text:
\section{\label{Introduction}Introduction}

Based on enforcement of Si nanowires (NWs) linked to thermal conductivity,~\cite{Khitun1999181} photodetectors~\cite{Servati200764} and solar cells,~\cite{Tian2007,nl9034384,Allon} nowadays a notable effort has been addressed to study Si/Ge and Ge/Si core/shell semiconductor NWs.~\cite{Peng-Logan-APL-2010,doi:10.1021/nl203356h,doi:10.1021/nl103718a,doi:10.1021/cr400261y} These typical type-II band structures display high mobility~\cite{PhysRevLett.98.026801} and can be used in many applications.~\cite{PhysRevB.77.195325,Peng-Tang-Logan-JPCM-2011,Huang-Shouting-Li-APL-2011} It is also well established that the band gap at $\Gamma$-point of core/shell Si/Ge and Ge/Si nanostructures increases with decreasing radius, an effect directly linked to the spatial confinement and to the intrinsic strain at the interface,~\cite{Peng-Tang-Logan-JPCM-2011,PhysRevB.80.115322} produced in turn by the 4\% lattice mismatch between Si and Ge materials.~\cite{PhysRevLett.92.236805} Yet, more interestingly, in the nanoscale regime the Si/Ge and Ge/Si core/shell structures show a direct band gap at $\Gamma$-point.~\cite{PhysRevB.74.165314,PhysRevB.76.205327,Peng-Logan-APL-2010}

Besides the intrinsic strain, it is important to considered the role of spatial confinement on  the acoustic-phonon modes and on the electron-phonon interaction.
The acoustic phonon dispersion is strongly modified~\cite{Pokatilov2005168} when the radius of the quantum wire is of the order or smaller than the phonon wavelength. The confined acoustic phonon in such a nanostructure plays an important role on the carrier scattering rate, on the flow of electric current, and on the mobility or carrier transport. A suppression of the thermal conductivity in the core/shell Si/Ge NWs has been reported in Refs.~\onlinecite{PhysRevB.84.165415,PhysRevB.85.205439,doi:10.1063/1.4807389}. It has been shown that certain combinations of the core/shell cross-section modulation and  the acoustic mismatch allow to control the thermal flux. This result is, in principle, a promissory candidate for thermoelectric applications.
Thus, the reduction of the thermal conductivity and the characteristic of the carrier mobility in core/shell NWs are directly linked to the confinement effects on the phonon dispersion relation.~\cite{Thermal,Thermal2,Mobility,Mobility2,doi:10.1063/1.4807389} Also, it is important to remark that the core/shell wire structures are useful for optical applications~\cite{nl403341x,Mayer2013} and for quantum computing engineering with spin qubits.~\cite{Hu2011,nl501242b}

Several works have been devoted to obtain the acoustic phonon dispersion in wires and core/shell nanowires using both \textit{ab initio} calculations~\cite{abinitio1,abinitio2} and phenomenological continuum approaches (see Refs.~\onlinecite{Pokatilov2005168,Huang1,Loss2014, app5040728} and references there in). In addition, studies of electron-phonon interaction for the conduction band have been reported.~\cite{Hattori2010880,JAP_104_053716,PhysRevB.51.4695}
However, the electron-acoustic-phonon interaction in core-shell NWs has not been fully tackled. A phenomenological theory, allowing for the
evaluation of the electron-phonon Hamiltonian due to a deformation potential interaction, for cylindrical structures with arbitrary radii for both core and shell at the nanoscale regime, is a central issue for understanding the fundamental physics of many of the phenomena aforementioned. In the present work we study the electron-phonon interaction in Ge-core/Si-shell and Si-core/Ge-shell NWs in the framework of the continuum model and the $\vec{k}\cdot \vec{p}$ band theory.

The paper is organized as follows: in Sec.~\ref{Electron-phonon} we write down the general expression for the electron- and hole-phonon
deformation-potential Hamiltonians. For the conduction band we assume the $\Gamma_{1c}$ symmetry to be valid for Ge/Si and Si/Ge NWs grown along [110],
while for the holes we adopt the Bir-Pikus Hamiltonian (BPH) for states near the top of the valence bands with $\Gamma_{15v}$ symmetry. Sec.~\ref{Confined-Phonon} is devoted to a description of the elastic continuum model and the general basis of solutions for the phonon amplitudes. We make special emphasis on the phonon spectrum
calculations, the role of the spatial confinement effect, the symmetry of the space of solutions and on the comparison with the homogeneous wire limit. In Sec.~\ref{Scattering-Rate} we present detailed derivations of the electronic-acoustic phonon scattering rate for conduction and valence bands and of the influence of the core and shell radii for electrons and holes on the scattering amplitudes. We report our main results in Sec.~\ref{Conclusion}. Finally, in the Appendices we summarize the most relevant technical elements in the development of the present work.

\section{\label{Electron-phonon}Electron-acoustic-phonon interaction}

We consider typical core/shell cylindrical NWs with core radius $r_{c} $, shell thickness $\Delta =r_{s}-r_{c}$, and the $z-$axis
parallel to the growth direction [110]. We assume that all parameters involved in the present theoretical model are piece-wise functions of $r$, that is, we have assumed the parameters of the constituent materials to be isotropic.

In the occupation number representation, the Hamiltonian of the electrons interacting with the acoustic phonons can be expressed as~\cite{Madel}
\begin{equation}
H_{\mathrm{e-ph}}=\sum_{\alpha ^{\prime },\alpha}M_{\alpha ^{\prime
},\alpha }\left[ a_{j}^{\dagger }(\mathbf{k}_{z})+a_{j}(-\mathbf{k}_{z})
\right] c_{\alpha ^{\prime }}^{\dagger }c_{\alpha }\;,
\label{Hel-ph}
\end{equation}
where $a_{j}^{\dagger }(\mathbf{k}_{z})$ ($a_{j}(-\mathbf{k}_{z})$) denotes the phonon creation (annihilation) operator in the $j-$branch with wavevector $
\mathbf{k}_{z} (-\mathbf{k}_{z})$ and $c_{\alpha ^{\prime }}^{\dagger }$ ($c_{\alpha }$), the corresponding operator for electron in the electronic state $\alpha ^{\prime }$ ($\alpha$). Here, $M_{\alpha ^{\prime },\alpha }$ takes into account the electronic scattering event between the states $\alpha \rightarrow \alpha ^{\prime }$ by the interaction with an acoustic phonon. It is well known that in Si and Ge semiconductors the electron-phonon coupling can be determined using the short range deformation potential (DP) model.~\cite{Cardona} In a first approach, we develop a theory where this interaction is treated in the same way as in the bulk DP approach. Nevertheless, it has been reported that the DP constants are anisotropic and that depend on the spatial confinement (see Ref.~\onlinecite{nl9034384} and references there in). Furthermore, the DP mechanism can be treated as a perturbation to the band energies due to the lattice distortion; as a consequence, the electron-phonon coupling
depends on the electronic band structure.~\cite{Cardona} As we stated above, the Ge/Si and Si/Ge core/shell nanowires grown in the [110] direction show a direct band gap at $\Gamma$-point of the Brillouin zone,~\cite{PhysRevB.74.165314,Fazzio_295706,PhysRevB.76.205327,Peng-Tang-Logan-JPCM-2011}
hence, the conduction band minimum shows a $\Gamma_{1c}$ symmetry, while the top valence band has a $\Gamma_{15v}$ one, respectively.

\subsection{Conduction band}

Following the above discussion, the electron-phonon scattering amplitude probability can be written as
\begin{equation}
M_{\alpha _{e}^{\prime },\alpha _{e}}=\langle \Psi _{\alpha _{e}^{\prime
}}|a(\Gamma _{1c})\nabla \cdot \mathbf{u}|\Psi _{\alpha _{e}}\rangle \;,
\label{M_Matrixelem}
\end{equation}
where $a(\Gamma _{1c})$ is the volume deformation potential,~\cite{Cardona} $\mathbf{u}$ is the phonon displacement vector in the branch $j$, and $|\Psi_{\alpha _{e}}\rangle $ is the electron wave function for the core/shell NW.

\subsection{Valence band}
For the scattering amplitude, $M_{\alpha _{h}^{\prime },\alpha _{h}}$, of a hole in the valence band interacting with an acoustic phonon we have
\begin{equation}
M_{\alpha _{h}^{\prime },\alpha _{h}}=\langle \Psi _{\alpha _{h}^{\prime
}}|H_{BP}|\Psi _{\alpha _{h}}\rangle \;,
\label{M_Matrixelem_Hole}
\end{equation}
where $|\Psi _{\alpha _{h}}\rangle $ is the hole wave function in the NW and $H_{BP}$ is the Bir-Pikus Hamiltonian for the $J=3/2$ valence band states.~\cite{bir1974symmetry,Cardona} Assuming the zinc-blende symmetry, the $H_{BP}$ Hamiltonian in cylindrical coordinates and in the framework of the axial approximation, can be written as
\begin{multline}
H_{BP}=\left[ a(\Gamma _{15v})-\frac{1}{2}b(\Gamma _{15v})\left(
J_{z}^{2}-J^{2}/3\right) \right] \nabla \cdot \mathbf{u}+ \\
b(\Gamma _{15v})\left[ \frac{1}{2}J_{\mp }^{2}\mathcal{X}^{\pm }+\sqrt{2}
\{J_{\mp },J_{z}\}\mathcal{Y}^{\pm }\right. \\
\left. +\frac{3}{2}(J_{z}^{2}-J^{2}/3)\varepsilon _{zz}\right] \text{ },
\label{eq:Hbp}
\end{multline}
with $a(\Gamma _{15v})$ and $b(\Gamma _{15v})$ being the volume and shear deformation potentials for the highest energy at $\Gamma_{15v}$ valence band,~\cite{Note5} $\mathcal{X}^{\pm
}=e^{\pm 2i\theta }(\varepsilon _{rr}-\varepsilon _{\theta \theta }\pm
2i\varepsilon _{r\theta })$, $\mathcal{Y}^{\pm }=e^{\pm i\theta
}(\varepsilon _{rz}\pm i\varepsilon _{\theta z}),$ $\{J_{\mp },J_{z}\}=\frac{
1}{2}(J_{\mp }J_{z}+J_{z}J_{\mp }),$ $J_{\pm }=(J_{x}\pm iJ_{y})/\sqrt{2}$, and $J_{i}$ the Cartesian angular momentum operators for a particle with
spin 3/2 and $\varepsilon _{ij}$ the components of the stress tensor (see Appendix~\ref{Phonon} Eq.~(\ref{stresscomp})).

\section{\label{Confined-Phonon}Acoustic-phonon dispersion}

For an evaluation of the Hamiltonian~(\ref{Hel-ph}) and, in consequence, the matrix elements (\ref{M_Matrixelem}) and (\ref{M_Matrixelem_Hole}), it is
necessary to know the dependence of the phonon displacement $\mathbf{u}$ as well as the phonon frequencies on the core/shell spatial symmetry. In the
framework of elastic continuum approach, the equation of motion for the acoustic phonon modes takes the form~\cite{Born}
\begin{equation}
\rho \omega ^{2}\mathbf{u}-\nabla \cdot \mathbf{\sigma }=0\;,
\label{Emotion}
\end{equation}
with $\rho$ the mass density, $\omega $ the phonon frequency and $\mathbf{\sigma }$ the mechanical stress tensor. Following Hooke's law, $\mathbf{\sigma =C\cdot \varepsilon}$, with $\mathbf{\varepsilon }$ the strain tensor, $\mathbf{C}$ the elastic stiffness tensor  and the results being compiled in the Appendix \ref{Phonon}, the equation of motion for the acoustic phonon takes the form

\begin{equation}
\rho \omega ^{2}\mathbf{u}=\nabla (\rho v_{_{L}}^{2}\nabla \cdot \mathbf{u}
)+\nabla \times (\rho v_{_{T}}^{2}\nabla \times \mathbf{u)}\;.
\label{Emotion2}
\end{equation}
The solution of~(\ref{Emotion2}) consists of one longitudinal ($L$) $\mathbf{u}_{\mathbf{L}}$ and two transverse ($T$) $\mathbf{u}_{\mathbf{T}_{
\mathbf{1}}},\mathbf{u}_{\mathbf{T}_{\mathbf{2}}}$ fields, i.e. $\mathbf{u=u}_{\mathbf{L}}\mathbf{+u}_{\mathbf{T}_{\mathbf{1}}}\mathbf{+u}_{\mathbf{T}_{
\mathbf{2}}}$. Since the system is not homogeneous, in general $\mathbf{u}_{\mathbf{L}}$, $\mathbf{u}_{\mathbf{T}_{\mathbf{1}}}$, $\mathbf{u}_{\mathbf{T}
_{\mathbf{2}}}$ are coupled by the matching boundary conditions at the interface. Thus, the acoustic dispersion relations for the \textit{L} and
\textit{T} branches are not independent and the normal modes become a hybrid combination of $L$, $T_{1}$ and $T_{2}$ phonon vibrational motions.

