  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.
