our heart rate.
However, sales of simple fitness trackers have begun to stagnate, perhaps because these monitors didn't deliver enough of the right kind of information. The data gathered by these devices on their own offer an incomplete picture of an individual's health, with limited insights into strategies for long-term health and wellness.
This situation has begun to change with the advent of a new generation of wearable monitoring devices that integrate new technologies to reveal more profound and personalized health and wellness insights. Advances in artificial intelligence (AI) and neural network technologies can provide health and medical analysis that goes far beyond the simple charting of physical activities. These powerful cognitive systems enable the analysis of individual health data within the context of much larger data sets, and with consent, draw from the latest medical insights, family medical histories, genomic data, and a vast network of medical databases to reveal highly personalized, proactive health findings and treatments.
However, to enable a new generation of smarter, more capable health monitoring, devices will require new microprocessors with the performance power and energy efficiency to run real-time computation of AI neural networks, algorithms, and analysis of significant data flows in a small portable device. These hardware-based processing systems will need to be designed from the ground up to support the neural network workloads and architectures that enable advanced health monitoring devices to deliver more predictive health insights and successful outcomes.
Next Generation Health Monitors
Based on the fast-evolving technologies associated with machine learning and neural networks, the next generation of wearable health trackers will be designed to focus more closely on the wearer's holistic and long-term health and wellness. These new wearable apps will not only monitor fitness, activity, and heart rate, they will pass the data they collect on to other applications that will evaluate, interpret, and customize this information so it is useful and relevant to the user.
These devices will have the capacity to learn about users on a deeply personal level, including information about diet, mood, and medical health history. This will provide insights and guide actions and choices that can help encourage healthier lifestyles, promote more informed health decisions, and overall wellness.
AI will change how a user experiences and interacts with health trackers. A smart interconnected device could monitor a wearer's heart rate, for example, and be able to analyze this data against a dataset comprised of millions of other heart rate readings to generate meaningful insights into what the particular user's heart rate should be, based on his or her age and history and on data from other patients of similar age or health status or a specific demographic group. Typically, networks take data from a wider study and then it is partitioned into training and test sets. It is trained on a representative part of the data and then is exposed to data it has not seen before, to understand its fit and error rates (accuracy).
Complex data can even be analyzed to measure mood changes. Response to stimuli can change in terms of galvanic skin response (GSR), eye pupil dilation, heartrate, blood pressure, and multiple other inputs. These can be synthesized to understand feeling states such as excitement, fear, arousal, passivity, or lack of interest.
This is where new technologies such as AI and neural networks come in. Comparative analysis of the data could reveal deep insights into the implications of the current readings and offer a suggested course of action based on that evaluation. For instance, detecting an abnormal heart rate involves looking at patterns and identifying irregularities to that pattern.
By evaluating an individual's health data in connection with the vast medical data ecosystem, AI and neural networks can help health monitoring devices identify areas of potential health vulnerabilities; issue alerts, advice, or warnings; and offer suggestions of what responses or treatments to pursue.
Powered by neural networks, these smart data services can also serve as an early warning system to help identify signs of disease or age-related early onset problems. By recognizing symptoms at the earliest possible stage and enabling faster more accurate treatment, users have the potential for taking steps to prevent illness from taking hold or making other proactive responses.
Building More Powerful Neural Networks
The larger and more complex that the network of health data and medical databases becomes, the more useful and powerful its insights. However, this size and complexity also increases the system's computational demands, and requires new levels of performance for neural networks, particularly in mobile use cases.
To do their work, neural networks need to be trained, and this is usually done offline on powerful server hardware. However, the recognizing of patterns and objects, known as inferencing, is done in real time.
In many cases, the inferencing is run on hardware in the cloud. However, when fast response times are required — such as real-time identification of health emergencies — latency issues make it generally not practical to run neural networks via the cloud.
To support these high performing neural networks, Imagination Technologies (Kings Langley, Hertfordshire, UK) has developed a new hardware neural network accelerator (NNA). Their PowerVR Series3NX offers a full hardware NNA solution built from the ground up to support leading neural net models and architectures as well as machine learning frameworks, such as Google's TensorFlow or BAIR Caffe, at a high level of performance and low power consumption.
As an example, an NNA could be used in a chip specifically designed to monitor athletes for maximizing their performance, where their value is extremely high and any indication of performance issues because of fatigue, or say overheating, could be the difference between winning and losing.
A neural network can be used to analyze and recognize particular types of responses from GSR (based around the conductivity of the skin due to sweat) to sensors that can analyze perspiration for the presence of certain compounds. This "signature" can be recognized by a neural network and alerts or actions can be taken as a result. A sensor could be in a smart-watch where the sensor for sweat is on the back of the watch, close to the skin. It could also be in a patch taped to the person or could be worn as a chest band. Indeed, several different signals could all be compared and used to drive the data.
Diabetes monitoring of hypoglycemia and other aspects of diabetes and the result of falling levels of insulin over time could be recognized as "expected" or as potentially dangerous, depending on time of day, time since last insulin intake, etc.
Using the NNA for neural network training enables inferencing to be performed on the edge device itself. Its high performance and efficient power management are extremely important for this new generation of wearable devices. Moving inferencing on-device also addresses security issues that are critical when processing health data.
In addition, to be truly effective, the neural networks used for health monitoring need to be functional in remote areas. Since cellular networks are not always available, dedicated local hardware to operate health-related networks will result in safer and more reliable coverage when "off the grid."
Benefits of a Full Hardware NNA Solution
The PowerVR Series3NX's ultra-low power consumption makes it possible to operate full neural networks in small form factors, opening the market for smart, predictive health monitors on mobile platforms. Although it is a very low-area component, it delivers an extremely high inference rate per square millimeter.
Neural networks are commonly trained in 32-bit precision, yet for edge inference, the NNA allows bit-depths of 16-bit and lower, which, depending on the task, means that the model size and bandwidth can be reduced with only a marginal tradeoff in precision. The Series3NX's flexible bit-depth support allows tuning on a layer-by-layer basis of each layer's bit-depth and can improve precision and optimize model size. A single core running at 1.2GHz, can offer up to 4,096 MACs per clock (the industry standard performance indicator); meaning it can run over 10 trillion operations a second. And it is a highly scalable solution — through the use of multiple cores, much higher performance can be achieved, if required.
Toward More Powerful Health Monitoring Devices
NNA represents an inflection point in neural network acceleration and performance. Solutions incorporating it can help health monitoring devices become more technically robust and capable of analyzing data faster using sophisticated AI, machine learning, and deep learning techniques.
It is important, that the requirements for deploying neural networks be achieved within the power and performance constraints of mobile hardware. With this kind of processing muscle in a small footprint, the next generation of health monitors will no longer be reactive, passively tracking activities and vital signs, but will act as a smart, proactive and personalized advocate that can constantly evaluate health data parameters to promote wellness, enable more informed medical decisions, and anticipate health risks for more positive outcomes.
This article was written by Andrew Grant, Senior Business Development Director, Imagination Technologies (Kings Langley, Hertfordshire, UK). For more information, visit here.