It is important to remark that the equation of motion~(\ref{Emotion2}) for $r < r_c$, or $r_c < r < r_s$, corresponds to an isotropic model where an average velocity for the sound is assumed. An analysis of the phonon calculations and more general expressions including the anisotropy are presented in Appendix~\ref{Phonon}. It is shown there the phonon frequency calculations present a discrepancy of $10\%$ in comparison with the isotropic model.

In cylindrical geometry, the solution of Eq.~(\ref{Emotion2}) has full axial symmetry; hence, the displacement vector in cylindrical coordinates can be cast
as $\mathbf{u=}(u_{r},u_{\theta },u_{z})\exp i(n\theta +k_{z}z)$. In consequence, and following the method of solution described in Refs.~\onlinecite{CubaLibro,PhysRevB.91.075312}, one can derive a general basis of solutions for $(u_{r},u_{\theta },u_{z})$, namely

\begin{multline}
\left(
\begin{array}{c}
u_{r} \\
u_{\theta } \\
u_{z}
\end{array}
\right) =A_{_{L}}\left(
\begin{array}{c}
q_{_{L}}r_{c}f_{n}^{~\prime }(q_{_{L}}r) \\
i\frac{nr_{c}}{r}f_{n}(q_{_{L}}r) \\
ik_{z}r_{c}f_{n}(q_{_{L}}r)
\end{array}
\right) + \\
A_{_{T_{1}}}\left(
\begin{array}{c}
k_{z}r_{c}f_{n}^{~\prime }(q_{_{T}}r) \\
i\frac{nk_{z}r_{c}}{rq_{_{T}}}f_{n}(q_{_{T}}r) \\
-iq_{_{T}}r_{c}f_{n}(q_{_{T}}r),
\end{array}
\right) +A_{_{T_{2}}}\left(
\begin{array}{c}
\frac{nr_{c}}{r}f_{n}(q_{_{T}}r) \\
iq_{_{T}}r_{c}f_{n}^{~\prime }(q_{_{T}}r) \\
0
\end{array}
\right) \;,
\label{amplitude}
\end{multline}
where $n=0,\pm 1,\pm 2,...$ labels for the azimuthal motion, $k_{z}$ is the $z$-component of the phonon wavevector, and $q_{_{L}}(q_{_{T}})$ is given by

\begin{equation}
q_{_{L}}^{2}(q_{_{T}}^{2})=\frac{\omega ^{2}}{v_{_{L}}^{2}(v_{_{T}}^{2})}
-k_{z}^{2}\;.
\label{q}
\end{equation}

In Eq.~(\ref{amplitude}), if $x^{2}>0$ $(x^{2}<0)$ the function $f_{n}(x)$ is taken as Bessel $J_{n}$ (or Infeld $I_{n})$ for $0\leq r\leq r_{c}$ and as
linear combination of $J_{n}$ and Neumann $N_{n}$ functions of integer order $n$ (or combination of $I_{n}(x)$ and MacDonald $K_{n}(x)$)~\cite{Abramowitz}
for $r_{c}\leq r\leq r_{s}$. From (\ref{amplitude}), it is easy to check that $\nabla \cdot \mathbf{u}_{\mathbf{L}}=-(q_{_{L}}^{2} \pm k_{z}^{2})A_{_{L}}r_{c}f_{n}(q_{_{L}}r)e^{i(n\theta+k_{z}z)}$ (sign + for the Bessel functions and - for the modified Bessel functions) with $\nabla \cdot \mathbf{u}_{\mathbf{T}_{\mathbf{1}}}= \nabla
\cdot \mathbf{u}_{\mathbf{T}_{\mathbf{2}}}=0$ and $\nabla \times \mathbf{u}_{\mathbf{
L}}=0$, underlying the transverse and longitudinal character of the fields $\mathbf{u}_{\mathbf{T}_{\mathbf{1}}}$, $\mathbf{u}_{\mathbf{T}_{2}}$ and $
\mathbf{u}_{\mathbf{L}}$.

The eigenfrequencies of the phonon modes are obtained by imposing appropriate boundary conditions. As in the case of optical phonons, the strains at the interface play an important role on the phonon frequencies (see Ref.~\onlinecite{Singh2011}). For the acoustic  phonons, the effects of lattice mismatch between Ge and Si are taken into account through the continuity of the normal component of the stress tensor. We consider a free boundary at the shell surface, $\mathbf{\sigma }\cdot \mathbf{e}_{r}|_{r_{s}}=0$. Besides, the mechanical displacement and the normal component of the stress tensor should
be continuous at the core/shell interface, i.e. $\mathbf{u}|_{r_{c}^{-}} = \mathbf{u}|_{r_{c}^{+}}$ and $\mathbf{\sigma }\cdot \mathbf{e}
_{r}|_{r_{c}^{-}}=\mathbf{\sigma }\cdot \mathbf{e}_{r}|_{r_{c}^{+}}$. We point out that in the case of free standing homogeneous nanowires the basis of
solutions (\ref{amplitude}) match those reported in Ref.~\onlinecite{Hattori2010880}.

The calculation for the acoustical modes in NWs with cylindrical symmetry is a complicated task. In general, the phonon displacement $\mathbf{u}$ has all
three components ($\mathbf{u}_{\mathbf{T}_{\mathbf{1}}}$, $\mathbf{u}_{\mathbf{T}_{2}}$ and $\mathbf{u}_{\mathbf{L}}$), since none of the coefficients $A_{_{L}}$, $A_{_{T_{1}}}$ and $A_{_{T_{2}}}$ is zero, therefore, it cannot be decoupled into independent motions. Fixing $n$ and $k_{z}$, the constants $A_{_{L}}$, $A_{_{T_{1}}}$ and $A_{_{T_{2}}}$ are fully determined by the matching condition at $r=r_{c}$ and by the boundary condition of free standing NWs at $r=r_{s}$. Due to the cylindrical symmetry we cannot characterize the motions as pure torsional, dilatational or flexural modes. The resulting modes are  combination of
transverse and longitudinal characters. Nevertheless, from the symmetry of general basis~(\ref{amplitude}) we are able to obtain the following results: (i) for $n=0$ and $k_{z}=0$, we are in the presence of three independent $L$, $T_{1}$ and $T_{2}$ uncoupled modes with amplitudes $u_{r}(r)$, $u_{z}(r)$ and $u_{\theta }(r)$, respectively; (ii) for $n=0$ and $k_{z}\neq 0$, the longitudinal and transverse $T_{1}$ motions, $L-T_{1}$, are coupled, while $
T_{2}$ vibrational mode remains uncoupled; (iii) for $n\neq 0$ and $k_{z}=0$, the $T_{1}$ transverse phonon mode is independent, while the other two, $L$ and
$T_{2}$, are mixed; (iv) for $n\neq 0$ and $k_{z}\neq 0$ the longitudinal, the transverse $T_{1}$ and $T_{2}$ motions are coupled.
Below, we focus on the most relevant case of phonons with axial symmetry, $n=0$.

\subsection{Phonons with $k_{z}=0$}

\begin{figure}[htb]
\begin{center}
\includegraphics[width=\columnwidth]{Fig1}\\[0pt]
\end{center}
\par
\caption{(Color online) Frequencies of the first five breathing modes as a function of the ratio $r_{c}/r_{s}$ for fixed shell radius $r_{s}=5$ nm in
Si/Ge (left panel) and Ge/Si (right panel) NWs grown along the [110] crystallographic direction. The limits of Ge and Si nanowires are shown by
red and blue diamonds, respectively (see text).}
\label{bcont}
\end{figure}

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=\columnwidth]{Fig2}\\[0pt]
\end{center}
\par
\caption{(Color online) The same as Fig.~\ref{bcont} for the uncoupled $L$, $T_{1}$ and $T_{2}$ phonon modes as a function of $2\pi /r_{c}$, for fixed shell thickness $\Delta =r_{s}-r_{c}=5$ nm.}
\label{Deltacont}
\end{figure}
As stated above, the present case shows three uncoupled vibrations, $L$, $T_{1}$ and $T_{2}$. The longitudinal modes correspond to radial breathing mode (RBM) and their eigenfrequencies are ruled by the secular equation

\begin{multline}
F_{s}(\gamma \lambda _{_{L}}x/)[G_{s}(\lambda _{_{L}}x)J_{1}(x)-\rho
_{r}F_{c}(x)N_{1}(\lambda _{_{L}}x)]- \\
G_{s}(\gamma \lambda _{_{L}}x/)[F_{s}(\lambda _{_{L}}x)J_{1}(x)-\rho
_{r}F_{c}(x)J_{1}(\lambda _{_{L}}x)]=0\;,
\label{modosL}
\end{multline}
where $c$ $(s)$ labels the core (shell) region, $x=\omega r_{c}/v_{_{L_{c}}}$, $\lambda _{_{L}}=v_{_{L_{c}}}/v_{_{L_{s}}}$, $\gamma =r_{s}/r_{c}$, $\rho
_{r}=\rho _{s}/\rho _{c}$, $F_{i}(x)=v_{_{L_{i}}}^{2}xJ_{0}(x)-2v_{_{T_{i}}}^{2}J_{1}(x)$, and $G_{i}(x)=v_{_{L_{i}}}^{2}xN_{0}(x)-2v_{_{T_{i}}}^{2}N_{1}(x)$ ($i=s,c$). The RBM modes have been studied in the past for both nanotubes~\cite{Thomsen,Kurti2003} and semiconductor NWs.~\cite{Bourgeois,Trejo} Because of  their particular relevance it becomes necessary to focus on these modes in Ge/Si and Si/Ge core/shell nanowires. It is expected that the frequencies of the RBM modes, described by Eq.~(\ref{modosL}), are strongly dependent on the material composition, $\lambda _{_{L}}=v_{_{L_{c}}}/v_{_{L_{s}}}$ and size ratio, $\gamma =r_{s}/r_{c}$. Firstly, note from~(\ref{modosL}) that the two limiting cases $r_{c}=0$ and $r_{c}/r_{s}=1$ are given by the secular equation $F_{i}(z_{i})=0$ with $z_{i}=\omega r_{0}/v_{_{L_{i}}}$ ($i=s, c$) and $r_{0}$ the radius of the wire, i.e. the homogeneous NW dispersion relation is recovered for shell or core semiconductors.
Figure~\ref{bcont} shows the frequency dependence on the core/shell ratio $r_{c}/r_{s}$, with the limiting cases $r_{c}=0$ and $r_{c}/r_{s}=1$ shown by
diamonds. In the calculations we employed the following data for Si [Ge]: $v_{_{L}}=9.36$ $[5.39]\times 10^{5}cm/s$, $v_{_{T}}=5.25[3.30]\times 10^{5}cm/s$,~\cite{Note4}$\rho =2.33$ $[5.32]$ $g/cm^{3}$.~\cite{Adachi} The oscillations observed in Fig.~\ref{bcont} of $\omega$ as a function of the ratio $r_{c}/r_{s}$ can be explained by the interference between shell and core structures. Thus, for small values of $r_{c}/r_{s}$, the influence of the shell on the core phonon amplitude becomes stronger inhansing the oscillations. Moreover, the lower phonon frequencies are less affected showing almost a flat dispersion as a function of $r_{c}/r_{s}$, while the higher excited modes are more sensitive and displaying pronounced oscillations. The same trend is obtained for the $T_{1}$ and $T_{2}$ phonon modes (see Fig.~\ref{Deltacont}).

The confined eigenfrequencies, $\omega(k_{z}=0)$, for the $T_{2}$ modes can be obtained from the general expression
\begin{equation}
x_{s}J_{1}(x_{c})P_{22}(x_{s})+\frac{\rho _{r}}{\lambda _{_{T}}^{2}}
x_{c}J_{2}(x_{c})P_{12}(x_{s})=0\;.
\label{T2}
\end{equation}
Here, $x_{c}[x_{s}]=r_{c}\sqrt{(\omega /v_{_{T_c}}[v_{_{T_s}}])^{2}-k_{z}^{2}}$, $\lambda _{_T}=v_{_{T_{s}}}/v_{_{T_{c}}}$ and $P_{n,m}(x)=J_{n}(x)N_{m}( \gamma x)-J_{m}( \gamma x)N_{n}(x)$. Also, in the particular case when $k_{z}=0$, is possible to get an explicit expression for the $T_{1}$ frequency mode.

