Unexpected phonon-transport properties of stanene among 2D group-IV materials from \textit{ab initio}

It has been argued that stanene has lowest lattice thermal conductivity among 2D group-IV materials because of largest atomic mass, weakest interatomic bonding, and enhanced ZA phonon scattering due to the breaking of an out-of-plane symmetry selection rule. However, we show that although the lattice thermal conductivity $\kappa$ for graphene, silicene and germanene decreases monotonically with decreasing Debye temperature, unexpected higher $\kappa$ is observed in stanene. By enforcing all the invariance conditions in 2D materials and including Ge $3d$ and Sn $4d$ electrons as valence electrons for germanene and stanene respectively, the lattice dynamics in these materials are accurately described. A large acoustic-optical gap and the bunching of the acoustic phonon branches significantly reduce phonon scattering in stanene, leading to higher thermal conductivity than germanene. The vibrational origin of the acoustic-optical gap can be attributed to the buckled structure. Interestingly, a buckled system has two competing influences on phonon transport: the breaking of the symmetry selection rule leads to reduced thermal conductivity, and the enlarging of the acoustic-optical gap results in enhanced thermal conductivity. The size dependence of thermal conductivity is investigated as well. In nanoribbons, the $\kappa$ of silicene, germanene and stanene is much less sensitive to size effect due to their short intrinsic phonon mean free paths. This work sheds light on the nature of phonon transport in buckled 2D materials.