Phonons and lattice thermal conductivities of graphene family

In the post-graphene era, there has been a significant upsurge of interest on the mechanical and thermal properties of two dimensional graphene-like honeycomb structures made of other group-IV elements. This article deals with application of first principle based density functional theory to investigate the lattice dynamics of the members of this extended graphene family. We explore the changes observed in the lattice thermal conductivity, adopting physical models for estimating phonon lifetimes. We use the Asen-Palmer modified version of Debye-Callaway theory to calculate the lattice thermal conductivity of graphene, as well as of low and double buckled silicene, germanene, and stanene. This allows us to establish a connection between the parameters such as group velocity, Grüneisen parameter, and Debye temperature of the acoustic phonon modes and the lattice thermal conductivity. Our calculations show that the presence of buckling reduces the group velocity and the Debye temperature of the sheets down the group, and hence, reduces their lattice thermal conductivity. However, there is no linear dependence between the buckling height and the observed lowering. An increase in buckling height in sheets with different geometries of the same atomic species, beyond a certain limit, does not lead to change in the group velocity and the Debye temperature of the sheets.