2008/02/29 by Pierre Gosselin, Alain Bérard, Hervé Mohrbach +1
Materials Science · Mathematics · Physics and Astronomy · #Berry connection and curvature #Condensed matter physics #Curvature #Distortion (music) #Electric field #Electron #Geometric phase #Geometry #Graphene #Graphene research and applications #Hall effect #Lattice (music) #Magnetic field #Mathematics #Physics #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Topological Materials and Phenomena #cond-mat.mes-hall #hep-th #quant-ph
paper · pdf · doi:10.1140/epjc/s10052-008-0839-4
Slightly modified version, to appear in EPJC
arxiv created 2008/11/24 · openalex publication_date 2009/01/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 \citeber0,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 \citeniu2 and is the analogue of the spin-Hall effect in semiconductors \citeMURAKAMI, SINOVA. Our general expressions for Berry curvature, for the special case of homogeneous distortion, reduce to the previously obtained results \citeniu2. We also discuss the Berry phase in the quantization of cyclotron motion.