Figure~\ref{Deltacont} displays the dependence on $2\pi /r_{c}$ of the uncoupled $L$, $T_{1}$ and $T_{2}$ phonon frequency modes for fixed shell thickness $\Delta =$ $r_{s}-r_{c}$. In the limit $r_{c}\rightarrow \infty $ we recover the phonon frequencies for pure Si and Ge wires. As $r_{c} \rightarrow \infty$, we find that the phonon frequency resembles the typical linear acoustic bulk phonon dispersion as a function of the phonon wavevector. The spatial confinement renormalizes the sound velocity and we can rewrite, for large values of $r_{c}$, that $\omega _{_{L,T}}^{(j)}=(2\pi /r_{c})v_{_{L,T}}^{(j)}$ ($j=1, 2,...$) with different slope $v_{_{L,T}}^{(j)}$ for each mode. Notice that the cylindrical symmetry breaks the $T_{1}$ and $T_{2}$ degeneracy and two different sound velocities, $v_{_{T_{1}}}^{(j)}$ and $v_{_{T_{2}}}^{(j)}$, appear.

\subsection{Phonon dispersion with $k_{z}\neq0$}

Following the secular Eq.~(\ref{T2}), in Fig.~\ref{kz_pequeno} we display the pure confined transverse $T_{2}$ phonon dispersion. For sake of
comparison the bulk phonon dispersions, $\omega _{_{\text{Ge}}}(k_{z})$ and $\omega _{_{\text{Si}}}(k_{z})$, are represented by blue and red dashed
lines, respectively. For small values of $k_{z}$ is possible to get useful analytical solutions. It should be remarked that in the case of Ge/Si,
if the set of the values ($\omega, k_{z})$ lies in the region $\omega _{_{\text{Ge}}}(k_{z})<\omega <\omega _{_{\text{Si}}}(k_{z})$, the parameter $x_{c}$ is
real while $x_{s}$ becomes a complex number. The opposite occur for  Si/Ge NWs. Accordingly, for the Ge/Si we get that the function $P_{nm}(x_{s})\Rightarrow P_{nm}(\left\vert x_{s}\right\vert)=$ $I_{n}(\left\vert x_{s}\right\vert )K_{m}( \gamma\left\vert x_{s}\right\vert )-I_{m}(\gamma\left\vert x_{s}\right\vert)K_{n}(\left\vert x_{s}\right\vert )$.

The numerical solution of Eq.~(\ref{T2}) shows a strong modification of the Si and Ge bulk phonon group velocities (see Fig.~\ref{kz_pequeno}) which
depend on the surrounding material, i.e. if the shell is composed by softer or harder material than the core semiconductor, the resulting group velocity
has lower or higher values. For example, in Ge/Si core/shell NWs the shell compresses the Ge core lattice while for Si/Ge the shell is compressed by the
core. Similar result have been achieved in Ref.~\onlinecite{Pokatilov2005168}.

Assuming small values of the wavenumber $k_z$, Eq.~(\ref{wlineal}) is obtained from Eq.~(\ref{T2}). Thus, the dispersion relation valid for Ge/Si ($x_c$ real, $x_s$ complex number) and Si/Ge ($x_c$ complex number, $x_s$ real) follows. This enables to better visualize the dependence of sound speed on materials parameters:
\begin{equation}
\omega =v_{_{T_{c}}}\sqrt{1+\frac{\left( \lambda _{_{T}}^{2}-1\right)
(\gamma ^{4}-1)\rho _{r}}{(\gamma ^{4}-1)\rho _{r}+1}}k_{z}=\overline{v_{_{T}}}k_{z}\;.
\label{wlineal}
\end{equation}
This equation shows that the lower modes present linear dependence in $k_{z}$, with a renormalized sound velocity $\overline{v_{_{T}}}$ that takes
into account the ratio between shell and core radii, as well as the densities and transverse velocities. Equation~(\ref{wlineal}) suggests the way to modify
the sound velocity as a function of the geometric factors ranging between the values ${v_{_{T}}^{\text{Ge}}}$ and ${v_{_{T}}^{\text{Si}}}$. The same expression has been found in Ref.~\onlinecite{Loss2014}.
\begin{figure}[tbp]
\begin{center}
\includegraphics[width=\columnwidth]{Fig3}\\[0pt]
\end{center}
\par
\caption{(Color online) Phonon dispersion for uncoupled $T_{2}$ modes as a function of the phonon wavevector $k_{z}$ in units of $\pi /r_{s}$. Left panel Si/Ge; right panel Ge/Si NWs. Dashed lines represent the bulk dispersion relations for Si and Ge. Open diamonds are solutions of Eqs.~(\ref{wlineal}) and (\ref{APRT2}).}
\label{kz_pequeno}
\end{figure}

In the domain ($\omega, k_{z})$ where $x_{c}$ and $x_{s}$ are both real functions, Eq.~(\ref{T2}) provides the dispersion relation for small values of $k_{z}$,
\begin{equation}
\omega _{_{T_{2}}}(k_{z})=\omega _{_{T_{2}}}(0)+\frac{1}{2}\frac{
v_{_{T_{s}}}^{2}}{\omega _{_{T_{2}}}^{2}(0)}k_{z}^{2}\;,
\label{APRT2}
\end{equation}
where $\omega _{_{T_{2}}}(0)$ is the confined phonon frequency of the core/shell NWs for $k_{z}=0$. In Fig.~\ref{kz_pequeno} the solutions given
by Eqs.~(\ref{wlineal}) and (\ref{APRT2}) are represented by open diamonds. By comparison with the numerical calculation of Eq.~\ref{T2}), it
can be seen that explicit expressions (\ref{wlineal}) and (\ref{APRT2}) are good approximations for $k_{z}(\pi /r_{s})\leq 1$.

Another subset of solutions corresponds to the hybridized longitudinal and transverse motions. Fig.~\ref{FigDesacoplados_kz} shows phonon
dispersion of mixed $L-T_{1}$ modes for $\gamma =1.25$. The longitudinal ($L $) and transverse ($T_{1}$) labels are taken from the character
of the mode at $k_{z}=0$. For the sake of comparison, the phonon dispersions for the homogeneous Si and Ge cylindrical wires are shown in Fig.~\ref
{FigDesacoplados_kz}. Here, the corresponding longitudinal and transverse modes are represented by red solid and red dash-dots lines, respectively.
Due to the strain effect at the interface, it can be seen in the Fig.~\ref{FigDesacoplados_kz} that for the Ge/Si core/shell NW the phonon frequencies lye above the Ge wire, while the opposite is obtained for the Si/Ge NW, where $\omega _{\text{Si}}$ values are well above the core/shell Si/Ge phonon frequencies. At $k_{z}$
approaching zero, the lower mode presents a linear dependence of $\omega_{_{L-T_{1}}}$ on the wavenumber $k_{z}$ with certain effective sound velocity $
v_{_{L-T_{1}}}$ that depends on the radii $r_{c}$ and $r_{s}$.~\cite{Note2,Note3}
The bendings appearing in the Fig.~\ref{FigDesacoplados_kz} are manifestations of the strongest coupling between $L$ and $T_{1}$ modes. The mixed character of the states avoid crossing points in the phonon dispersion relation, i.e. the repulsion between near modes with the same symmetry occurs. This effect is observed in all dispersion relations having an important consequence in the electron-phonon Hamiltonian $H_{\mathrm{e-ph}}$ (see
discussion below). In Fig.~\ref{FigDesacoplados_kz}, some anticrossings associated with the mixing between $L$ and $T_{1}$ states, have been indicated by
full diamonds. The proximity of the levels belonging to the same space of solution or with the same symmetry is avoided by the repulsion between the
phonon states. At the anticrossings, a strong mixing between $L$ and $T_{1}$ states occurs and an exchange of character of the constants $A_{_{L}}$ and $
A_{_{T_{1}}}$ is obtained as a function of $k_{z}$.

Notice that higher excited states for $k_{z}\sim 0$ do not present strong mixing effect and the phonon dispersion relation can be described by simple parabolic law, $\omega_{_{L(T_{1})}}(k_{z})=\omega_{_{L(T_{1})}}(0)+\beta_{_{L(T_{1})}}^{2}k_{z}^{2}$. Here, $\beta_{_{L(T_{1})}}$ measures the curvature of the phonon dispersion and $\omega_{_{L-T_{1}}}(0)$ are the NW phonon frequencies for $k_{z}=0$. We arrived to the same results for the homogeneous Si and Ge cylindrical wires.

\begin{figure}[tbh]
\begin{center}
\includegraphics[width=\columnwidth]{Fig4}\\[0pt]
\end{center}
\caption{(Color online) The same as Fig.~\ref{kz_pequeno} for the mixed $L-T_1$ modes. Phonon dispersion relations for homogeneous Si and Ge
cylindrical wires are represented by red solid (longitudinal modes) and dashed-dots (transversal modes) lines. Full diamonds represent the anticrossings
between two nearby modes as explained in the text.}
\label{FigDesacoplados_kz}
\end{figure}

\section{\label{Scattering-Rate}Scattering rate}

Due to translational and cylindrical symmetries, the matrix element $M_{\alpha ^{\prime },\alpha }$ can be cast as follows

\begin{equation}
M_{\alpha ^{\prime },\alpha }=S_{e-ph}\delta_{{m}^{\prime},m+n}\delta_{{k}
^{\prime},k+k_{z}}\;,
\end{equation}
where the angular momentum and linear momentum conservations are written explicitly. $S_{e-ph}=\left\langle m^{\prime }\right\vert H_{e-ph}\left\vert m\right\rangle$ is the scattering amplitude due to the electronic transition assisted by an acoustical phonon, between the electron or hole states $\left\vert
m^{\prime}\right\rangle \rightarrow $ $\left\vert m\right\rangle $ (see Appendices~\ref{Conduction-Band} and \ref{Valence-Band}). For the phonon eigenvectors {$\mathbf{u}_{n,k_{z}}$} we choose the normalization condition

\begin{equation}
\int \rho (r)|\mathbf{u}_{n,k_{z}}(\mathbf{r})|^{2}dV=\frac{\hbar }{2\omega
_{n}(k_{z})}\;,
\label{Norma}
\end{equation}
with $\omega _{n}(k_{z})$ the acoustic-phonon dispersion of the core/shell problem. Let us discuss a general formulation for the electron-acoustic
deformation potential Hamiltonian, $H_{E-P}$ and an evaluation of the scattering amplitudes for the electrons and holes.

