Berry Curvature in Graphene: A New Approach
Abstract
In the present paper we have directly computed the Berry curvature terms relevant for Graphene in the presence of an inhomogeneous lattice distortion. We have employed the generalized Foldy Wouthuysen framework, developed by some of us ber0,ber1,ber2. We show that a non-constant lattice distortion leads to a valley-orbit coupling which is responsible to a valley-Hall effect. This is similar to the valley-Hall effect induced by an electric field proposed in niu2 and is the analogue of the spin-Hall effect in semiconductors MURAKAMI, SINOVA. Our general expressions for Berry curvature, for the special case of homogeneous distortion, reduce to the previously obtained results niu2. We also discuss the Berry phase in the quantization of cyclotron motion.