Freshly renovated and beautifully decorated, this apartment is the perfect Surfers Paradise escape. Located high up on Level 23, you will see the waves rolling in day and night from the balcony, the living room and the bedrooms. No expense has been spared to give you the most comfortable stay, featuring a massive 65″ flat screen TV in the living area and TV's in both bedrooms.
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There are 3 replies in this Thread. The last Post ( Jul 15th 2018 ) by Splinter.
Look at the new plane to come in the next years.
Still subsonic, as the operation to check in and load de luggage is still too long. And if the planes are supersonic the flight itself could be of less time than the previus operation to get into the plane, and leave it.
That's impressive! Its design is a bit intimidating, though. Reminds me of a shark.
Somehow the idea of being on a 100-passenger plane makes me feel claustrophobic. Still, if the flight time were cut in half, perhaps the trade off would ameliorate the feeling of cattle being herded to market.
That's nothing more than a user made mock up of a not very realistic model from Microsoft Flight Simulator and nothing to do with Boeing at all.
This is what in fact was announced recently.


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News » Politics
Advocates: Biden Will Move America Away from Trump's 'Discrimination Administration'
by Kilian Melloy
EDGE Staff Reporter
President-elect Joe Biden (Source:Associated Press)
LGBTQ equality advocates are confident that President-elect Joe Biden will move America away from Trump's "discrimination administration," reports the Washington Post.
Biden was the first Obama administration official to publicly support marriage equality, though his record on the issue over the years wasn't supportive. Nonetheless, he has vowed to prioritize the passage of the Equality Act, a long-sought update of federal anti-discrimination law that would include the LGBTQ community.
The Trump administration, by contrast, continues to attack LGBTQ Americans in its waning days. A rollback of Obama-era protections relevant to sexual minorities came into effect just last week - the day after a pro-Trump mob stormed the U.S. Capitol Building in Washington, D.C.
"Just weeks before it leaves office, the Trump administration handed out a 400-page document detailing how federal contractors and recipients of government grants can cite their religious views to refuse to provide health coverage for birth control and other reproductive care and adoption services to single people or LGBTQ couples," detailed the Post.
Biden, the Post recalled, "has called religious freedom 'a fundamental American value,' but also promised to reverse Trump administration policies that are 'misusing these broad exemptions,' " especially those that target the transgender community.
Biden has said that he will restore the rights of trans patriots to serve openly in uniform and restore protections for transgender youth in America's schools, the Post article added. Biden has publicly stated that equality for transgender Americans is "the civil rights issue of our time."
The president-elect has also directly acknowledged the epidemic of violence that has seen the killings of trans women - many of them people of color - skyrocket in the last few years. "Advocates praised Biden for bringing the issue to the national stage and vowing to direct federal resources to prevent and prosecute such homicides," the Post noted.
That in itself constitutes a landmark departure from the Trump years. The Post quoted the National Black Justice Coalition's Executive Director, David J. Johns, as saying, "Even though the transgender community may have more visibility in TV shows like 'Pose,' the vitriol at the policy level that exists within the system leaves no promise of justice."
But with Democrats and Republicans 50/50 in the Senate and the House retaining a narrower majority than it had before the 2020 elections, getting the Equality Act passed might be a challenge, the Post noted.
"Some Republicans have instead backed the Fairness for All Act, which provides some LGBTQ protections while also granting certain exceptions for religious institutions and organizations," the Post pointed out, adding that another hurdle is the fact that many state legislatures have taken up anti-LGBTQ - and, more specifically, anti-trans - legislation over the past few years.
Still, the story said, the nation's president does help set the tone of the country and words that come from the Oval Office carry considerable weight with many Americans.
The Post quoted Drew Anderson, formerly of GLADD, who said of anti-gay bias and the discriminatory policies it fosters: "It always helps to have an LGBTQ ally in the White House who will call it for what it is: Hatred for an everyday American."
Kilian Melloy serves as EDGE Media Network's Assistant Arts Editor. He also reviews theater for WBUR. His professional memberships include the National Lesbian & Gay Journalists Association, the Boston Online Film Critics Association, The Gay and Lesbian Entertainment Critics Association, and the Boston Theater Critics Association's Elliot Norton Awards Committee.
Donald Trump Jr. Slams Transgender Athletes at Rally Before D.C. Riots
Watch: Trumpers Wave LGBTQ Flag at Capitol Protest While Trump's Gay Toadie Grenell Continues to Spread Falsehoods
TOP GUN 4K Ultra HD from Paramount Home Entertainment!
Iconic LA Gay Bar Oil Can Harry's Shutters After Half a Century
Marcus D'Amico, 'Mouse' in 'Tales of the City,' Has Died


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\section{Introduction}

The interplay of superconductivity and magnetism raises a number of interesting fundamental questions, particularly in systems where both coexist~\cite{sigrist1991,annett1990,volovik1984,ueda1985,bulaevskii1985a,luke1998,joynt2002,yuan2003,dai2012,mineev2017,stolyarov2018,ribak2020,aoki2019,ran2019}, where a rich variety of unconventional superconducting phases have been observed. Superconductors are defined by their ability to screen and expel external magnetic fields - the Meissner effect, but high enough fields can destroy the superconductivity. What happens when a superconductor hosts \emph{internal} magnetism? How do pairs interact with \emph{local} moments that cannot be screened by orbital currents?

