Spin and valley dependent transport in a biased dice lattice

Abstract

We study the spin and valley-dependent transport in a spin-orbit coupled biased dice lattice. We find that the presence of a bias term and the spin-orbit interaction (SOI) give rise to the spin-split energy spectrum. The SOI couples the valley and the spin degrees of freedom, resulting in a spin and valley-resolved Berry curvature. We find a profound variation in the Berry curvature for different spin states around both valleys. The spin and valley Hall conductivities are calculated for various values of the bias term. We find the interplay between the bias term and SOI term leads to a quantum phase transition from a topological insulating phase to a trivial band insulating phase accompanied by the emergence of the valley Hall effect and the suppression of the spin Hall effect.