Berry Curvature in Graphene: A New Approach

TL;DR

This paper introduces a new method to compute Berry curvature in graphene with inhomogeneous lattice distortions, revealing a valley-Hall effect analogous to spin-Hall phenomena in semiconductors.

Contribution

It presents a generalized framework for calculating Berry curvature in graphene under lattice distortions, linking valley-orbit coupling to the valley-Hall effect, extending previous homogeneous distortion results.

Findings

Inhomogeneous lattice distortions induce valley-orbit coupling.

The approach generalizes previous Berry curvature results for homogeneous distortions.

Identifies a valley-Hall effect similar to spin-Hall effect in semiconductors.

Abstract

In the present paper we have directly computed the Berry curvature terms relevant for Graphene in the presence of an \textit{inhomogeneous} lattice distortion. We have employed the generalized Foldy Wouthuysen framework, developed by some of us \cite{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 \cite{niu2} and is the analogue of the spin-Hall effect in semiconductors \cite{MURAKAMI, SINOVA}. Our general expressions for Berry curvature, for the special case of homogeneous distortion, reduce to the previously obtained results \cite{niu2}. We also discuss the Berry phase in the quantization of cyclotron motion.