https://doi.org/10.1140/epjc/s10052-008-0839-4
Regular Article - Theoretical Physics
Berry curvature in graphene: a new approach
1
Institut Fourier, UMR 5582 CNRS-UJF, UFR de Mathématiques, Université Grenoble I, BP74, 38402, Saint Martin d’Hères Cedex, France
2
Laboratoire de Physique Moléculaire et des Collisions, ICPMB-FR CNRS 2843, Université Paul Verlaine-Metz, 57078, Metz Cedex 3, France
3
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Calcutta, 700108, India
* e-mail: subir_ghosh2@rediffmail.com
Received:
30
September
2008
Revised:
10
November
2008
Published online:
9
January
2009
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. We show that a non-constant lattice distortion leads to a valley–orbit coupling which is responsible for a valley–Hall effect. This is similar to the valley–Hall effect induced by an electric field proposed in the literature and is the analogue of the spin–Hall effect in semiconductors. Our general expressions for Berry curvature, for the special case of homogeneous distortion, reduce to the previously obtained results. We also discuss the Berry phase in the quantization of cyclotron motion.
© Springer-Verlag , 2009
