Faraday rotation in bilayer and trilayer graphene in the quantum Hall regime

TL;DR

This paper theoretically investigates Faraday rotation in bilayer and trilayer graphene, revealing how band structure features like trigonal warping and stacking order influence optical Hall conductivity and resonance spectra.

Contribution

It provides a detailed theoretical analysis of Faraday rotation in multilayer graphene, highlighting the effects of band dispersion, warping, and stacking on optical responses.

Findings

Trigonal warping significantly affects resonance structures in bilayer graphene.

Distinct resonance spectra are identified for ABA and ABC trilayer graphene.

Low-energy Dirac cones produce observable signals due to large Lifshitz transition energy.

Abstract

Optical Hall conductivity, as directly related to Faraday rotation, is theoretically studied for bilayer and trilayer graphene. In bilayer graphene, the trigonal warping of the band dispersion greatly affects the resonance structures in Faraday rotation not only in the low-energy region where small Dirac cones emerge, but also in the higher-energy parabolic bands as a sequence of satellite resonances. In ABA-stacked trilayer, the resonance spectrum is a superposition of effective monolayer and bilayer contributions with band gaps, while ABC trilayer exhibits a distinct spectrum peculiar to the cubic-dispersed bands with a strong trigonal warping, where the signals associated with low-energy Dirac cones should be directly observable owing to a large Lifshitz transition energy ($\sim 10 meV$).