Electrodynamics of Thin Sheets of Twisted Material

TL;DR

This paper develops a minimal theoretical framework to describe the optical activity of twisted thin materials like bilayer graphene, revealing phase-dependent behaviors of Faraday rotation and introducing the concept of twisted electrical conductivity.

Contribution

It introduces the notion of twisted electrical conductivity and analyzes the phase-dependent optical responses of twisted materials, including insulators, superconductors, and metals.

Findings

Faraday angle scales as ω^2 in insulators at low frequencies

In superconductors, Faraday rotation is constant below the gap

In metals, twisted conductivity relates to magnetic helicity of quasiparticles

Abstract

We construct a minimal theory describing the optical activity of a thin sheet of a twisted material, the simplest example of which is twisted bilayer graphene. We introduce the notion of "twisted electrical conductivity", which parametrizes the parity-odd response of a thin film to a perpendicularly falling electromagnetic waves with wavelength larger than the thickness of the sheet. We show that the low-frequency Faraday rotation angle has different behaviors in different phases. For an insulator, the Faraday angle behaves as $\omega^2$ at low frequencies, with the coefficient being determined by the linear relationship between a component of the electric quadrupole moment and the external electric field. For superconductors, the Faraday rotation angle is constant when the frequency of the incoming EM waves is below the superconducting gap and is determined by the coefficient of the Lifshitz invariant in the Ginzburg-Landau functional describing the superconducting state. In the metallic state, we show that the twisted conductivity is proportional to the "magnetic helicity" (scalar product of the velocity and the magnetic moment) of the quasiparticle, averaged around the Fermi surface. The theory is general and is applicable to strongly correlated phases.