\subsection{Electron-LA Hamiltonian}

According to Eq.~(\ref{M_Matrixelem}), a transverse or torsional mode does not induce volume change and only the longitudinal acoustic motion $\mathbf{u
}_{\mathbf{L}}(\mathbf{r})$ contributes to electron-phonon Hamiltonian $H_{E-DP}$. Hence, by assuming $A_{_{L}}$ as independent constant in Eq.~(\ref{amplitude}), we have
\begin{multline}
H_{E-DP}=a(\Gamma _{1c})\nabla \cdot \mathbf{u}_{\mathbf{L}}= \\
-\sqrt{\frac{\hbar \omega _{n}^{3}(k_{z})}{4\pi r_{c}^{2}L\rho
_{c}v_{_{L}}^{4}}}\frac{a(\Gamma _{1c})}{\mathcal{N}_{n,k_{z}}}
f_{n}(q_{_{L}}r)e^{i(n\theta +k_{z}z)}\;,
\label{EDP}
\end{multline}
\begin{figure}[tbh]
\begin{center}
\includegraphics[width=\columnwidth]{Fig5}\\[0pt]
\end{center}
\caption{(Color online) Contour plots of the Hamiltonian (\ref{EDP}) in units of $H_{OE}$ as function dimensionless wavenumber $k_{z}/(\pi /r_{s})$ and radius $r/r_{c}$ for the phonon modes a) $\omega_{_{L}}^{(1)}$, b) $\omega _{_{T_1}}^{(1)}$, c) $\omega_{_{T_1}}^{(2)}$, and d) $\omega _{L}^{(2)}$ of the Ge/Si core/shell
NW (see text). In the calculation we fixed $k_{z}=0$ and $z=0$.}
\label{Fig5}
\end{figure}where $\mathcal{N}_{n,k_{z}}=\sqrt{\int_{0}^{\gamma }\rho (z)|\overline{\mathbf{u}_{n,k_{z}}(z)}|^{2}zdz/(\rho _{c}A_{_{L_{c}}}^{2})}$ is the
normalization constant for the dimensionless phonon amplitude $|\overline{\mathbf{u}_{n,k_{z}}(z)}|$. In Fig.~\ref{Fig5} the characteristic contour map for the electron-LA Hamiltonian~(\ref{EDP}) is shown for the Ge/Si NWs. We choose the first four modes of Fig.~\ref{FigDesacoplados_kz} where $\omega _{n=0}(k_{z}=0)\neq 0$. According to the general basis of solutions~(\ref{amplitude}), for $n=0$, the longitudinal displacement vector $\mathbf{u}_{\mathbf{L}}$ have non-zero radial and axial components. Figures~\ref{Fig5} a), b), c) and d) correspond to the uncoupled confined frequencies $\omega_{_{L}}^{(1)}$, $\omega_{_{T_{1}}}^{(1)}$, $\omega_{_{T_{1}}}^{(2)}$, and $\omega_{_{L}}^{(2)}$ for $k_{z}=0$ of the $L$ and $ T_{1}$ motions. In the panels a) and d) one finds, for $r=0$, the stronger spatial localization in correspondence with the longitudinal character of these modes. In panel a) we observe, as $k_{z}$ increases, that the $T_{1}$ component becomes stronger, in particular for $k_{z}>1.1$ the contribution of the $\omega _{_{L}}^{(1)}$ mode to $H_{E-DP}$ is almost zero. The same is observed in panel d) for the state $L^{(2)}$, but the limiting value is $k_{z}>1.8$. These two values of $k_{z}$ are in correspondence with the anticrossings shown by full diamonds in the Figure~\ref{FigDesacoplados_kz} for the $L^{(1)}$ and $L^{(2)}$ phonon states. Note in Fig.~\ref{FigDesacoplados_kz} that for $k_{z}\sim 2.8$ an anticrossing occurs and the $L^{(2)}$ mode presents stronger $L$ character and, in consequence, the spatial distribution of $H_{E-DP}$ is enhanced. In panel b) the observed strong spatial localization of $H_{E-DP}$ at $r=0$ with $k_{z}\approx 0.2$ is explained by the reduction of the coefficient $A_{_{T_{1}}}$ as a function of $k_{z}$, in the state $T_{1}^{(1)}$. Due to the anticrossing between the states $T_{1}^{(1)}$ and $T_{1}^{(2)}$ for $
k_{z}\approx 2$, the $\omega _{_{T_{1}}}^{(1)}$ mode is almost transverse and its contribution to the spatial distribution $f_{n=0}(q_{_{L}}r)|_{\omega
=\omega_{_{T_{1}}}^{(1)}}$ decays to zero. At the same time, the mode $T_{1}^{(2)}$ increases the $A_{L}$ amplitude, and $H_{E-DP}$ at $\omega
=\omega_{_{T_{1}}}^{(2)}$ increases in the region $1.9 < k_{z} < 2.9$ as seen in Fig.~\ref{Fig5}c). Thus, the phonon dispersion of the Ge/Si NWs for a given ratio of $r_{s}/r_{c}$ has a preponderant influence on the spatial distribution of $H_{E-DP}$ as a function of $k_{z}$.
\begin{figure}[tbh]
\begin{center}
\includegraphics[width=\columnwidth]{Fig6}\\[0pt]
\end{center}
\caption{(Color online) Electron scattering amplitude for the excited frequencies $\omega_{_{L}}^{(1)}$, $\omega_{_{L}}^{(2)}$ and $\omega_{_{L}}^{(3)}$ (see text) as a function of the ratio $r_{c}/r_{s}$. Dashed lines: homogeneous wires as given by Eq.~(\ref{SHED}). Upper panel Si/Ge, lower panel Ge/Si.}
\label{Fig6}
\end{figure}
Taking into account the Eqs.~(\ref{EDP}), (\ref{electrwave}) and (\ref{ME}), the electron scattering amplitude can be written as
\begin{equation}
S_{E-DP}=\frac{1}{r_{c}^{2}}\left\langle F_{m_{e}^{\prime }}\right\vert
H_{OE}\frac{\omega _{n}}{v_{_{L}}\mathcal{N}_{n,k_{z}}}f_{n}\left\vert
F_{m_{e}}\right\rangle \;,
\label{SED}
\end{equation}
where $H_{OE}=-a(\Gamma _{1c})\sqrt{\hbar \omega _{n=0}(k_{z}=0)/4\pi r_{c}^{2}L_{0}\rho _{c}v_{_{L}}^{2}}$. From Eq.~(\ref{SED}) immediately follows that phonon modes with $n=0$ assist to electron intrasubband transitions, $m_{e}^{\prime }=m_{e}$, while for $n\neq 0$ intersubband transitions with $m_{e}^{\prime }\neq m_{e}$ occur fo. Note that in the case of homogeneous wire, $\left\langle F_{m_{e}^{\prime}}\right\vert f_{n}\left\vert F_{m_{e}}\right\rangle /r_{c}^{2}$ corresponds to the electron form factor or overlap integral between the normalized radial electronic states and the phonon function $f_{n}$ of the quantum wire. For comparison, we consider the Eq.~(\ref{SED}) for a homogeneous wire. Assuming the size-quantum limit (strong spatial confinement) where electrons populate the lowest subband $(m_{e}^{\prime}=m_{e}=0$ and $n=0)$ and intersubband transitions $|p_{e}^{\prime}\rangle \rightarrow |p_{e}\rangle $ are discarded, the scattering amplitude at $k_{z}=0$ reduces to

\begin{multline}
S_{E-DP}^{H}=H_{OE}\left( \frac{r_{c}^{2}q_{_{L}}^{2}}{4}\delta ^{4}-\delta
^{2}+1\right) ^{-\frac{1}{2}}
\label{SHED} \\
\times \frac{\langle J_{0}(p_{e})|J_{0}(q_{_{L}})|J_{0}(p_{e})\rangle }{
r_{c}^{2}J_{1}^{2}(p_{e}r_{c})J_{0}(q_{_{L}}r_{c})}\;,
\end{multline}
with $\delta =v_{_{L}}/v_{_{T}}$.

It is instructive to compare the behavior of the electron scattering amplitudes for core/shell Si/Ge and Ge/Si NWs. Fig.~\ref{Fig6} displays the reduced scattering amplitude $S_{E-DP}/H_{OE}$ as a function of the ratio $r_{c}/r_{s}$ for both core/shell NWs. In the calculation for the Si/Ge [Ge/Si] NWs we fixed the value of $H_{OE}$ with the parameters of Si [Ge] semiconductor. For each structure, in the quantum limit approach, the first three $L$ modes of the structure with frequencies $\omega_{_{L}}^{(j)}$ ($j=1,2,3 $)$\neq 0$ at $k_{z}=0$ are considered. In the figure the form factor, using Eq.~(\ref{SHED}) and $r_{c}=5$ nm, is represented by dashed lines. In  Si/Ge NWs, electrons are confined in the core whereas in Ge/Si NWs they are in the shell. For the evaluation of Eq.~(\ref{SED}) we employed the results displayed in Appendix~\ref{Conduction-Band}. In the upper panel of Fig.~\ref{Fig6} (Si/Ge NWs) the influence of the shell of Ge on the $S_{E-DP}$ is shown.  If $r_{c}=r_{s}$ we have a quantum wire of Si and $S_{E-DP}/H_{OE}$ as described by Eq.~(\ref{SHED}). If $r_{c}/r_{s}\neq 1$ we are in the presence of a Si/Ge core/shell system. Thus, we can observe that the value of $S_{E-DP}$, for the $\omega_{_{L}}^{(1)}$ modes, firstly increases, reaching a maximum for $\gamma _{\max }^{(1)}=(r_{c}/r_{s})_{\max }^{(1)}\approx 0.4$ and for $\gamma<\gamma _{\max }^{(1)}$ the quantity $S_{E-DP}/H_{OE}$ reaches asymptotically the homogeneous Si wire value. In the case of $\omega_{_{L}}^{(j)}$ ($ j=2,3 $), the reduced scattering amplitude grows, reaching a maximum value near ($r_{c}/r_{s})_{\max }^{(2)}\approx 0.23$. For $\gamma
<\gamma _{\max }^{(2)}$, $S_{E-DP}/H_{OE}$ decreases to the limiting value of Eq.~(\ref{SHED}). In the lower panel of Fig.~\ref{Fig6} (Ge/Si NWs) the wire of Ge is reached at $r_{c}=r_{s}$. From the figure we can observe the strong influence of the shell on the $S_{E-DP}^{H}$ for $r_{c}/r_{s} < 0.8$ besides oscillations of $S_{E-DP}$ around the $S_{E-DP}^{H}$ values, a fact reflecting the oscillatory behavior of the phonon modes with $\gamma $ (see Fig.~\ref{bcont}). A similar result for the electron scattering amplitude has been reported in Ref.~\onlinecite{Ramayya} for Si nanowires.

\subsection{Hole-Acoustical-Phonon Hamiltonian}

By employing the solutions for the phonon amplitudes~(\ref{amplitude}), the matrix representation of the angular momentum $J=3/2$~\cite{PhysRev.102.1030,PhysRevB.84.195314} and the strain relations given in Appendix~\ref{Phonon}, the hole scattering amplitudes for the Hamiltonian~(\ref{eq:Hbp}) can be cast as

\begin{equation}
S_{H-BP}=\left\langle \widehat{F}_{m_{h}^{\prime }}^{(i)}\right\vert
H_{BP}\left\vert \widehat{F}_{m_{h}}^{(i)}\right\rangle \;,
\label{SHbp}
\end{equation}
where $i=hh^{+}$, $lh^{+}$, $lh^{-},hh^{-}$,

\begin{widetext}
\begin{equation}
S_{H-BP}=\left\langle
\begin{array}{c}
a_{1i}F_{m_{h}+n} \\
a_{2i}F_{m_{h}+n+1} \\
a_{3i}F_{m_{h}+n+2} \\
a_{4i}F_{m_{h}+n+3}
\end{array}
\right\vert ^{\dagger }\left(
\begin{array}{cccc}
\mathcal{T}_{+} & \mathcal{Y}^{-} & \mathcal{X}^{-} & 0 \\
\mathcal{Y}^{+} & \mathcal{T}_{-} & 0 & \mathcal{X}^{-} \\
\mathcal{X}^{+} & 0 & \mathcal{T}_{-} & -\mathcal{Y}^{-} \\
0 & \mathcal{X}^{+} & -\mathcal{Y}^{+} & \mathcal{T}_{+} \\
\end{array}
\right) \left\vert
\begin{array}{c}
a_{1i}F_{m_{h}} \\
a_{2i}F_{m_{h}+1} \\
a_{3i}F_{m_{h}+2} \\
a_{4i}F_{m_{h}+3}
\end{array}
\right\rangle \;,
\label{SHHbp}
\end{equation}
\end{widetext}
\begin{widetext}
\begin{eqnarray}
\mathcal{T}_{\pm } &=&-\left[ A_{_{L}}\left( \left[ a(\Gamma _{15v})\pm
\frac{1}{2}b(\Gamma _{15v})\right] \frac{\omega ^{2}}{v_{_{L}}^{2}}\mp \frac{
3}{2}k_{z}^{2}b(\Gamma _{15v})\right) f_{n}(q_{_{L}}r)\pm \frac{3}{2}
A_{_{T_1}}b(\Gamma _{15v})k_{z}q_{_{T}}f_{n}(q_{_{T}}r)\right] \text{ },
\notag \\
\mathcal{Y}^{\pm } &=&\mp i\sqrt{3}b(\Gamma _{15v})\left[
A_{_{L}}k_{z}q_{_{L}}f_{n\pm 1}(q_{_{L}}r)\mp \frac{1}{2}\left[
A_{_{T_1}}\left( q_{_{T}}^{2}-k_{z}^{2}\right) +A_{_{T_2}}k_{z}q_{_{T}}\right]
f_{n\pm 1}(q_{_{T}}r)\right] \text{ },  \notag \\
\mathcal{X}^{\pm } &=&\frac{\sqrt{3}}{2}b(\Gamma _{15v})\left[
A_{_{L}}q_{_{L}}^{2}f_{n\pm
2}(q_{_{L}}r)+(A_{_{T_1}}k_{z}q_{_{T}}-A_{_{T_2}}q_{_{T}}^{2})f_{n\pm
2}(q_{_{T}}r)\right] \text{ }.
\label{MEL}
\end{eqnarray}
\end{widetext}