For a plain-vanilla singlet superconductor, a single magnetic impurity can only be screened by Kondo coupling to the electron spin - so magnetic impurities are pair-breaking and host localized fermionic states inside the superconducting gap~\cite{yu1965,shiba1968,rusinov1969}. Pairs with internal degrees of freedom, such as spin or orbital, can however directly couple to the local moments (Fig.~\ref{fig:schematic}) and we present a microscopic derivation of this exchange interaction, by which moments can be screened without pair-breaking.

\begin{figure}
    \centering
    \includegraphics[width=0.4\textwidth]{schematic.pdf}
    \caption{\textbf{Schematic demonstration of pair-Kondo coupling for triplet pairs:} An $S=1,S_y=0$ triplet pair scatters off a local moment into an $S=1,S_z=0$ state, rotating the d-vector about the $x$-axis along which the moment is aligned. The process is equivalent to an antiferromagnetic superexchange of the pair spin with the $S_x$ component of the moment. }
    \label{fig:schematic}
\end{figure}

On a Kondo lattice, with singlet pairing, these Yu-Shiba-Rusinov states can form a band of effectively spinless fermions, and in presence of spin-orbit coupling, realize a p-wave topological superconductor~\cite{kitaev2001}. Tunneling signatures of Majorana bound states have been observed at the ends of a one-dimensional realization of this setup~\cite{nadj-perge2014}. This has generated significant interest in view of potential applications to a new paradigm of quantum computation, because these spatially separated Majorana bound states non-locally encode the Hilbert space of a charged fermion, effectively realizing a qubit that is immune to local sources of decoherence~\cite{kitaev2003}.

There are several heavy fermion superconductors~\cite{yuan2003,joynt2002,bulaevskii1985a,mineev2017,aoki2019} in which superconductivity emerges from a magnetic normal state, and coexists with magnetism at low temperatures. The superconducting order parameters are then classified by the irreducible representations (irreps) of the magnetic point group of the normal state where time-reversal is already broken. A more interesting class of materials involves the spontaneous breaking of time-reversal symmetry at a superconducting transition, a truly bizarre phenomenon for two ordering tendencies that seem \emph{by definition} antagonistic. The most celebrated instance of this class is the A-phase of superfluid $^3$He~\cite{leggett1975, wheatley1975}, described by the equal-spin pairing potential of Anderson, Brinkman and Morel~\cite{anderson1961, anderson1973} $\Delta_{\uparrow\uparrow}=-\Delta_{\downarrow\downarrow}\sim\hat{k}_y+i\hat{k}_z$ where $\hat{k}_i$ is the direction cosine of the momentum $k$. Another extensively studied instance~\cite{mackenzie2003, mackenzie2017,pustogow2019} is ${\rm Sr_2RuO_4}$, supported by muon-spin rotation~\cite{luke1998} and magneto-optical Kerr effect~\cite{xia2006} experiments both indicating the onset of time-reversal breaking at the superconducting transition temperature $T_c$.

In a lattice, two-particle states with zero center-of-mass momentum $\sum_{\bf k} c^\dagger_{{\bf k}\alpha} \Phi_{{\bf k}\alpha\beta}^\Gamma c^\dagger_{-\bf{k}\beta}|0\rangle$ can be classified by the irreps $\Gamma$ of the space group modulo lattice translations~\cite{herring1942,cvetkovic2013}, where $\alpha,\beta$ are general orbital indices, including spin. If the normal state Hamiltonian is time-reversal invariant, two-particle eigenstates belonging to one-dimensional irreps can generically be expanded as $\Phi_{\bf{k}n}^\Gamma=\sum_{n'} c_{nn'} \phi_{\bf{k}n'}^\Gamma$ in a basis of orthonormal time-reversal invariant form-factors $\phi_{\bf{k}n'}$ with real coefficients $c_{nn'}$. To break time-reversal, the condensate wavefunction must contain a complex superposition of atleast two such time-reversal invariant eigenfunctions, which are generically non-degenerate. Without an accidental degeneracy, a direct continuous phase transition into a time-reversal broken superconductor must involve atleast a two-dimensional irrep, so that complex superpositions can be formed from the degenerate eigenspace. Alternatively, a time-reversal breaking superconductor can develop from two second order phase transitions with the two non-degenerate components of the complex pair wavefunction condensing at different temperatures.

A vexing challenge to this general symmetry argument is posed by the emergence of time-reversal broken superconductivity~\cite{hayes2021} from a non-magnetic normal state in UTe$_2$~\cite{aoki2022, coleman2022}, whose orthorhombic symmetry allows only one-dimensional irreps. While the samples in Ref.~\cite{hayes2021} did show signatures of a two-step transition, subsequent studies showed that when similar samples were cut up, the two transitions seemed to come from different fragments~\cite{thomas2021}. This suggests that intrinsically there is a single transition, with $T_c$ sensistively dependent on the crystal environment. Presently, samples with a single observable transition at ambient pressure have been grown reproducibly by various groups (see Fig 1d of \cite{sundar2022}) and the best available samples with highest residual resistivity ratios and $T_c$, consistently show no split in $T_c$~\cite{rosa2022,aoki2022a}. We are then left with two scenarios, either that time-reversal breaking at $T_c$ is present only in inhomogeneous samples~\cite{willa2021a} with split $T_c$ or there are two accidentally degenerate pairing order parameters. In Ref.~\cite{shaffer2022} a mechanism was proposed for stabilizing such an accidental degeneracy by studying the RG flow of interactions in an accidentally $C_4$ symmetric bandstructure.

However, the presence of an accidental degeneracy of $T_c$ is hard to reconcile with experiments~\cite{braithwaite2019} that do not observe any split in $T_c$ below a finite amount of pressure. In contrast, accidentally degenerate transition temperatures should split linearly in the presence of non-symmetry breaking perturbations~\cite{zinkl2021}, such as pressure. The vanishing of the splitting over an extended range of pressure, rather than a single fine-tuned pressure, presents a conundrum in the observed phase diagram in Fig. \ref{fig:PhaseDiag}(b) - a second-order phase boundary cannot end at a point. If we eliminate the impossible, what remains is the possibility that the observed phase boundaries in Fig. \ref{fig:PhaseDiag}(b) are not all continuous transitions.

