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Coordinate shift in the semiclassical Boltzmann equation and the anomalous Hall effect

N. A. Sinitsyn·Q. Niu·A. H. MacDonald
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Abstract

We propose a gauge invariant expression for the side jump associated with scattering between particular Bloch states. Our expression for the side jump follows from the Born series expansion for the scattering T-matrix in powers of the strength of the scattering potential. Given our gauge invariant side jump expression, it is possible to construct a semiclassical Boltzmann theory of the anomalous Hall effect which expresses all previously identified contributions in terms of gauge invariant quantities and does not refer explicitly to off-diagonal terms in the density-matrix response.

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N. A. Sinitsyn, Q. Niu, A. H. MacDonald. 2006-01-27. Coordinate shift in the semiclassical Boltzmann equation and the anomalous Hall effect. https://doi.org/10.1103/physrevb.73.075318

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