Geometric and nongeometric contributions to the surface anomalous Hall conductivity

Abstract

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.

arXiv comment10 pages, 4 figures

References in corpus (13)

• Berry Phase Effects on Electronic Properties
• Maximally-localized generalized Wannier functions for composite energy bands
• Topological Field Theory of Time-Reversal Invariant Insulators
• Higher-Order Topological Insulators
• Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
• Mapping topological order in coordinate space
• Orbital magnetoelectric coupling in band insulators
• Theory of orbital magnetoelectric response
• Topological insulators in magnetic fields: Quantum Hall effect and edge channels with non-quantized θ-term
• Chern-Simons orbital magnetoelectric coupling in generic insulators
• Surface theorem for the Chern-Simons axion coupling
• Locality of the anomalous Hall conductivity
• Adiabatic Pumping of Chern-Simons Axion Coupling

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