Here we present a generic mechanism for a weakly first-order transition into a time-reversal broken superconductor in systems close to a magnetic instability.
There is extensive evidence that above the superconducting $T_c$ UTe$_2$ is also on the verge of a ferromagnetic instability, from a divergent $a$-axis magnetic susceptibility~\cite{ran2019}, a critical slowing down of magnetic fluctuations in muon-spin rotation~\cite{sundar2019}, emergence of low-frequency magnetic fluctuations in nuclear magnetic resonance~\cite{tokunaga2019} and a divergent ferromagnetic susceptibility seen in field trained polar Kerr effect measurements~\cite{wei2022}. If the moments are slowly fluctuating on the timescale of electronic motion~\cite{machida2020}, even in inhomogeneous samples, puddles of magnetic order~\cite{sundar2022} can harbour puddles of magnetic superconductivity over the magnetic correlation
length. When these inhomogenous puddles grow with decreasing temperature, there is a first-order transition into a state with phase coherence and long-range superconducting order over the entire sample.

\begin{figure}
    \centering
    \includegraphics[width=\textwidth]{PhaseDiag.pdf}
    \caption{(a) Theoretical phase diagram as a function of temperature and tuning parameter $r$. Solid black (blue) line is a first(second)-order phase boundary. SC2 is a time-reversal invariant triplet superconductor with $\Delta_1\neq0,\Delta_2=M=0$. SC1 is a time-reversal breaking superconductor with $\Delta_1,\Delta_2,M\neq0$. Dashed lines indicate the underlying critical temperatures in absence of coupling between magnetic and superconducting orders: $T_{c1}/J=1+0.001r, T_m/J=1-0.002r,a/J=0.005(1+0.04 r),\alpha_1=\alpha_m=b/2=J$. Color scale is defined by the RGB values Red=$255(1-\Delta_1/Max)$, Green=$255(1-\Delta_2/Max)$, Blue=$255(1-M/Max)$ with $Max=0.15J$. c.f. (b) Experimental phase diagram from AC calorimetry (from Ref.~\cite{braithwaite2019}) as a function of pressure and temperature, where the second transition at low pressure (dashed) is not observed. The observed phase boundaries at low-pressure (boxed) are qualitatively captured by the free energy in \eqref{eq:FreeEn}. (c) Theoretical phase diagram for a different parameterization of the free energy in \eqref{eq:FreeEnalt} with $T_{c1}/J=1+0.001r, T_{c2}/J=0.995(1-0.0004r), T_m/J=1-0.0014r,\alpha_1=\alpha_2=\alpha_m=b/2=J$}
    \label{fig:PhaseDiag}
\end{figure}

To capture this effect, we introduce an interaction of unconventional pairs with local moments - an extension of Kondo coupling to electron pairs with an internal degree of freedom, such as spin. This is captured by the local Hamiltonian
\begin{equation}
H_{PK}=-iJM_{\Gamma\times\Gamma^{'}}\left(b_{\Gamma^{\phantom{'}}}^{\dagger}b_{\Gamma^{'}}-b_{\Gamma^{'}}^{\dagger}b_{\Gamma^{\phantom{'}}}\right)\label{eq:PairKondo}
\end{equation}
where \textbf{$b_{\Gamma(\Gamma^{'})}^{\dagger}$ }creates a pair
in the irrep $\Gamma(\Gamma^{'})$ and
the pair bilinear couples to the component of the local moment that
transforms under the product of the two irreps. We present two complementary microscopic derivations of this pair-Kondo interaction in Section \ref{sec:microscopic}, in terms of a weak-coupling picture of single-particle spin-exchange with an S=1/2 local moment and a strong-coupling picture of pair-spin exchange with an S=1 local moment.

The upshot of this machinery is a generic mechanism for coupling unconventional pairs to incipient magnetism, so that instead of local moments being pair-breaking perturbations, unconventional pairs can actually gain energy by coupling to near-critical moments as a chiral combination of two components. As a result, even when only one component is near critical, coupling to incipient magnetism can induce the second component, forming local chiral pairs that can condense above the underlying superconducting and magnetic critical temperatures. We demonstrate the onset of this transition using a Landau free energy in  Section \ref{landau}, showing that there is a direct transition to a time-reversal broken superconductor over an extended parameter range, reconciling the experimental phase diagram with thermodyamics. Since the superconducting and magnetic order parameters are close to a continuous transition, the transition is weakly first-order and the associated jumps in order parameters and peak in $C_v/T$ may be small as is demonstrated in Fig. \ref{fig:SCv}.

Alongside evidence for ferromagnetic criticality, there is also evidence for incommensurate antiferromagnetic fluctuations in UTe$_2$, from a neutron-spin resonance that is sensitive to the onset of superconductivity~\cite{duan2020, duan2021, knafo2021, raymond2021}, and from evidence of a antiferromagnetic quantum critical point under pressure~\cite{braithwaite2019, li2021, thomas2020}. Pair-Kondo coupling to antiferromagnetism induces a phase modulating secondary superconducting order - a condensate at finite momentum corresponding to the anti-ferromagnetic wavevector, and may lead to a modulation of order parameter amplitude in spin sectors where primary and secondary pair potentials interfere as we discuss in Section \ref{sec:finmompair}. Pair-density wave order has been observed in STM experiments on UTe$_2$~\cite{aishwarya2022, gu2022} although we stress at the outset that the type of pair density wave that can induce a charge density wave requires pair-Kondo coupling to incipient ferromagnetism \emph{and} antiferromagnetism, and there seems to be no experimental evidence of antiferromagnetic criticality near ambient pressure.

\section{First order transition via triplet pair scattering off local moments}\label{landau}

The presence of two pair potentials in distinct irreps allows for a direct coupling of pair bilinears to the local moment as in \eqref{eq:PairKondo}.
Rather than breaking pairs, scattering off local moments results in a \emph{gain
}in pairing energy for a complex superposition of the pair potentials
$b_{\Gamma}\pm ib_{\Gamma^{'}}$, relative to the pairs $b_{\Gamma(\Gamma^{'})}^{\dagger}$
in the irreps of the crystal symmetry group. Even when the moments
are not ordered but near-critical as in ${\rm UTe_{2}}$, such a coupling
may drive a first-order transition that pre-empts the second-order
superconducting transition at $T_{c1,2}$ of the individual pair potentials.

