A thermodynamic measure of the Magneto-electric coupling in the 3D topological insulator

TL;DR

This paper establishes a thermodynamic relationship linking the magneto-electric coupling in 3D topological insulators to the second derivative of bulk magnetization, enabling easier experimental measurement of this property.

Contribution

It derives a new formula connecting magneto-electric coupling to measurable magnetization derivatives, simplifying experimental access and clarifying disorder effects in 3D topological insulators.

Findings

Magneto-electric coupling relates to the second derivative of magnetization.

The formula is an analog of the Streda formula for Hall conductivity.

Disorder affects the response only through the density of states.

Abstract

We show that the magneto-electric coupling in 3D (strong) topological insulators is related to a second derivative of the bulk magnetization. The formula we derive is the non-linear response analog of the Streda formula for Hall conductivity (P. Streda, J. Phys. C: Solid State Physics, 15, 22 (1982)), which relates the Hall conductivity to the derivative of the magnetization with respect to chemical potential. Our finding allows one to extract the magneto-electric coefficient by measuring the magnetization, while varying the chemical potential and one more perturbing field. Such an experimental setup could circumvent many of the current difficulties with measuring the magneto-electric response in 3D topological insulators. The relation we find also makes transparent the effect of disorder on the magneto-electric response, which occurs only through the density of states, and has no effect when the system is gapped.