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The anomalous Hall effect (AHE) is a consequence of spin-orbit coupling in aferromagnetic metal and is related primarily to density-matrix response to anelectric field that is off-diagonal in band index. For this reason disordercontributions to the AHE are difficult to treat systematically using asemi-classical Boltzmann equation approach, even when weak localizationcorrections are disregarded. In this article we explicitly demonstrate theequivalence of an appropriately modified semiclassical transport theory whichincludes anomalous velocity and side jump contributions and microscopicKubo-Streda perturbation theory, with particular unconventional contributionsin the semiclassical theory identified with particular Feynman diagrams whencalculations are carried out in a band-eigenstate representation. Theequivalence we establish is verified by explcit calculations for the case ofthe two-dimensional (2D) Dirac model Hamiltonian relevant to graphene.Comment: 17 pages, 13 figure

Anomalous Hall effect in a two-dimensional Dirac band: The link between the Kubo-Streda formula and the semiclassical Boltzmann equation approach