Physically founded phonon dispersions of few-layer materials, and the   case of borophene
  An increasing number of theoretical calculations on few-layer materials have been reporting a non-zero sound velocity for all three acoustic phonon modes. In contrast with these reports, here we show that the lowest phonon dispersion branch of atomistically described few-layer materials should be quadratic, and this can have dramatic consequencies on calculated properties, such as the thermal conductivity. By reformulating the interatomic force constants (IFC) in terms of internal coordinates, we find that a delicate balance between the IFCs is responsible for this quadraticity. This balance is hard to obtain in ab-initio calculations even if all the symmetries are numerically enforced a posteriori, but it arises naturally in our approach. We demonstrate the phenomenon in the case of borophene, where a very subtle correction to the ab-initio IFCs yields the physically correct quadratic dispersion, while leaving the rest of the spectrum virtually unmodified. Such quadraticity nevertheless has a major effect on the computed lattice thermal conductivity, which in the case of borophene changes by more than a factor 2, and reverses its anisotropy, when the subtle IFC correction is put in place. 
Jes\'us Carrete, Wu Li, Lucas Lindsay, David A. Broido, Luis J.   Gallego and Natalio Mingo
cond-mat.mtrl-sci