From Eqs.~(\ref{SHbp}), (\ref{MEL}) and the basis of solutions~(\ref{amplitude}), we extract the following conclusions: a) For phonon states with $n=0$ and $k_{z}=0$ we have three independent hole-phonon interaction Hamiltonians, accounting for the three uncoupled subspaces, $L$, $T_{1}$, $T_{2}$, with eigenfrequencies $\omega_{_{L}}$, $\omega_{_{T_{1}}}$ and $\omega_{_{T_{2}}}$, respectively. Evaluating~(\ref{MEL}) at $\omega =\omega _{_{L}}$ and using the fact that $A_{_{L}}\neq 0$ and $A_{_{T_{1}}}, A_{_{T_{2}}}=0$, we see that the Hamiltonian~(\ref{SHbp}) couples the diagonal intraband hole sates $\left\vert i\right\rangle
\Rightarrow \left\vert i\right\rangle $ and the weak coupling interband between $\left\vert lh^{\pm }\right\rangle \Leftrightarrow \left\vert hh^{\mp }\right\rangle $ states; if we choose $\omega =\omega _{_{T_{1}}}$ where $A_{_{L}},A_{_{T_{2}}}=0$ and $A_{_{T_{1}}}\neq 0$, we are in the presence of interband transitions $\left\vert lh^{\pm }\right\rangle \Leftrightarrow \left\vert hh^{\pm }\right\rangle$. Also, for $\omega =\omega_{_{T_{2}}}$
with $A_{_{L}},A_{_{T_{1}}}=0$ and $A_{_{T_{2}}}\neq 0$, results in scattering $ \left\vert lh^{\mp }\right\rangle \Leftrightarrow \left\vert hh^{\pm
}\right\rangle $. b) Fixing $n=0$ and $k_{z}\neq 0$ there are two independent subspaces, $L-T_{1}$ and $T_{2}$. The first one couples $L$ and $T_{1}$ motions, while the second corresponds to pure $T_{2}$ transverse phonons. Similar expressions are obtained for homogeneous wires by choosing properly the function $F_{m_{h}}(r)$ and $f_{n}(r)$ inside the cylinder.
\begin{figure}[tbh]
\begin{center}
\includegraphics[width=\columnwidth]{Fig7}\\[0pt]
\end{center}
\caption{(Color online) Reduced valence band scattering amplitude $S_{H-BP}/H_{OH}$ for Ge/Si NWs as a function of the ratio $r_{c}/r_{s}$. For $k_{z}=0$ and $n=0$, the two sets of independent subspaces are displayed (see text): Upper panel transverse phonons with frequencies, $\omega_{T_2}^{(j)}$  ($j=1,2,3$); lower panel longitudinal modes and frequencies $\omega _{_{L}}^{(j)}$. Dashed lines: homogeneous Ge NW.}
\label{Fig7}
\end{figure}

In the size-quantum limit and not too large values of $k_{z}$, the Luttinger-Kohn (LK) Hamiltonian splits into two independent $2\times2$ matrices,
coupling ($\left\vert hh^{+}\right\rangle$, $\left\vert lh^{-}\right\rangle)$ or ($\left\vert hh^{-}\right\rangle$, $\left\vert lh^{+}\right\rangle)$
Bloch states (see Appendix~\ref{Valence-Band}). For $k_{z}=0$ and angular momentum quantum number $n=0$, the scattering amplitude~(\ref{SHHbp}) splits
into two independent terms, which correspond to the subspaces $L$ and $T_{2}$ of the hole-phonon interaction Hamiltonian.

Figure~\ref{Fig7} is devoted to the hole scattering amplitude~(\ref{SHHbp}) in units of $H_{OH}=-a(\Gamma _{15v})\sqrt{\hbar \omega _{n=0}(k_{z}=0)/4\pi
r_{c}^{2}L_{0}\rho _{c}v_{_{L_0}}^{2}}$ for the first three $T_{2}$ transverse modes (upper panel) and three $L$ longitudinal modes (lower panel) of the Ge/Si structure as a function of the ratio $r_{c}/r_{s}$. In the calculation we assumed that the lower hole state is completely confined in the core (hard wall potential approximation). As in Fig.~\ref{Fig6}, dashed lines represent the form factor for Ge NW with a radius of 5 nm. Here, the influence of the shell is solely due to Ge/Si phonon spectrum. From the figure we observe that $S_{H-BP}$ for the longitudinal modes are one order of magnitude larger than the transverse ones, reflecting the strength of coupling
between hole states. In the case of $T_{2}$ we have a coupling between $\left\vert hh\right\rangle $ and $\left\vert lh\right\rangle$, while for
the $L$ we are in the presence of the diagonal transitions $\left\vert hh\right\rangle \rightarrow \left\vert hh\right\rangle $ and $\left\vert
lh\right\rangle \rightarrow \left\vert lh\right\rangle$. Another feature is the strong oscillation of the $S_{H-BP}$ for transverse modes with
respect to the $L$ phonons. The $T_{2}$ vibrations couple the cylindrical function of second order, while for the $L$ modes, $S_{H-BP}$ is
proportional to the Bessel function $J_{0}$. In addition, a useful result can be extracted from Fig.~\ref{Fig7}, that is, we can obtain the minimum value
of $r_{c}/r_{s}$ where the hole-phonon Hamiltonian for core/shell NWs can be considered as a pure Ge wire. Notice that this result depends on the type of
interaction; for $L$ modes: $r_{c}/r_{s}\geq 0.6$ and for $T_{2}$ modes: $r_{c}/r_{s}\geq 0.8$.

\section{\label{Conclusion}Conclusion}

In summary, we have studied the acoustical phonon dispersions, the phonon displacement vectors and the electron- and hole-acoustical phonon Hamiltonians in
core/shell Ge/Si and Si/Ge NWs. Our results show the influence of the core radius and shell thickness of Si-Ge based nanowires on the phonon frequencies and electron-phonon and hole-phonon interaction Hamiltonians. Due to the presence of the shell, the phonon frequencies exhibit oscillations as function of the ratio $r_{c}/r_{s}$ leading to a strong influence on the interaction Hamiltonians and scattering amplitudes.  The gapless phonons have a tuned renormalized group sound velocities in terms of
the geometrical factor $r_{c}/r_{s}$.  Also, it is shown that scattering amplitudes for the conduction and valence bands can be handled by the shell thickness. The obtained results can be viewed as a basic tool for exploration of electron and hole transport phenomena and Brillouin light scattering, as well as for device applications of these one-dimensional Ge/Si and Si/Ge core/shell nanostructures. The systematic derivation and explicit, relatively simple, solutions of the electron and Bir-Pikus hole deformation potential Hamiltonians, incorporating the characteristics of the phonon modes for the wavenumber $k_{z}=0$, present straight applications to the resonant Raman scattering processes in core/shell NWs. Thus, searching at different light scattering configurations of the Brillouin and Raman processes, it possible to study the dependence of the $L$ and $T_{2}$ phonon modes on the spatial confinement and the intrinsic stress at the interface.

redpajama_set_name: RedPajamaArXiv


Last year we organised a Peacebuilders Workshop to create space for practitioners involved in peacebuilding work locally to come together and critically appraise our practice and identify the lessons learned about peacebuilding in conflict/post-conflict contexts. The discussion at that workshop calls to mind a number of important aspects of peacebuilding work that align with our approach at IISC.
Social change networks are complex, compared with other human organizational forms; they are not so easily controlled, directed or predicted. And that is as it should be, especially when dealing with real life diversity and uncertainty. This can cause some anxiety on the part of those who would like to be able to better control for outcome and process and may not be very comfortable with emergence and self-organization. But these are the life blood of complex networks, part of their intelligence and effectiveness, even as people may struggle to wrap their heads around the full picture of what is happening. That's the way life works.
IISC works with clients to expand dimensions of success beyond results. For long-term change to take hold, we help groups understand process and relationships are key factors. In the Communications Unit, we have created a daily practice to keep track of results, process, and relationships in our work. We call this practice "Rays" and we've found it works in person, on video chat, over the phone, or even as text or Slack messages.
Rays is a 15 minute meeting each day where we briefly share a ray of light in our life, the tasks on our plate, and anything blocking production. Here's the story of how we do it and what we've learned about its value.


