Orbital magnetoelectric coupling in band insulators

TL;DR

This paper develops a comprehensive method to compute orbital contributions to the magnetoelectric response in band insulators, including topological insulators, revealing new insights into their fundamental electromagnetic properties.

Contribution

It introduces a novel approach to calculate orbital magnetoelectric coupling, including the Chern-Simons term, in materials with broken or preserved symmetries, expanding understanding beyond spin and lattice effects.

Findings

Orbital contributions can be computed using a new response formula.

The Chern-Simons term can be quantized in topological insulators.

Additional orbital effects vanish in certain symmetric or simplified models.

Abstract

Magnetoelectric responses are a fundamental characteristic of materials that break time-reversal and inversion symmetries (notably multiferroics) and, remarkably, of "topological insulators" in which those symmetries are unbroken. Previous work has shown how to compute spin and lattice contributions to the magnetoelectric tensor. Here we solve the problem of orbital contributions by computing the frozen-lattice electronic polarization induced by a magnetic field. One part of this response (the "Chern-Simons term") can appear even in time-reversal-symmetric materials and has been previously shown to be quantized in topological insulators. In general materials there are additional orbital contributions to all parts of the magnetoelectric tensor; these vanish in topological insulators by symmetry and also vanish in several simplified models without time-reversal and inversion those magnetoelectric couplings were studied before. We give two derivations of the response formula, one based on a uniform magnetic field and one based on extrapolation of a long-wavelength magnetic field, and discuss some of the consequences of this formula.