We demonstrate this process by the following Landau free energy functional
which describes two near critical order parameters - a superconducting
order $\Delta_{1}$ and a magnetic order $M$ - which individually
condense at $T_{c1},T_{m}$, and a second superconducting order $\Delta_{2}$
(with a finite mass gap $a>0$), which is induced by the coexistence
of $\Delta_{1}$ and $M$
\begin{equation}
F=\alpha_{1}\left(\frac{T}{T_{c1}}-1\right)\left|\Delta_{1}\right|^{2}+a\left|\Delta_{2}\right|^{2}+\alpha_{m}\left(\frac{T}{T_{m}}-1\right)M^{2}-\frac{iJM}{2}\left(\Delta_{1}^{*}\Delta_{2}-\Delta_{1}\Delta_{2}^{*}\right)+b\left(\left|\Delta_{1}\right|^{4}+\left|\Delta_{2}\right|^{4}+M^{4}\right)\label{eq:FreeEn}
\end{equation}
where the form of the fourth order terms have been chosen to be symmetric
for simplicity. The cubic coupling in the free energy represents a coupling of the total moment of the Cooper pairs to the incipient magnetization and has been introduced on symmetry grounds in \cite{hillier2012, nevidomskyy2020} for a single-band non-unitary triplet order parameter. The individual critical temperatures depend on material
parameters like pressure, strain and fields and may have an accidental
crossing where, $T_{c1}=T_{m}$. At this temperature, the free energy
takes the form
\begin{equation}
F=a\left|\Delta_{2}\right|^{2}-\frac{iJM}{2}\left(\Delta_{1}^{*}\Delta_{2}-\Delta_{1}\Delta_{2}^{*}\right)+b\left(\left|\Delta_{1}\right|^{4}+\left|\Delta_{2}\right|^{4}+M^{4}\right)
\end{equation}
and has a non-trivial global minimum for $J^{2}>8ab$ at $\Delta_{2}=\frac{\sqrt{J^{2}-8ab}}{4b},\Delta_{1}=M=\frac{\sqrt[4]{J^{2}\left(J^{2}-8ab\right)}}{4b}$.
Thus, there is a finite threshold for the pair-Kondo coupling $J_{c}$
above which the two continuous phase transitions at $T_{c1},T_{m}$
in the vicinity of the accidental crossing, are pre-empted by a single
weakly first-order transition. Both superconducting order parameters
develop simultaneously at this transition with a discontinuous jump
that scales as $\sqrt{J-J_{c}}$ close to $J=J_{c}$.

\begin{figure}
    \centering
    \includegraphics[width=\textwidth]{SCv.pdf}
    \caption{(a) Entropy and (b) specific heat across the first-order transition for $\alpha_1=\alpha_m=T_{c1}=T_m=J,b=2J,a=0.005J$ c.f. (c) experimentally measured specific heat near the transition (boxed) (From Ref.~\cite{aoki2022a}).}
    \label{fig:SCv}
\end{figure}

The latent heat of the first-order transition
is given by the discontinuity in the entropy across the transition
$\Delta Q=T_{c}\left(S(T_{c}^{+})-S(T_{c}^{-})\right)$ that corresponds
to integrated weight in the spike in the specific heat $C_{v}/T$
across the transition $\Delta Q/T_{c}=\int_{T_{c}^{-}}^{T_{c}^{+}}dT\frac{C_{v}}{T}$.
We estimate the latent heat to scale as $\left(J-J_{c}\right)^{2}$
close to $J=J_{c}$. In such a weakly first-order transition, the
small spike in the specific heat coexists with a much larger jump
in the specific heat $\Delta\frac{C_{V}}{T}$, which in BCS theory
is proportional to the Sommerfeld coefficient in the heavy Fermi liquid
normal state. In Fig \ref{fig:SCv} we show the entropy and specific heat
across the transition, and compare with the experimentally observed
temperature dependence of the specific heat.

As a generic demonstration of how this mechanism captures the emergence of time-reveral
breaking superconductivity with a single transition over an extended
parameter regime, let us consider the phenomenological variation
of the underlying second-order transition temperatures indicated by dashed lines in Fig~\ref{fig:PhaseDiag} with
a tuning parameter $r$ that stands in for pressure, strain or other
fields. We then find the global minima of the free energy in \eqref{eq:FreeEn}
as a function of temperature to get the phase diagram in Fig \ref{fig:PhaseDiag}.
The red, green and blue levels of the markers are mapped to the normalized
values of the three order parameters, so that the disordered phase
at high temperature is white and the dark phase at low temperature
has all three order parameters finite.

For an extended range of $r$ in Fig \ref{fig:PhaseDiag}, there is a weakly-first-order
transition into the time-reversal broken superconductor (SC2) with a jump
in all order parameters. As the underlying phase boundaries separate,
beyond a critical $r_{c}\sim J^{2}/b$, there is a two-step transition
- first into a time-reversal symmetric single-component superconductor (SC1)
and then via a weakly first-order transition where the second component
and the concomittant magnetism emerges discontinuously. The jump across
the first order transition decreases as the underlying phase boundaries
separate further, and eventually at large $r$, the first order transition
becomes second-order at a critical point (not shown).

The phenomenological description above reconciles the lack of an
observed second transition in the low pressure data for ${\rm UTe_{2}}$
(Fig.~\ref{fig:PhaseDiag}b). In particular, it is sufficient to have an accidental degeneracy either between one superconducting order and magnetism, or two superconducting orders to create a finite region of the phase diagram where unsplit transition into a time-reversal broken superconductor exists.
The experimental data is also consistent with three
near critical order parameters described by the free energy
\begin{align}
    F=\alpha_{1}\left(\frac{T}{T_{c1}}-1\right)\left|\Delta_{1}\right|^{2}+\alpha_2\left(\frac{T}{T_{c2}}-1\right)\left|\Delta_{2}\right|^{2}+\alpha_{m}\left(\frac{T}{T_{m}}-1\right)M^{2}-\frac{iJM}{2}\left(\Delta_{1}^{*}\Delta_{2}-\Delta_{1}\Delta_{2}^{*}\right)+b\left(\left|\Delta_{1}\right|^{4}+\left|\Delta_{2}\right|^{4}+M^{4}\right)\label{eq:FreeEnalt}
\end{align}
with a crossing between say, $T_{c1}$
and $T_{m}$ as shown in Fig.~\ref{fig:PhaseDiag}(c), if $T_{c2}$ is close enough
that $J^{2}>8\alpha_{2}\left(T_{c1}/T_{c2}-1\right)b$. In this case, the critical
pair-Kondo coupling may be parametrically small if $T_{c1}-T_{c2}\rightarrow0$.
Since the existence of a weakly first order transition depends on
a delicate balance between the Landau free energy coefficients and
the pair Kondo coupling, it is important to understand the microscopic
origins of the symmetry allowed coupling introduced in \eqref{eq:PairKondo}.

\section{Microscopic origin of pair-kondo coupling}\label{sec:microscopic}

We discuss the microscopic mechanism by which Cooper pairs can change
their symmetry representations by scattering off local moments. Intuitively,
this can be captured by two processes. By Kondo coupling to an S=1/2
moment, one of the electrons in the pair can rotate their spin. Alternately,
by coupling to an S=1 moment, the pair spin itself can rotate in the
scattering process. In presence of spin-orbit coupling and crystal
fields, the intuition from spin-rotation translates to a change in
the irreducible representation of the Cooper pair. We capture this
intuition by explicitly calculating the pair-Kondo coupling from microscopic
Hamiltonians in the following subsections.