text:
Study population, cell lines, culture medium, and reagents
Construction of recombinant lentivirus expressing MART-127–35 TCR
Transduction of CD4+ T cells with lentiviral vector
Cytokine synthesis by the transduced T cells
Cytotoxicity assay
CD4+CD25− T Cells Transduced to Express MHC Class I-Restricted Epitope-Specific TCR Synthesize Th1 Cytokines and Exhibit MHC Class I-Restricted Cytolytic Effector Function in a Human Melanoma Model1
Arvind Chhabra;
Arvind Chhabra
*Department of Medicine, University of Connecticut Health Center, Farmington, CT 06030;
Lili Yang;
Lili Yang
†Division of Biology, California Institute of Technology, Pasadena, CA 91125;
Pin Wang;
Pin Wang
‡University of Southern California, Los Angeles, CA 90089;
Begoña Comin-Anduix;
Begoña Comin-Anduix
¶Department of Medicine and Surgery, University of California, Los Angeles, CA 90095; and
Raja Das;
Raja Das
Nitya G. Chakraborty;
Nitya G. Chakraborty
Swagatam Ray;
Swagatam Ray
Shikhar Mehrotra;
Shikhar Mehrotra
∥Department of Surgery, Medical University of South Carolina, Charleston, SC 29425
Haiguang Yang;
Haiguang Yang
Cinnamon L. Hardee;
Cinnamon L. Hardee
§Children's Hospital Los Angeles, Los Angeles, CA 90027;
Roger Hollis;
Roger Hollis
David I. Dorsky;
David I. Dorsky
Richard Koya;
Richard Koya
Donald B. Kohn;
Donald B. Kohn
Antoni Ribas;
Antoni Ribas
James S. Economou;
James S. Economou
David Baltimore;
David Baltimore
Bijay Mukherji
Address correspondence and reprint requests to Dr. Arvind Chhabra and Dr. Bijay Mukherji, University of Connecticut Health Center, 263 Farmington Avenue, Farmington, CT 06030. E-mail addresses: arvindac@yahoo.com and mukherji@NSO2.uchc.edu
Accepted: May 15 2008
J Immunol (2008) 181 (2): 1063–1070.
https://doi.org/10.4049/jimmunol.181.2.1063
Arvind Chhabra, Lili Yang, Pin Wang, Begoña Comin-Anduix, Raja Das, Nitya G. Chakraborty, Swagatam Ray, Shikhar Mehrotra, Haiguang Yang, Cinnamon L. Hardee, Roger Hollis, David I. Dorsky, Richard Koya, Donald B. Kohn, Antoni Ribas, James S. Economou, David Baltimore, Bijay Mukherji; CD4+CD25− T Cells Transduced to Express MHC Class I-Restricted Epitope-Specific TCR Synthesize Th1 Cytokines and Exhibit MHC Class I-Restricted Cytolytic Effector Function in a Human Melanoma Model1. J Immunol 15 July 2008; 181 (2): 1063–1070. https://doi.org/10.4049/jimmunol.181.2.1063
Cytolytic T cell-centric active specific and adoptive immunotherapeutic approaches might benefit from the simultaneous engagement of CD4+ T cells. Considering the difficulties in simultaneously engaging CD4+ and CD8+ T cells in tumor immunotherapy, especially in an Ag-specific manner, redirecting CD4+ T cells to MHC class I-restricted epitopes through engineered expression of MHC class I-restricted epitope-specific TCRs in CD4+ T cells has emerged as a strategic consideration. Such TCR-engineered CD4+ T cells have been shown to be capable of synthesizing cytokines as well as lysing target cells. We have conducted a critical examination of functional characteristics of CD4+ T cells engineered to express the α- and β-chains of a high functional avidity TCR specific for the melanoma epitope, MART-127–35, as a prototypic human tumor Ag system. We found that unpolarized CD4+CD25− T cells engineered to express the MART-127–35 TCR selectively synthesize Th1 cytokines and exhibit a potent Ag-specific lytic granule exocytosis-mediated cytolytic effector function of comparable efficacy to that of CD8+ CTL. Such TCR engineered CD4+ T cells, therefore, might be useful in clinical immunotherapy.
Cancer vaccines and adoptive immunotherapy for cancer have achieved impressive clinical responses in some patients (1, 2), but the overall result of such treatments has been somewhat modest. Intense efforts are underway to improve the outcome of these forms of therapy. Most cancer vaccines and adoptive immunotherapeutic strategies seek to achieve a robust and long-lived CTL response, because most cancer cells express only MHC class I-restricted epitopes. The task of generating a robust and long-lived CTL response to tumor-associated Ags, most of which are self-Ags, faces many constraints. Among these is the lack of an effective strategy to engage CD4+ Th cells.
Clinical trials with various forms of non-cognate help (universal class II epitope, tetanus toxoid, KLH, etc.) have been undertaken without clear evidence of benefit. A limited number of studies with MHC class II determined helper epitopes—as cognate help—has also been initiated. Unfortunately, only a few class II-restricted determinants have so far been defined, and only a limited number of patients can be matched for the appropriate MHC class I and class II alleles for which epitopes are available. The task of engaging cognate help targeting MHC class II-restricted epitopes in anti-tumor immunity, therefore, has turned out to be difficult. Lately, redirecting CD4+ T cells to MHC class I-restricted epitopes through engineered expression of class I-restricted epitope-specific T cell receptors in CD4+ T cells has emerged as a strategic consideration. It has been shown that CD4+ T cells engineered to express relevant MHC class I-restricted epitope-specific T cell receptors can function as effector cells (3, 4, 5, 6, 7). They usually exhibit a mixed (i.e., Th1 as well as Th2/3) cytokine synthesis profile (3, 5, 6), unless before transduction they are polarized to Th1 phenotype (7). It has also been shown that MHC class I-restricted epitope-specific TCR-engineered CD4+ T cells provide help toward the generation of memory CTL response in animal models (8, 9). These observations, and the pressing need for developing an effective method that would engage cognate help in tumor immunotherapy in humans, prompted us to undertake a critical examination of the biology of CD4+ T cells engineered to express a relevant set of MHC class I-restricted human tumor epitope-specific TCR. In this study we show that human CD4+CD25− T cells engineered to express a TCR specific for the HLA-A2.1-restricted melanoma epitope, Melan-A/MART-127–35 (M1),3 synthesize only Th1 cytokines IFN-γ and IL-2 and not IL-4 or IL-10. They also exhibit MHC class I-restricted and granule-mediated cytolytic activity in recognition of the M1 epitope presented on HLA-A2.1-positive surrogate target cells, as well as melanoma cells naturally displaying the M1 epitope.
HLA-A2-positive melanoma patients and healthy donors were included in the study with informed consent. Culture medium and other reagents used to generate M1 epitope-specific T cells have been described previously (10). T2 cells, human melanoma cell line A375, was a gift of Steven A. Rosenberg (Surgery Branch, National Cancer Institute, Bethesda, MD). A375 cells engineered to express Melan-A/MART-1, A375-M have been described before (11). The melanoma cell lines PT-M and JL-M were established from two HLA-A2.1-positive melanoma patients.
A MART-127–35 antigenic epitope-specific oligoclonal CTL line was generated from a limiting dilution microwell seeded with three MART-127–35 peptide-pulsed dendritic cell-activated CD8+ T cells generated as described before (10, 11). Total RNA was extracted from the CTL line using a Qiagen RNeasy kit, and was used to clone out the TCR genes using the BD SMART™ RACE kit following the manufacturer's instructions. In brief, the first-strand cDNA was synthesized in two steps: step 1 constituted the first-strand synthesis coupled with deoxy cytidine tailing by reverse transcriptase; step 2 constituted the template switching and extension by reverse transcriptase, resulting in the 5′-RACE-Ready cDNA capped with a common primer at the 5′ end. The cDNA was then used to run 5′-RACE PCR to clone the TCR genes. From the oligoclonal CTL line, three productively rearranged TCR α-chain genes and three productively rearranged TCR β-chain genes were cloned. Using a TCR pairing assay, two TCR pairs, α3β15 and α2β14, were determined to be specific for the MART127–35 epitope based on the HLA-A2/MART-1 tetramer (Beckman Coulter) staining. To construct the FUW-M1-TCR/sr39tk lentivector, the α- and β-chains of M1 TCR and the sr39tk imaging/suicide gene were linked with F2A and P2A elements (12) using assembly PCR and were then cloned into the FUW lentivector (13).
The lentiviral vector was packaged by transient transfection of 293T cells with the vector plasmid, a plasmid expressing the HIV-1 gag and pol proteins (p8.9) and a plasmid encoding the VSV-G protein, as described before (14). The vector supernatant was concentrated ∼500-fold by ultrafiltration (Centricon plus 70 ultrafiltration filters; Millipore) followed by ultracentrifugation at 500 × g for 2 h. Concentrated vector supernatants were resuspended in X-Vivo15 serum-free medium and stored at −70°C until used. Titers were determined by transduction of subconfluent HT29 cells with serial dilutions of vector supernatant, followed by extraction of genomic DNA after 1 wk and quantification of integrated vector copy number by quantitative PCR using primers to the HIV-1 leader region (15). The numbers of transducing units per milliliter were calculated by multiplying the vector copy number, which was extrapolated from a standard curve of known vector copy number, the number of cells at the time of supernatant addition, and the supernatant dilution.
Purified CD4+CD25− subsets of CD4+ T cells were isolated from CD4+ T cells by magnetic beads purification method (Invitrogen) from Ficoll-Hypaque density gradients purified human peripheral blood lymphocytes as reported before (10, 11). Purified CD4+CD25− T cells were then activated with 5 μg plate-bound anti-CD3 Ab and cultured in the presence of 100 μ/ml IL-2 for 5 days. Activated CD4 T cells (0.5–1 X106 cells) were transduced with the recombinant virus at 10 multiplicity of infection. Transduction was conducted for 120 min by slow shaking (∼100 rpm) on a bench top mixer at room temperature. The next day, cells were transduced again under identical conditions and then cultured for 5 days in the presence of 1000 μ/ml IL-15. Transduction efficiency was quantified by staining transduced cells with M1 epitope-specific tetramer (Beckman Coulter). When needed, the TCR-transduced populations were expanded by in vitro stimulation with M1 peptide-pulsed matured dendritic cells, once or twice, as reported earlier (10, 11).
The ability of the TCR-transduced CD4+ T cells to produce cytokines was determined in cytokine synthesis assay as previously described (10, 11). In brief, they were stimulated by T2 cells pulsed with the cognate peptide (MART-127–35) or the control peptide (MAGE-3271–279) at effector T cells to a target ratio of 10 for 16 h. Supernatants were then analyzed for various cytokines. Melanoma cells were also used to stimulate the transduced cells to determine whether they would respond to them.
The cytolytic ability of T cells was examined by the chromium release microcytotoxicity assay, done as described previously (16).
IL-2, IL-4, IL-10, and IFN-γ cytokines were measured by sandwich ELISA kit (Immunotech) according to the manufacturer's instructions. The details have been published (10).
An oligoclonal MART-127–35 epitope-specific CTL line was generated by limiting dilution culture from the in vitro activated/expanded CD8+ T cells obtained from a patient who exhibited a remarkable high frequency of the M1 epitope-specific TCR-positive T cells in circulation (Fig. 1,A). The M1 epitope-specific TCR-positive T cells in circulation of the donor were predominantly V β14 positive (Fig. 1,B). Coexpression of the M1 epitope-specific TCR α- and -β-chains, derived from the M1 epitope-specific CTL line led to the identification of two M1 epitope-specific functional TCRs (Fig. 2,A). Both of these TCR contained the Vβ14 region and Vα 2.1 and 2.2 regions, respectively (Fig. 2,A). Based on preliminary comparative studies, we elected to use the Vα 2.2/Vβ14 (M14.2) TCR to study the biology of TCR-transduced CD4 T cells. A recombinant lentiviral vector encoding the M14.2 TCR was constructed (Fig. 2,B). A human ubiquitin-C promoter was used to drive the expression of three transgenes: MART-1 TCR α, MART-1 TCR β, and suicide/imaging gene sr39tk. The suicide/imaging gene sr39tk was incorporated in our constructs for in vivo imaging studies in a future clinical trial. Two self-cleavage 2A-like liners (F2A, derived from food-and-mouth disease virus; P2A, derived from porcine teschovirus) (12) were used to link the three transgenes to achieve the optimal stoichiometric expression of these three proteins (Fig. 2,C). The functional integrity of the two TCR chains was confirmed by transducing Jurkat cells (Fig. 2,D). A dose-dependent increase in M1-specific tetramer and anti-V β14 Ab-stained Jurkat was observed in transduced populations (Fig. 2 D).
Generation of MART-127–35 epitope-specific CTL line from the peripheral blood-derived CD8 T cells of a melanoma patient. Ai, An oligoclonal CTL line was generated from a melanoma patient's peripheral blood-derived CD8+ T cells, in a dendritic cell-T cell coculture expansion protocol. Aii, The Ag-specific effector function of the CTL line was tested by measuring IFN-γ release in the supernatant upon coculture with either surrogate target cells, T2 (left panel), or MART-1-expressing human melanoma cells PT-M (right panel). CTL were cocultured with target cells alone (T2/PT-M) or target cells pulsed with either cognate peptide, MART-127–35 (T2/PT-M +M1), or MAGE-3271–279 control peptide (T2/PT-M+M3), and cytokine released in supernatant was measured next day. B, TCR V-β clonotypic analysis of patient-derived MART-127–35 epitope-specific CD8 T cells.
Construction of a recombinant lentivirus vector encoding MART-127–35 epitope-specific TCR. A, Coexpression of PCR amplified α- and β-chains led to the identification of two functional M1 epitope-specific TCRs. Both of these TCR consisted of Vβ14 region and Vα2.1 and Vα2.2 regions, respectively. The Vα2.1/Vβ14 TCR was named as M14.1, while Vα2.2/Vβ14 TCR was named as M14.2 TCR. M14.2 TCR was used in follow-up studies. B, Cloning of M14.2 TCR α and β-chains in a FUW-M1-TCR/sr39tk lentivirus vector. C, 293T cells were transduced with the lentiviral vector FUW-M14-TCR/sr39tk, lysed, and immunoblotted. Specific Abs were used to detect the constant region of the α- and β-chains of TCRs and the HSV1-tk. In the figure, arrows point to the expected size bands for each protein. Weaker high molecular weigh bands correspond to uncleaved products. The cleavage efficiency of the linkers was estimated to be ≥90%. D, Transduction of Jurkat cells with transgenic TCR.
