Orbital magnetoelectric coupling at finite electric field

TL;DR

This paper extends the theory of orbital magnetoelectric coupling to finite electric fields, showing that the total response remains unchanged despite individual contributions being modified, confirmed by numerical tests.

Contribution

It provides a modified theoretical framework for orbital magnetoelectric coupling under finite electric fields, maintaining the zero-field formula through cancellation of correction terms.

Findings

Correction terms are modified by electric field but sum to zero.

Total magnetoelectric response remains consistent with zero-field formula.

Numerical tests confirm theoretical predictions.

Abstract

We extend the band theory of linear orbital magnetoelectric coupling to treat crystals under finite electric fields. Previous work established that the orbital magnetoelectric response of a generic insulator at zero field comprises three contributions that were denoted as local circulation, itinerant circulation, and Chern-Simons. We find that the expression for each of them is modified by the presence of a dc electric field. Remarkably, the sum of the three correction terms vanishes, so that the total coupling is still given by the same formula as at zero field. This conclusion is confirmed by numerical tests on a tight-binding model, for which we calculate the field-induced change in the linear magnetoelectric coefficient.