\subsection{Coupling to S=1/2 moment}

We start with a mean-field pairing Hamiltonian with Kondo coupling
to S=1/2 local moments
\begin{equation}
H=H_{c}+H_{K}+H_{\Delta}
\end{equation}
with
\begin{align}
H_{c} & =\sum_{{\bf k}}c_{{\bf k}\alpha}^{\dagger}\epsilon_{{\bf k}}c_{{\bf k}\alpha}\nonumber \\
H_{K} & =J_{K}\sum_{j}{\bf S}_{j}\cdot c_{j\alpha}^{\dagger}\boldsymbol{\sigma}_{\alpha\beta}c_{j\beta}=J_{K}\sum_{kq}{\bf S}_{q}\cdot c_{k-q,\alpha}^{\dagger}\boldsymbol{\sigma}_{\alpha\beta}c_{k\beta}\nonumber \\
H_{\Delta} & =\sum_{{\bf k}}\Delta_{1}c_{{\bf k}}^{\dagger}\phi_{1{\bf k}}c_{-{\bf k}}+\Delta_{2}c_{{\bf k}}^{\dagger}\phi_{2{\bf k}}c_{-{\bf k}}+{\rm h.c.}
\end{align}
where $c_{j\alpha}^{\dagger}$ creates an electron at site $j$ with
spin $\alpha$, $c_{{\bf k}}^{\dagger}=\sum_{j}c_{j}^{\dagger}e^{-ik\cdot r_{j}}/\sqrt{N}$,
$N$ is the number of sites,${\bf S}_{j}$ is the local moment spin
at site $j$, ${\bf S}_{{\bf q}}=\sum_{j}{\bf S}_{j}e^{-iq\cdot r_{j}}/N$
and the form-factors $\phi_{1,2}$ transform under different irreps $\Gamma_{1,2}$ of the crystal space group
modulo lattice translation and are chosen to be hermitian. Our goal
is to find the leading free energy dependence on the three fields
$\Delta_{1},\Delta_{2}$ and ${\bf S}_{q=0}$. Since We are interested
in systems close to a ferromagnetic instability, it is a reasonable
approximation to ignore finite momentum spin scattering ${\bf S}_{q\neq0}=0$.
This allows us to express the partition function in the form
\begin{equation}
Z=\int\mathcal{D}\left[\Delta_{1},\Delta_{2},{\bf S},\bar{\psi},\psi\right]\exp\left[T\sum_{{\bf k},n}\Psi_{{\bf k},n}^{\dagger}G_{{\bf k},n}^{-1}\Psi_{{\bf k},n}\right]
\end{equation}
where the Nambu spinor $\Psi_{{\bf k}}^{\dagger}=\left(\begin{array}{cc}
\bar{\psi}_{{\bf k}} & \psi_{-{\bf k}}\Theta\end{array}\right)$ contains the Grassmann fields of the electrons, $\Theta=i\sigma_y \mathcal{K}$ (with $\mathcal{K}$: conplex conjugation) is the
time-reversal operator, and inverse of the Nambu-Gorkov Green's function
$G_{{\bf k},n}^{-1}=G_{0{\bf k},n}^{-1}+\Sigma_{{\bf k}}$ can be
decomposed into a bare inverse Green's function $G_{0{\bf k}}^{-1}=i\omega_{n}-h_{{\bf k}}\tau_{3}$
and the self energy
\begin{equation}
\Sigma_{{\bf k}}=\left(\begin{array}{cc}
J_{K}{\bf S}\cdot\boldsymbol{\sigma} & \Delta_{1}\phi_{1{\bf k}}+\Delta_{2}\phi_{2{\bf k}}\\
\Delta_{1}^{*}\phi_{1{\bf k}}+\Delta_{2}^{*}\phi_{2{\bf k}} & J_{K}{\bf S}\cdot\boldsymbol{\sigma}
\end{array}\right)
\end{equation}
where $\omega_{n}$ are fermionic Matsubara frequencies and $\tau_{i}$
are Pauli matrices in Nambu space. Integrating out the fermionic fields,
We arrive at the free energy
\begin{equation}
F=T\sum_{{\bf k},n}\Tr\log G_{{\bf k},n}^{-1}=F_{0}+T\sum_{{\bf k},n}\Tr\log\left(1+G_{0{\bf k},n}\Sigma_{{\bf k}}\right)
\end{equation}
where $F_{0}=T\sum_{{\bf k},n}\Tr\log G_{0{\bf k},n}^{-1}$ is the
normal state free energy. The leading order terms in the Taylor expansion
of the logarithm that survive the Nambu trace and the sum over the
Brillouin zone are $F-F_{0}=F_{2}+F_{3}+...$
\begin{equation}
F_{2}=T\sum_{{\bf k},n}\Tr\left[\frac{|\Delta_{1}|^{2}\phi_{1{\bf k}}^{2}+|\Delta_{2}|^{2}\phi_{2{\bf k}}^{2}}{\left(i\omega_{n}-\epsilon_{{\bf k}}\right)\left(i\omega_{n}+\epsilon_{{\bf k}}\right)}+J_K^{2}\left(\frac{1}{\left(i\omega_{n}-\epsilon_{{\bf k}}\right)^{2}}+\frac{1}{\left(i\omega_{n}+\epsilon_{{\bf k}}\right)^{2}}\right)\right]
\end{equation}

