Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach

Abstract

The anomalous Hall effect (AHE) is a consequence of spin-orbit coupling in a ferromagnetic metal and is related primarily to density-matrix response to an electric field that is off-diagonal in band index. For this reason disorder contributions to the AHE are difficult to treat systematically using a semi-classical Boltzmann equation approach, even when weak localization corrections are disregarded. In this article we explicitly demonstrate the equivalence of an appropriately modified semiclassical transport theory which includes anomalous velocity and side jump contributions and microscopic Kubo-Streda perturbation theory, with particular unconventional contributions in the semiclassical theory identified with particular Feynman diagrams when calculations are carried out in a band-eigenstate representation. The equivalence we establish is verified by explcit calculations for the case of the two-dimensional (2D) Dirac model Hamiltonian relevant to graphene.

17 pages, 13 figures

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• Semiclassical framework for the calculation of transport anisotropies
• Intrinsic anomalous Hall effect in ferromagnetic metals studied by the multi d-orbital tight-binding model
• Transport theory for disordered multiple-band systems: Anomalous Hall effect and anisotropic magnetoresistance
• Anomalous Hall Effect in $t_{2g}$ Orbital Kagome Lattice due to Non-collinearity:Significance of Orbital Aharonov-Bohm Effect
• Disorder and temperature dependence of the Anomalous Hall Effect in thin ferromagnetic films: Microscopic model
• Anomalous Hall effect in a two dimensional electron gas with magnetic impurities
• On the nature of steady states of spin distributions in the presence of spin-orbit interactions
• Hybrid skew scattering regime of the anomalous Hall effect in Rashba systems: unifying Keldysh, Boltzmann, and Kubo formalisms
• Spin-Hall conductivity of a spin-polarized two-dimensional electron gas with Rashba spin-orbit interaction and magnetic impurities
• Theory of AC Anomalous Hall Conductivity in d-electron systems