Berry Curvature in Graphene: a New Approach

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 [4, 5]. Our general expressions for Berry curvature, for the special case of homogeneous distortion, reduce to the previously obtained results [13]. We propose some new phenomena, termed in the present paper as ”valley-Hall” effect, (in analogy to spin-Hall effect [14]), which can arise intrinsically due to the non-constant lattice distortion. The Hamiltonian dynamics is studied in detail where the Berry curvature terms in the effective non-commutative algebra modify the dynamics by generating anomalous velocity contributions.