Geometric and nongeometric contributions to the surface anomalous Hall conductivity

Tomas Rauch, Thomas Olsen, David Vanderbilt, Ivo Souza

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A static electric field generates circulating currents at the surfaces of a magnetoelectric insulator. The anomalous Hall part of the surface conductivity tensor describing such bound currents can change by multiples of e(2)/h depending on the insulating surface preparation, and a bulk calculation does not fix its quantized part. To resolve this ambiguity, we develop a formalism for calculating the full surface anomalous Hall conductivity in a slab geometry. We identify a Berry-curvature term, closely related to the expression for the bulk anomalous Hall conductivity, whose value can change by quantized amounts by adjusting the surface Hamiltonian. In addition, the surface anomalous Hall conductivity contains a nongeometric part that does not depend on the surface preparation.
Original languageEnglish
Article number115108
JournalPhysical Review B
Issue number11
Number of pages9
Publication statusPublished - 2018


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