On the Verdet constant and Faraday rotation for graphene-like materials

TL;DR

This paper provides a rigorous analysis of the Verdet constant in graphene-like materials using magnetic perturbation theory, resulting in an explicit formula valid across temperatures and frequencies, and reveals symmetry properties of the conductivity tensor.

Contribution

It introduces a gauge-invariant perturbation approach to compute the Verdet constant and uncovers symmetry properties of the conductivity tensor in graphene models.

Findings

Explicit formula for the Verdet constant at all temperatures and frequencies.

The transverse conductivity tensor's even-power coefficients vanish asymptotically.

The analysis applies to a standard nearest-neighbor tight-binding model of graphene.

Abstract

We present a rigorous and rather self-contained analysis of the Verdet constant in graphene- like materials. We apply the gauge-invariant magnetic perturbation theory to a nearest- neighbour tight-binding model and obtain a relatively simple and exactly computable formula for the Verdet constant, at all temperatures and all frequencies of sufficiently large absolute value. Moreover, for the standard nearest neighbour tight-binding model of graphene we show that the transverse component of the conductivity tensor has an asymptotic Taylor expansion in the external magnetic field where all the coefficients of even powers are zero.