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 \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.

Slightly modified version, to appear in EPJC

References in corpus (21)

• Electric Field Effect in Atomically Thin Carbon Films
• Valley contrasting physics in graphene: magnetic moment and topological transport
• Quantum Spin Hall Effect
• Universal Intrinsic Spin-Hall Effect
• Dissipationless Quantum Spin Current at Room Temperature
• Berry phase correction to electron density of states in solids
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3
• Efficient $\mathcal{O}(N^2)$ approach to solve the Bethe-Salpeter equation for excitonic bound states
• Spontaneous parity breaking of graphene in the quantum Hall regime
• Spin Hall effect and Berry phase of spinning particles
• Spin Hall effect of Photons in a Static Gravitational Field
• Topological spin transport of relativistic electron
• Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects
• Monopole and Berry Phase in Momentum Space in Noncommutative Quantum Mechanics
• Semiclassical Diagonalization of Quantum Hamiltonian and Equations of Motion with Berry Phase Corrections
• Semiclassical Dynamics of Electrons in Magnetic Bloch Bands: a Hamiltonian Approach
• Comment on "Berry phase correction to electron density in solids" by Xiao et al
• Semiclassical Dynamics of Dirac particles interacting with a Static Gravitational Field
• On the Hamiltonian nature of semiclassical equations of motion in the presence of an electromagnetic field and Berry curvature
• Recursive Diagonalization of Quantum Hamiltonians to all order in $\hslash$

Cited by in corpus (14)

• Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models
• Topics in Noncommutative Geometry Inspired Physics
• Graphene quantum dots for valley-based quantum computing: A feasibility study
• Graphene-based qubits in quantum communications
• Comparative analysis of direct and "step-by-step" Foldy-Wouthuysen transformation methods
• Exact form of the exponential Foldy-Wouthuysen transformation operator for an arbitrary-spin particle
• A Noncommutative Space Approach to Confined Dirac Fermions in Graphene
• Kinetic theory of spin-polarized systems in electric and magnetic fields with spin-orbit coupling: I. Kinetic equation and anomalous Hall and spin-Hall effects
• Relativistic quantum mechanics of a Proca particle in Riemannian spacetimes
• Non-relativistic expansion of single-nucleon Dirac equation: Comparison between Foldy-Wouthuysen transformation and similarity renormalization group
• Tunneling in the Brillouin Zone: Theory of Backscattering in Valley Hall Edge Channels
• Electrical valley filtering in transition metal dichalcogenides
• All-electrical valley filtering in graphene systems (I): A path to integrated electro-valleytronics
• All-electrical valley filtering in graphene systems (II): Numerical study of electron transport in valley valves