The origin of diverse lattice dynamics in the graphene family

We explore the lattice dynamics of the members of the graphene family from first principles. We
calculate the lattice thermal conductivity of the sheets by modelling their phonon lifetimes from the
group velocity, Gruneisen parameter, and Debye temperature of their acoustic phonon modes using
the Debye Callaway formalism modified for solids. The formalism underestimates the lattice thermal
conductivity of graphene, while successfully applies to low and double buckled silicene, germanene,
and stanene. In case of the latter, the buckling offers a definite third dimension, making them ideal
test cases for the formalism. The lattice thermal conductivity of the low buckled sheets is found to
be orders of magnitude lower than graphene. Double buckled germanene and stanene are calculated
to have ultralow lattice thermal conductivity. We use different geometries of the low and double buckled
sheets to elucidate on the role of buckling on lowering of the group velocity and Debye temperature
of the acoustic phonon modes.