\begin{align}
F_{3} & =-TJ_K S_{m}\sum_{{\bf k},n}\Tr\sigma_{m}\frac{\Delta_{1}\Delta_{2}^{*}\phi_{1{\bf k}}\phi_{2{\bf k}}+\Delta_{1}^{*}\Delta_{2}\phi_{2{\bf k}}\phi_{1{\bf k}}}{\left(i\omega_{n}-\epsilon_{{\bf k}}\right)^{2}\left(i\omega_{n}+\epsilon_{{\bf k}}\right)}+\frac{\Delta_{1}\Delta_{2}^{*}\phi_{2{\bf k}}\phi_{1{\bf k}}+\Delta_{1}^{*}\Delta_{2}\phi_{1{\bf k}}\phi_{2{\bf k}}}{\left(i\omega_{n}-\epsilon_{{\bf k}}\right)\left(i\omega_{n}+\epsilon_{{\bf k}}\right)^{2}}\nonumber \\
 & =-TJ_KS_{m}\sum_{{\bf k},n}\Tr\sigma_{m}\frac{\Im\left[\Delta_{1}\Delta_{2}^{*}\right]\left(\phi_{1{\bf k}}\phi_{2{\bf k}}-\phi_{2{\bf k}}\phi_{1{\bf k}}\right)}{\left(i\omega_{n}-\epsilon_{{\bf k}}\right)\left(i\omega_{n}+\epsilon_{{\bf k}}\right)}\left(\frac{1}{\left(i\omega_{n}-\epsilon_{{\bf k}}\right)}-\frac{1}{\left(i\omega_{n}+\epsilon_{{\bf k}}\right)}\right)
\end{align}
where $S_{m}={\bf S}_{\Gamma_{1}\times\Gamma_{2}},$the spin-component
that transforms under the product irrep $\Gamma_{1}\times\Gamma_{2}$.
The hermitian form-factors $\phi_{1,2}$ can be expanded in the basis
of Pauli matrices with real coefficients $\phi_{1{\bf k}}=\phi_{1{\bf k}}^{0}\sigma_{0}+{\bf d}_{1{\bf k}}\cdot\boldsymbol{\sigma}$,
so that the pair-Kondo coupling between local moment and two-component
pairs takes the form
\begin{equation}
F_{3}=-J_{PK}S_{m}\Im\left[\Delta_{1}\Delta_{2}^{*}\right]
\end{equation}
with $J_{PK}=J_K T\sum_{{\bf k}}\left({\bf d}_{1{\bf k}}\times{\bf d}_{2{\bf k}}\right)\cdot m\sum_{n}\left[\left(i\omega_{n}-\epsilon_{{\bf k}}\right)^{-2}\left(i\omega_{n}+\epsilon_{{\bf k}}\right)^{-1}-\left(i\omega_{n}-\epsilon_{{\bf k}}\right)^{-1}\left(i\omega_{n}+\epsilon_{{\bf k}}\right)^{-2}\right].$
Evaluating the Matsubara summations gives a closed form expression
for the coupling constant
\begin{equation}
J_{PK}=J_K\sum_{{\bf k}}\hat{m}\cdot\left({\bf d}_{1{\bf k}}\times{\bf d}_{2{\bf k}}\right)\left[\frac{1}{2\epsilon_{{\bf k}}}\left(\frac{df}{d\epsilon}|_{\epsilon_{{\bf k}}}+\frac{df}{d\epsilon}|_{-\epsilon_{{\bf k}}}\right)-\frac{1}{2\epsilon_{{\bf k}}^{2}}\left(f(\epsilon_{{\bf k}})-f(-\epsilon_{{\bf k}})\right)\right].
\end{equation}

\subsection{Coupling to S=1 moment}

Pairs can also couple to local moments by mediating charge-2e valence
fluctuations, similar to how electrons Kondo-couple to moments by
mediating charge-e valence fluctuations. We demonstrate this process
for an S=1 $f^{2}$ local moment with three states $|S_{x}=0\rangle,|S_{y}=0\rangle,|S_{z}=0\rangle$
in the ground state manifold. Charge fluctuations are captured by
the mixed-valence Hamiltonian
\begin{equation}
H=\sum_{j}\left(E_{0}X^{00}(j)+\sum_{m=\{x,y,z\}}\left(VX_{m}^{02}(j)b_{jm}^{\dagger}+{\rm h.c.}\right)\right)
\end{equation}
 where the Hubbard operator $X_{m}^{02}=|f^{0}\rangle\langle f_{m}^{2}|$
removes two f electrons from the $S_{m}=0$ state of the ground state
triplet, $b_{jm}^{\dagger}=\sum_{\boldsymbol{\delta}}c_{j}^{\dagger}\phi_{m\boldsymbol{\delta}}c_{j+\boldsymbol{\delta}}^{\dagger}$
creates a pair with the same local symmetry as a triplet pair with
d-vector along $m$.

In the limit $V/E_{0}\ll1$, the perturbative effect of virtual valence
fluctuations on the ground state manifold is captured by a Schrieffer-Wolff
transformation after which the Hamiltonian $e^{iS}He^{-iS}$ is block-diagonal
to second order in $V/E_{0}$. This is effected by $iS=\sum_{jm}E_0^{-1}\left(V X_{m}^{02}(j)b_{jm}^{\dagger}-{\rm h.c.}\right)$.
The transformed Hamiltonian is then
\begin{equation}
e^{iS}He^{-iS}=\frac{\left|V\right|^{2}}{E_{0}}\left[X^{00}(j)b_{jm}^{\dagger}b_{jm}-X_{mm'}^{22}(j)b_{jm}b_{jm'}^{\dagger}\right]+O\left(\left(V/E_{0}\right)^{3}\right)\label{eq:SWHam}
\end{equation}
The second term can be simplified using the Fierz identity for Gell-Mann
matrices~\cite{cheng1994} $\delta_{\alpha\beta}\delta_{\gamma\delta}=\frac{1}{3}\delta_{\alpha\delta}\delta_{\gamma\beta}+\frac{1}{2}\boldsymbol{\lambda}_{\alpha\delta}\cdot\boldsymbol{\lambda}_{\gamma\beta}$. Thus
\begin{align}
X_{mm'}^{22}b_{m}b_{m'}^{\dagger} & =X_{mm'}^{22}b_{n}b_{n'}^{\dagger}\delta_{mn}\delta_{m'n'}\nonumber \\
 & =\frac{1}{3}b_{m}b_{m}^{\dagger}+\frac{1}{2}|f_{m}^{2}\rangle\boldsymbol{\lambda}_{mm'}\langle f_{n}^{2}|\cdot b_{n}\boldsymbol{\lambda}_{nn'}b_{n'}^{\dagger}
\end{align}
where we can identify the three imaginary Gell-Mann matrices as the
S=1 generators of SU(2) following Ref.~\cite{wang1997} $S_{l}=i|f_{m}^{2}\rangle\epsilon_{lmn}\langle f_{n}^{2}|$.
Projecting the canonically transformed Hamiltonian \eqref{eq:SWHam}
to the low energy spin-sector of the f-electrons, and ignoring potential
scattering of pairs, then gives the pair-Kondo Hamiltonian
\begin{equation}
H_{PK}=J_{PK}\sum_{jlmn}i\epsilon_{lmn}S_{l}(j)b_{jm}^{\dagger}b_{jn}\label{eq:PairKondolocal}
\end{equation}
with $J_{PK}=\frac{\left|V\right|^{2}}{2E_{0}}.$ If we restrict ourselves to zero-momentum pairing in a translationally invariant system, then this takes the form
\begin{equation}
H_{PK}=J_{PK}\sum_{jlmn}i\epsilon_{lmn}{\bf S}_{l,q=0}\sum_{{\bf k,k'}}c_{{\bf k}}^{\dagger}\phi_{m{\bf k}}c_{{\bf -k}}^{\dagger}c_{-{\bf k}'}\phi_{m'{\bf k'}}^{*}c_{{\bf k'}}\label{eq:pairKondokSpace}
\end{equation}
with $\phi_{m{\bf k}}=\sum_{\delta}\phi_{m\boldsymbol{\delta}}e^{-i{\bf k}\cdot\boldsymbol{{\bf \delta}}}/\sqrt{N}$, describing a change in pairing symmetry via scattering off the uniform component of the magnetization.

