Proc. Natl Acad. Sci. USA http://doi.org/bzn6 (2017)
When graphene hit the condensed-matter scene in 2004, many a (theoretical) physicist got confused. Didn't the celebrated Mermin–Wagner theorem, penned nearly 40 years earlier, implicate that 2D crystals cannot exist? Subtleties surround this apparent paradox, but the theorem does imply that in two dimensions, at finite temperature, long-wavelength density fluctuations lead to particle displacements that grow logarithmically with distance. In graphene's case, phonons save the day, because they mediate long-range density fluctuations.
Bernd Illing and colleagues have now contemplated Mermin–Wagner fluctuations in 2D amorphous solids. A comparison of experimental structural data from 2D and 3D colloidal crystalline and glassy systems with simulations of 2D crystals enabled the authors to make a series of noteworthy conclusions.
After confirming that the fluctuations do occur in 2D glasses, and hence that periodicity is not a requirement, Illing et al. showed that they provide a channel for structural decay — a situation different from the 3D case. The presence of Mermin–Wagner fluctuations does not, however, lead to different microscopic glass transition mechanisms for 2D and 3D systems.
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Verberck, B. 2D materials: Amorphous and fluctuating. Nature Phys 13, 205 (2017). https://doi.org/10.1038/nphys4065