We next examined the functional integrity of the transgene in CD4+ T cells and characterized the nature of Ag-specific cytokine response exhibited by the M14.2 TCR-transduced CD4 T cells. Fig. 3,A shows that 12% of the non-polarized but preactivated CD4+CD25− T cells transduced with the FUW vector expressing the M14.2 TCR. A fraction of the M14.2 TCR-positive cells expressed CD4 molecules at lower density. The reason for this under-expression of CD4 molecules in the TCR-transduced population presently remains unclear. The M14.2 TCR-engineered CD4+ T cells synthesized IFN-γ and IL-2, but not IL-4 or IL-10 in an epitope-specific manner (Fig. 3,B). Of note, this Th1 type bias was also seen with the M14.2 TCR-engineered CD4+ T cells from three other donors in six separate experiments (Fig. 4). The TCR-transduced CD4+ T cells also recognized M1 Ag on the HLA-A2.1-positive MART-1-transduced melanoma line A375, as well as the HLA-A2.1-positive melanoma cell line PT-M, naturally expressing the MART-1 Ag (Figs. 3,C and 5B). In contrast, they did not recognize the melanoma line JL that was HLA-A2.1-positive but did not express the MART-1 protein (Figs. 3,C and 5B). Fig. 3,D shows the epitope recognition profile of autologous CD8+ CTL. As can be seen, CD8+ CTL, generated from the same donor in our standard in vitro CTL generation protocol (10), also exhibited essentially identical epitope recognition profile and comparable cytokine synthetic capacity. The M14.2 TCR-transduced CD4+ T cells also exhibited Th1 type bias against the melanoma lines (Fig. 5,A). Of note, the TCR-transduced CD4+ T cells exhibited a comparable high functional avidity for the cognate peptide as displayed by the natural M1 epitope-specific high affinity TCR-expressing CD8+ CTL (Fig. 6). The functional avidity of TCR-transduced CD4 T cells and CD8+ CTL was examined at different peptide doses and at different E:T ratios (Fig. 6, A–D).
Transduction of T cells with transgenic TCR and analysis of the effector cytokine response. A, Transduction of activated human primary CD4 T cells with transgenic TCR. B, Characterization of effector cytokine response of TCR-engineered CD4 T cells. Transduced CD4 T cells were cocultured with T2 cells alone or T2 pulsed with MART-127–35 peptide or MAGE-3271–279 control peptide, and cytokines released in the supernatant were quantified 16 h following coculture. C, Effector cytokine response of TCR-engineered CD4 T cells against human melanoma cells. Transduced CD4 T cells were cocultured with human melanoma cell lines, A375 wild type, and MART-1 expressing A375 (A375-M), PT-M, and JL-M. Coculture was set up either with cells alone or cells pulsed with MART-127–35 peptide or MAGE-3271–279 control peptide, and cytokines released in the supernatant were quantified 16 h following coculture. D, Effector cytokine response analysis of human peripheral blood-derived MART-127–35 epitope-specific CD8+ CTL against surrogate target, T2, or human melanoma cells. CTL were cocultured with T2 or melanoma cells alone or cells pulsed with cognate peptide (M1) or control peptide (M3), and IFN-γ released in the supernatant was measured 16 h following coculture, as done with TCR-engineered CD4 T cells (C).
Characterization of cytokine response of TCR-engineered CD4 T cells. CD4 T cells derived from three different donors were transduced with M14.2 TCR and cocultured with T2 cells alone or T2 pulsed with MART-127–35 peptide or MAGE-3271–279 control peptide, and cytokines released in the supernatant were quantified 16 h following coculture.
Characterization of cytokine response of TCR-engineered CD4 T cells, in response to human melanoma cell lines. A, M14.2 TCR transduced CD4 T cells were cocultured with human melanoma cell lines, A375 wild type, and MART-1 expressing A375 (i), PT-M (ii), and JL-M (iii). Coculture was set up either with cells alone or cells pulsed with MART-127–35 peptide or MAGE-3271–279 control peptide, and cytokines released in the supernatant were quantified 16 h following coculture. B, Analysis of human melanoma cell lines, A375, A375-MART-1, PT-M, and JL-M, for the expression of HLA-A2 molecules and MART-1 Ag.
Transgenic TCR-engineered CD4 T cells function as high avidity effector T cells. A, Analysis of effector cytokine (IFN-γ and IL-2) release by transgenic TCR-engineered CD4 T cells at a peptide dose range of 1 ng-10 μg. B, Tetramer analyses of MART-127–35 antigenic epitope-specific CTL population expanded from human peripheral blood, in a peptide pulsed dendritic cell-T cell coculture expansion protocol. C, Analysis of effector cytokine (IFN-γ) release by human peripheral blood-derived CD8+ CTL precursor-expanded MART-127–35-specific CTL population, at a peptide dose range of 1 ng-10 μg. D, Analysis of effector cytokine (IFN-γ and IL-2) release by transgenic TCR-engineered CD4 T cells at different E:T ratios.
We next examined the cytolytic potential of transduced CD4 T cells (Fig. 7). As shown, the M14.2 TCR-engineered CD4+ T cells lysed the M1 peptide loaded surrogate targets as well as lysed melanoma cells naturally expressing the epitope (Fig. 7, A and B) just as efficiently as the in vitro generated natural CD8+ CTL (Fig. 7, C and D).
Cytolytic potential of MART-127–35 epitope-specific TCR-engineered CD4 T cells. Cytolytic potential of TCR-engineered CD4 T cells against peptide pulsed T2 cells (A) or MART-1 expressing melanoma cells, PT-M (B). Cytotoxicity assays were set up with target cells alone or pulsed with the MART-127–35 peptide or MAGE-3271–279 control peptide, and Cr51 release was quantified 6 h post coculture. Of note, lysis of the PT-M cells was observed at all E:T ratios examined; the level of lysis was considerably higher at E:T of 50 when the PT-M cells were pulsed with the peptide (B). Cytolytic potential analysis of MART-127–35 epitope-specific human peripheral blood-derived CD8+ T cells against T2 (C) or PT-M melanoma cells (D). Cytotoxicity assay was done by Cr51 release assay with Cr51-loaded T2 or PT-M melanoma cells, as done for MART-127–35 epitope-specific M14.2 TCR-engineered CD4 T cells (A and B).
Next we compared the mechanism of the cytolytic effector function displayed by the transgenic TCR-transduced CD4 T cells with the MART-127–35 epitope-specific natural CD8+ CTL (Fig. 8). As shown in Fig. 8,A, the cytolytic effector function exhibited by TCR-engineered CD4 T cells was MHC class I-restricted and the calcium chelant EGTA blocked this cytolytic activity. Because calcium is required for release of perforin and granzyme B leading to cytotoxic death of target cells, these data suggest that the lytic activity of these cells was mediated by the release of lytic granules (Fig. 8,B). The M14.2 TCR-engineered CD4+ T cell expressed cytolytic effector molecules, granzyme and perforin, and they underwent degranulation after encountering the cognate epitope (Fig. 8,C), similar to the M1 epitope-specific CD8+ CTL (Fig. 8, D and E).
MART-127–35 epitope-specific TCR-engineered CD4 T cells mediate cytolytic effector function in a MHC class I-restricted and cytolytic granule exocytosis-dependent manner. Analyses of cytolytic potential of MART-127–35 epitope-specific M14.2 TCR-engineered CD4 T cells (A) and MART-127–35 epitope-specific human peripheral blood-derived CD8+ CTL (B), in a Cr51 release assay, with Cr51 labeled T2 cells alone or T2 cells pulsed with MART-127–35 cognate peptide or MAGE-3271–279 control peptide. Cytotoxicity assay was set up either in the absence or presence of anti-MHC class I, anti-MHC class II Abs. EGTA (4 mM) pretreatment was done to block the release of cytolytic granules. C, M14.2 TCR-engineered CD4 T cells express cytolytic effector molecules, granzyme, and perforin (i), and undergo degranulation following Ag encounter with T2 cells pulsed with MART-127–35 peptide epitope (ii). Transgenic CD4 T cells were cocultured either with T2 cells alone or T2 cells pulsed with MART-127–35 cognate peptide or MAGE-3271–279 control peptide, and degranulation was measured by quantifying CD107 molecules, surface exposed upon Ag encounter. Analyses of the expression of granzyme and perforin (D), and degranulation assay (E) were conducted with MART-127–35 epitope-specific human peripheral blood-derived CD8+ CTL, as done for TCR-engineered CD4 T cells (C).
Most active specific and adoptive immunotherapeutic approaches for cancer center around CTL-based responses generated through immunization or transferred adoptively with ex vivo-generated CTL. CD4+ T cells might contribute in these strategies substantially (17, 18, 19), but the task of simultaneously engaging CD4+ Th cells and CTL has turned out to be quite difficult, especially in an Ag-specific manner. Accordingly, redirecting CD4+ T cells to recognize MHC class I-restricted epitopes through engineered expression of MHC class I-restricted epitope-specific TCR has gained attention. In animal models, it has indeed been shown that such TCR-engineered CD4+ T cells can provide help (8, 9) as well as exhibit cytolytic effector function (20). In human systems, MHC class I-restricted epitope-specific TCR-engineered CD4+ T cells have been shown to synthesize different cytokines in coreceptor-dependent as well as coreceptor-independent manners (3, 4, 5, 6, 7). In general agreement with these studies, our results attest to the potential usefulness of such MHC class I-restricted epitope-specific TCR-engineered CD4+ T cells in tumor immunotherapy. Our studies also reveal a number of additional interesting aspects of their biology.
First, our studies clearly show that the MHC class I-restricted epitope-specific TCR-engineered CD4+ T cells can function in a coreceptor-independent manner. Coreceptor-dependent and -independent function by such TCR-engineered CD4+ T cells has been described (21, 22). It is believed that a high affinity/avidity TCR might transmit productive signals without the participation of coreceptors. The affinity of the M14.2 TCR on CD4+ T cells was found to be in the nanomolar range, and it was comparable to that of the naturally grown CD8+ CTL (Fig. 6). These transgenic TCR-transduced CD4 T cells recognized the naturally expressed M1 epitope on melanoma cells, just as efficiently as the naturally grown CD8+ CTL (Fig. 3).
Second, in contrast to previous reports of MHC class I-restricted epitope-specific TCR-engineered CD4+ T cells synthesizing both type 1 and type 2/3 cytokines (3, 5, 6), the M14.2 TCR engineered CD4+ T cells synthesize only Th1 type cytokines (Figs. 3, 4, and 5). The reason for this Th1/Tc1 bias in the M14.2 TCR engineered CD4+ T cells remains unclear. It should be noted that we used only CD4+CD25− subsets. Additionally, we did not polarize them in Th1 type condition before transduction, as was done in another study where Th1 type bias by this type of TCR-engineered CD4+ T cells was reported (7). Given that CD4+ T cells from three different donors engineered to express the M14.2 TCR elaborated only Th1/Tc1 cytokine (Fig. 4), it does not appear to be an isolated incidence. Careful studies will be needed to understand whether a given set of transgenic TCR dictates polarization or the functional polarization is an imprinted property acquired inherently during ontogeny or acquired in culture conditions. Whatever the explanation might turn out to be, one can envision a distinct advantage with the TCR-engineered CD4+ T cells exhibiting Th1 bias from a translational viewpoint. TCR-engineered CD4+ T cells exhibiting Th1 bias are likely to be true helper cells and more effective effector cells.
Third, the MHC class I-restricted and granule-mediated cytolytic property of the M14.2 TCR-engineered CD4+ T cells provides a different understanding on the functional separation between a CD4+ T cell and a CD8+ T cell. Traditionally, CD8+ T cells are viewed as quintessential cytolytic T cells and CD4+ T cells as helper cells. Although a role of CD4+ T cells in anti-tumor immunity is well documented in certain models (23, 24, 25), the mechanism by which CD4+ T cells exhibit anti-tumor immunity in these models has never been fully clarified. The M14.2 TCR-engineered CD4+ T cells appear to be just as good killer cells as their CD8 counterparts; they use granule-mediated lytic machinery (Figs. 7 and 8), and they also elaborate a comparable amount of IFN-γ (Fig. 3, C and D). The mechanism(s) that re-directs CD4+ T cells to perform as killer T cells presently remain unclear. Additional studies will be needed to address this issue. Though how CD4+ T cells are re-directed to function as cytolytic T cells by signals through the transgenic CTL-derived TCR remains an open question, our data clearly show that the M14.2 TCR-engineered CD4+ T cells can function as formidable effector cells. They could, therefore, expand the effector response repertoire substantially in an active specific or adoptive immunotherapy schema.
Finally, it should be pointed out that engaging such MHC class I-restricted epitope-specific and coreceptor-independent TCR-engineered CD4+ T cells in tumor immunotherapy would have many advantages. For example, making CD4 T cells function through the same epitope that the CTL precursors also recognize resolves the problem in engaging the CTL precursors, Thp, and the APC presenting separate class I and class II epitopes simultaneously, a conundrum in orchestrating help in a three cell model. Second, the strategy does not rely on recruiting a rare Thp. By introducing a fairly large number of TCR-engineered CD4+ T cells, the scope for providing cognate help could be vastly improved. Additionally, such CD4+ T cells could do more than help. They could provide effector function of their own. The strategy can be used for active specific as well as in adoptive therapy models. Most importantly, as a large number of MHC class I-restricted tumor-associated epitopes and CD8+ T cells capable of recognizing them are defined, a large number of patients could be matched for administration of MHC class I epitope-specific TCR-engineered CD4+ T cells. As such, the translational potential of MHC class I epitope-engineered CD4+ T cells in the setting of active specific or adoptive immunotherapy will be considerable.
This work was supported by Public Health Service Grants CA 83130 (to B.M.), CA 88059 (to B.M.), CA129816 (to J.S.E.), grants from the Dowling Foundation (to B.M.), General Clinical Research Grant MO1RR06192 (to University of Connecticut Health Center), Samuel Waxman Foundation, and WM Keck Foundation (to J.S.E. for UCLA-CALTECH-CHLA-USC-UCONN Consortium on Translational Program in Engineered Immunity).
Abbreviations used in this paper: M1, Melan-A/MART-127–35; M14.2, Vα 2.2/Vβ14.
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redpajama_set_name: RedPajamaCommonCrawl


