Relation Between the Spin Hall Conductivity and the Spin Chern Number for Dirac-like Systems

Abstract

A semiclassical formulation of the spin Hall effect for physical systems satisfying Dirac-like equation is introduced. We demonstrated that the main contribution to the spin Hall conductivity is given by the spin Chern number whether the spin is conserved or not at the quantum level. We illustrated the formulation within the Kane-Mele model of graphene in the absence and in the presence of the Rashba spin-orbit coupling term.

21 pages, minor corrections and ref added

References in corpus (4)

• Robustness of the Spin-Chern number
• Reply to Comment on "Berry phase correction to electron density of states in solids"
• Spin dynamics with non-abelian Berry gauge fields as a semiclassical constrained hamiltonian system
• A Semiclassical Formulation of the Chiral Magnetic Effect and Chiral Anomaly in Even d+1 Dimensions

Cited by in corpus (8)

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• Thin film of a topological insulator as a spin Hall insulator
• A Semiclassical Kinetic Theory of Dirac Particles and Thomas Precession
• Spin Currents of Charged Dirac Particles in Rotating Coordinates
• Bulk spin conductivity of three-dimensional topological insulator