\section{Finite momentum pairing from coupling to antiferromagnetism}\label{sec:finmompair}

It is clear from \eqref{eq:PairKondolocal} that the incoming pair locally scatters
into a different channel (irrep of the site symmetry group) with a
phase that depends on the orientation of the magnetic moment. If this
orientation is staggered, coupling to static or near-critical antiferromagnetism
can therefore induce a phase-modulating Fulde-Ferrell~\cite{fulde1964} superconducting
order parameter from a uniform pair potential. Consider for instance,
the following Hamiltonian describing an $S_{y}=0$ triplet superconductor
below $T_{c1}(g_{1})$ and moments aligned antiferromagnetically along
$z$ below $T_{m}(J_{I})$
\begin{equation}
H=\sum_{{\bf k}}c_{{\bf k}}^{\dagger}h_{{\bf k}}^{0}c_{{\bf k}}-\frac{g_{1}}{N}b_y^\dagger b_y+J_{I}\sum_{\left\langle jj'\right\rangle }S_{zj}S_{zj'}
\end{equation}
where $b_{y}^{\dagger}=\sum_{{\bf k}}c_{{\bf k}}^{\dagger}d_{{\bf k}y}\sigma_{y}i\sigma_{y}c_{-{\bf k}}^{\dagger}$ and $\langle...\rangle$ denotes nearest neighbors.
A finite pair-Kondo coupling couples the uniform superconducting fluctuations
with the magnetic fluctuations at the antiferromagnetic wavevector
$Q=-Q$
\begin{equation}
H_{PK}=iJ_{PK}S_{z}(Q)\left(b_{x}^{\dagger}(-Q)b_{y}(0)-b_{y}^{\dagger}(0)b_{x}(Q)\right)
\end{equation}
where $b_{m}^{\dagger}(q)=\sum_{{\bf k}}c_{{\bf k+q}/2}^{\dagger}d_{{\bf k}m}\sigma_{m}i\sigma_{y}c_{{\bf -k+q}/2}^{\dagger}$.
Suppose we fix $d_{{\bf k}y}\in\mathbb{R}$, then to leading order,
this coupling induces a pair potential with imaginary $d_{{\bf k}x}$
\begin{align}
H_{induced} & =i\sum_{{\bf k}}c_{{\bf k+Q}/2}^{\dagger}|d_{{\bf k}x}|\sigma_{x}i\sigma_{y}c_{-{\bf k+Q}/2}^{\dagger}+{\rm h.c.}\\
 & =i\sum_{j}c_{j}^{\dagger}(-1)^{j}|d_{\delta x}|\sigma_{x}i\sigma_{y}c_{j+\delta}^{\dagger}+{\rm h.c.}
\end{align}
whose phase oscillates on neighbouring sites along $\text{Q}$. Here
$d_{{\bf k}m}=\sum_{\delta}d_{\boldsymbol{\delta}m}e^{-i{\bf k}\cdot\boldsymbol{{\bf \delta}}}/\sqrt{N}$.
The net pair potential for equal-spin pairs
\begin{align}
H_{\Delta}=\sum_{{\bf k}}c_{j\uparrow}^{\dagger}\Delta_{\uparrow\uparrow\delta}(j)c_{j+\delta\uparrow}^{\dagger}+c_{j\downarrow}^{\dagger}\Delta_{\downarrow\downarrow\delta}(j)c_{j+\delta\downarrow}^{\dagger}
\end{align}
oscillates in \emph{amplitude} due to the interference between the primary and induced order
\begin{align}
\Delta_{\uparrow\uparrow\delta}(j) & =i\left(d_{\delta y}+(-1)^{j}|d_{\delta x}|\right)\notag\\
\Delta_{\downarrow\downarrow\delta}(j) & =i\left(d_{\delta y}-(-1)^{j}|d_{\delta x}|\right).
\end{align}
leading to a Larkin-Ovchinnikov~\cite{larkin1971} superconducting order. The onset of long-range order and the possibility of a single-step first-order transition to this phase is captured by the same free energy in \eqref{eq:FreeEn}, where $M$ and $\Delta_2$ are now finite momentum order parameters.

The possibility of an induced charge-density wave is captured by coupling to incipient ferromagnetic and antiferromagnetic order. The induced pair potential in the second channel then has both a uniform and a phase-modulating component, and breaks the same residual symmetries as a charge-density wave.

\section{Discussion}

The cubic coupling of incipient pairing and magnetism presents a natural mechanism for pre-empting their individual continuous phase transitions by a weakly first order transition into a spontaneously time-reversal broken superconductor. This represents to my current limited knowledge the only scenario in the UTe$_2$ literature by which the experimental phase diagram (Fig.~\ref{fig:PhaseDiag}(b)) under pressure can be reconciled with thermodynamics for homogeneous samples of UTe$_2$. Careful measurements of the presence or absence of latent heat at the superconducting transition would place strong constraints on the possible discontinuity in the order parameters. Careful modeling of how the theoretical phase diagram evolves under magnetic fields and fitting to experimental data would place constraints on the possible pairing mechanisms in UTe$_2$.

The mechanism for time-reversal broken superconductivity via pair-Kondo coupling between non-degenerate pairs and local moments is applicable quite generally beyond UTe$_2$, and is not restricted to triplet pairing.
In a single-band model, singlet pairs in different irreps do not couple to local moments because the pairing form-factors in \eqref{eq:pairKondokSpace} commute. However, in multi-orbital systems,
the pairing form-factor can have structure in orbital space that allows even spin-singlet pairs to couple to local moments. This allows for a weak first order transition into time-reversal breaking superconducting phase by the mechanism described above.

\textbf{Acknowledgements:} We are grateful to J\"org Schmalian, Erez Berg, Aline Ramires, Piers Coleman, Priscila Rosa and Mohit Randeria for very useful discussions on this issue.

\bibliographystyle{apsrev4-1}

redpajama_set_name: RedPajamaArXiv


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