As an admirer from afar, or even if you're lucky enough like to be a guest like myself at a Chanel show, the only certainty is that you must expect the unexpected. Every season the Chanel universe evolves, morphs and transforms so greatly, that we may assume that only Mr Lagerfeld himself knows where the next destination will be.
Cue music (and goosebumps) and we arrive at the Chanel solar system, where planets metamorphosis into bespoke handheld clutches, the stars are glitter-clad booties and the moon may well have been fashioned into the pearl trim circumnavigating the sleeves of the signature tweed jackets.


You can also request an individual on-line session, please write to international.office@fm-kp.si to schedule a date.
Candidates are requested to submit applications for enrolment in the electronic form on the eVS web portal, following the link http://portal.evs.gov.si/prijava/?locale=en.
Read Call for Enrolment and Common Provisions.
Check if you fulfill all the admission criteria.
Choose university and faculty offering the study programme.
Check which documents you need to submit togetther with you application.
Print and sign your application.
mark the envelope with "Application to postgraduate studies 2019/2020"
Candidates apply with a qualified digital certificate or with username and password. Each candidate may only submit one application.
The study programme will be delivered in English if there are at least 15 students enrolled.
Please read Call for Enrolment 2019/2020 - Common provisions before applying.


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TV Guy
'Game of Thrones,' 'Madam Secretary': weekend highlights
By Hal Boedeker
Staff writer |
On the weekend of the Kentucky Derby and a huge boxing match, "Game of Thrones" offers a bit of sports, too, at 9 p.m. Sunday on HBO. You'll see a sword fight so unusual that it becomes an instant classic. The episode also offers a frank Jon Snow, a chatty Tyrion Lannister (he talks in desperate times) and a violent sequence that's genuinely disturbing, even for this show.
The Kentucky Derby coverage on NBC starts at 4 p.m. Saturday. Post time is put at about 6:40 p.m. Pay-per-view coverage of the Floyd Mayweather-Manny Pacquiao fight comes from HBO and Showtime at 9 p.m. Saturday.
The week's other highlights include:
"The Good Wife" explains what's next for an adrift Alicia Florrick at 9 p.m. Sunday on CBS. She takes the case of a former client accused of murder, and she sure could use some good news. The drama offers its season finale on May 10.
The season finales this weekend include "Blue Bloods" at 10 p.m. Friday on CBS, "Secrets and Lies" at 9 p.m. Sunday on ABC and "The Last Man on Earth" at 9:30 p.m. Sunday on Fox. "Madam Secretary" concludes its successful first season at 8 p.m. Sunday on CBS by giving star Tea Leoni a showy turn as the risk-taking secretary of state. Treason and romance drive the plot, and fans can expect more of that romance next season.
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"Penny Dreadful" starts its chilling second season with Vanessa Ives (Eva Green) tormented by new evil at 10 p.m. Sunday on Showtime. We learn more about that evil represented by Evelyn Poole (Helen McCrory acting with nasty bravura) and her associates. The Creature (Rory Kinnear) seeks employment, and Dr. Frankenstein (Harry Treadaway) keeps working on his latest creation. Horror fans should be impressed by the effects, and drama fans will appreciate the poignant moments.
"Mad Men" offers an episode called "Lost Horizon" at 10 p.m. Sunday on AMC. Don receives a big award, but Joan may be the reason to watch, because she clashes with a co-worker. The Emmy-laden drama delivers its series finale May 17.
ABC keeps "Shark Tank" at 8 p.m. Friday to usher in a companion series, "Beyond the Tank," at 9 p.m. The new series explains what happens to entrepreneurs after "Shark Tank" and will run for three weeks.
Scarlett Johansson hosts "Saturday Night Live" at 11:30 p.m. Saturday on NBC. She gets to remind everyone, as if they need it, that the "Avengers" sequel is in movie theaters. Wiz Khalifa is the musical guest.


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World leaders: Before and after they took office
As John Key resigns as New Zealand Prime Minister, we look at the dramatic transformations of six world leaders.
Presidents and Prime Ministers
Love them or loathe them, there is no doubt that being the leader of a country is more high pressure than the vast majority of jobs.
And with every politician sure they can make a difference to the nation they serve, many of them begin their terms in the White House, the Beehive or Downing Street, fresh faced and full of youthful enthusiasm.
But after a decade running a country, the stress of doing so can sure start to take its toll.
In December, Prime Minister of New Zealand John Key announced he would step down from his position as he had nothing more to give the country. We took a look at how he's changed since a forty-something leader in 2008, and how other world leaders fared over their terms of office.
Click through for John Key's thank you to New Zealand.
*You may also like: John and Bronagh through the years.
John Key was only in his forties when he became the 38th Prime Minister of New Zealand in 2008.
He announced he would step down from the role in December 2016, after deciding he needed to put family first.
Tony Blair, of the Labour Party, led the UK from 1997 to 2007.
Although he was a popular Prime Minister for many years, he received huge backlash for embarking on the invasion of Iraq and the Iraq War, along with then American President George Bush. The Iraq Inquiry, published in 2016, criticised his actions and deemed the invasion unnecessary.
Bill Clinton was a Democrat and President of America from 1993 to 2001. He served for two terms and endured several scandals, including the affair with a 22-year-old colleague, Monica Lewinsky.
Bill left the White House after two terms in 2001.
George W Bush was elected after Clinton, to become the 43rd President of the United States. He came from a political family, with both his father and grandfather having being politicians.
During his 8 year, two term rule, Bush launched the War on Terror, in response to the attacks on The World Trade Centre.
Helen Clark was Prime Minister of New Zealand between 1999 and 2008.
Following her three terms as Prime Minister, Clark has gone onto work for the United Nations, and has been named by Forbes as one of the World's Most Influential Women.
The world's coolest leader - Barack Obama - took office in 2008. He was the first African-American President of the United States.
He served for two terms until 2016, when Donald Trump was elected President.


NGC 1851 is a globular cluster in the southern constellation of Columba that's easily visible with binoculars. It's an unusual cluster since it was probably a former member of the Canis Major Dwarf galaxy. This dwarf galaxy and Local Group member was discovered in 2003.
James Dunlop, a Scottish astronomer based in Australia, discovered NGC 1851 on May 29, 1826. It shines at mag. +7.3 and spans 11 arc minutes of sky, making it the brightest and largest deep sky object in Columba.
This globular is best seen during the months of December, January and February. From northern temperate locations it appears low down, apart from latitudes above 50N where it's not even visible at all. The object is number 73 in the Caldwell catalogue.
Columba is not a difficult constellation to recognise under a dark sky. Its brightest stars shining at third magnitude. To locate NGC 1851, look towards the southwestern corner of the constellation, 9 degrees southwest of Phact (α Col - mag. +2.7). In this barren region of sky you will find NGC 1851.
Through popular 7x50 or 10x50 binoculars, the globular appears as a small fuzzy ball of light. With an 80mm (3.1-inch) refractor at low magnifications, it's unresolved, spans about 5 arc minutes and looks somewhat like the halo of a comet. The brightest individual members are of 13th magnitude and a 200mm (8-inch) scope will resolve some of them, especially under dark skies. NGC 1851 is a superb site when seen through large backyard scopes. A 300mm (12-inch) instrument reveals a large, bright round ball of stars that's well resolved at 250x magnification. There are several chains of stars visible that branch outwards from the centre.
NGC 1851 is 39,500 light-years distant. It has an actual diameter of 130 light-years and is estimated to contain 200,000 stars. The cluster is 9.2 billion years old.


Quiz: Build Your Dream NFL Team and We'll Guess Your Favorite Legendary Coach!
As with any sport, the history of the NFL is one filled with coaches who left their stamp on the game through innovation, inspiration, and dedication. Through their efforts, these coaches became legends on the gridiron, widely recognized around the football community for their accomplishments.
When you reflect on what's important to you about football, do you know which legendary coach is your favorite? Why not let us tell you? Here's a quiz where we will do just that!
One of the most important components of being a legendary coach, of course, is putting together a championship roster that is capable of competing in any era against any opposition. That means selecting the best quarterback to lead your offense, the best skill positions to fit your strategy, and the best defenders to defend your end zone.
Are you ready to put together a championship roster that matches your legendary coach's personality? From receivers to linemen to safeties, you will have some tough options to pick from in this quiz as you form a complete NFL team from some of the greatest stars the game has ever seen.
When you're ready, get started with selecting your team so we can tell you which coach fits your personality!
Which of these legendary quarterbacks would you want?
Which deep threat wide receiver fits your team's needs?
Which current running back do you think would be a good team addition?
Who do you want snapping the ball to your quarterback?
Which tight end best fits your offense?
Which guard do you need to get your run game going?
Which tackle do you want guarding your quarterback's blind side?
Which of these superb route-running wide receivers are you adding to your team?
These running backs were so elusive that they rarely got touched. Which one would you take?
Which of these young quarterbacks would you put on your roster?
Who do you want covering the other team's best receiver?
Which of these players do you want getting after the quarterback?
Who do you want stopping up the middle on the defensive line?
Which defensive end do you want covering the end of the line?
Which cornerback in the game today do you want on your team?
Which linebackers do you want operating in the middle of your defense?
Which of these strong safeties do you want making tackles?
Who do you want covering the deep field on defense?
Which outside linebacker best fits your team needs?
These running backs could power through entire defenses. Which one would you take?
Which of these 2018 NFL draft picks are you taking?
Which of these defensive stars currently in the NFL could make plays on your team?
Who do you want from the 1990s All-Decade Team?
These offensive players exploded in 2018. Who would you want on your team?
Which of these Hall of Famers would get a spot on your roster?
Which former NFL MVP quarterback do you think could star on your team?
Each of these running backs had a 2,000-yard season during their careers. Who do you want on your team?
Which of these single-season sack leaders could rush passers for your squad?
Which of these Super Bowl MVPs could play in the big game for you?
Which of these players from the 1980s All-Decade Team would you pick for your team?


The Gatorskin is famous as a hard wearing, puncture protected tyre designed for fast riding and commuting. It's probably the most popular road bike tyre in the UK (maybe Europe) with its cut-resistant Duraskin and Kevlar-reinforced layers. This tyre is ideal for training, commuting, winter riding and even sportives.
The smooth rolling tread which provides exceptional grip in both wet and dry conditions makes it a winter and all-year favourite. It's well worth your while fitting Gatorskins for winter because of the minimal risk of puncturing and you having to be changing tubes in the bitter cold.
The Duraskin® external mesh forms a protective shield over the entire casing to help prevent cuts, punctures and abrasions. It's a lightweight cut-resistant layer which gives the Gatorskin its distinctive brown sidewalls.
This densely woven Polyester fibre provides some of the Gatorskin's puncture protection and stops debris penetrating beyond the tread.
Once known as the Ultra Gatorskin, before the new GatorHardshell was introduced, there are also wider options to add a little extra comfort to your ride. This folding bead Gatorskin is lighter than the rigid bead version.
High mileage, durable and fast rolling tyre.
Duraskin® cut-resistant layer from bead to bead.
180 thread per inch casing with Kevlar-reinforced layer directly under the tread.
Four widths for all requirements.
Quality German made natural rubber tread.
We recommend Continental inner tubes which are available in a range of relevant sizes.
The Continental Gatorskin made into into our top eight autumn, winter and wet weather tyres. Read here.
Continental supplies tyres to a large percentage of the UCI World Tour teams as well as several UK-based UCI Continental teams. Continental is the only bicycle tyre manufacturer in Germany and one of the last major bicycle tyre manufacturers in Europe. Over 100 years of experience in the manufacturing of bicycle tyres has made Continental into the unique, outstanding company that it is today.
Great tyre and good value.
I use these for my commuterbike. Good puncture resistance and good grip in Most circumstances. For the discount price this was a no brainer.
Continental tyres are the favorites anyway, but with BF prices its definitely best buy!
Very Happy. Great everyday tyre. Easy store collection.


Have you ever thought about having your Mercedes serviced or repaired in Germany? In our experience, shop prices in Scandinavia can make this a cost-effective solution. Some customers have even been able to finance their trip with the money they saved.
Enjoy your vacation in Berlin and bring your Mercedes to us. We are confident you will enjoy our city along with our service and our prices.
If you would like any assistance or advice for your stay in Berlin, we will be happy to help.


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IKARIA nominated for 3 Awards!!
I am so thrilled and honored. IKARIA, my latest book, has been nominated for three awards this year: It's a nominee for the "Books for a Better Life Award," by the MS Foundation; it's been long-listed on the Art of Eating Book of the Year award; and, most recently, IKARIA is up for an IACP award in the International Category . I think this is a sign. People are really interested in living better, simpler lives and …
I am so thrilled and honored. IKARIA, my latest book, has been nominated for three awards this year: It's a nominee for the "Books for a Better Life Award," by the MS Foundation; it's been long-listed on the Art of Eating Book of the Year award; and, most recently, IKARIA is up for an IACP award in the International Category.
I think this is a sign. People are really interested in living better, simpler lives and learning to eat a more plant-based diet, like those 103 year old Ikarians who flourished on a diet of weeds and mushrooms in the early part of their lives, when the island experienced extreme poverty and hardship.