Generalized quantization condition in topological insulator

TL;DR

This paper derives a generalized, material-independent quantization condition for the topological magnetoelectric effect in topological insulators, enabling easier experimental verification through angle tuning rather than precise wavelength or thickness adjustments.

Contribution

It introduces $SL(2, Z)$ covariant expressions for Kerr and Faraday angles at oblique incidence, generalizing the quantization condition for topological insulators.

Findings

Derived a generalized quantization condition independent of material specifics.

Proposed an experimentally feasible optical setup tuning only the incidence angle.

Provided covariant formulas for Kerr and Faraday rotations at oblique angles.

Abstract

The topological magnetoelectric effect (TME) is the fundamental quantization effect for topological insulators in units of the fine structure constant $\alpha$. In [Phys. Rev. Lett. 105, 166803(2010)], a topological quantization condition of the TME is given under orthogonal incidence of the optical beam, in which the wave length of the light or the thickness of the TI film must be tuned to some commensurate values. This fine tuning is difficult to realize experimentally. In this article, we give manifestly $SL(2,\mathbb{Z})$ covariant expressions for Kerr and Faraday angles at oblique incidence at a topological insulator thick film. We obtain a generalized quantization condition independent of material details, and propose a more easily realizable optical experiment, in which only the incidence angle is tuned, to directly measure the topological quantization associated with the TME.