Prediction of topological Nernst effect in silicene and similar 2D materials

We consider Berry phase mediated Nernst effect in silicene. The low energy band structure of silicene consists of two valleys near the Dirac points, similar to graphene. The low energy transport properties of the quasiparticles can be described as Berry phase dependent phenomena. By contrast to graphene, silicene has strong spin-orbit interaction leading to opening of the gap in the energy spectrum and spin-splitting of the bands in each valley. If an electric field is applied perpendicular to the silicene sheet, it allows tunability of the gap. \ We show that this results in Berry-phase-supported spin and valley polarized Nernst effect when the system is subjected to a temperature gradient. The Nernst response can be used to create valley and spin polarization at the transverse edges of silicene sheet. The applied electric field also allows control of valley and spin polarization in silicene. The predicted valley and spin polarized Nernst effect in silicene is more general and applies to other two-dimensional (2D) buckled Dirac Fermion systems such as 2D germanium and tin.