Optical response and nonlinear Hall response of twisted bilayer graphene in the insulating state

TL;DR

This paper investigates the optical and nonlinear Hall responses of various insulating states in twisted bilayer graphene, providing theoretical predictions to distinguish these states through spectroscopy and transport experiments.

Contribution

It introduces a detailed calculation of optical and nonlinear Hall responses for multiple insulating states in twisted bilayer graphene, offering a method to identify these states experimentally.

Findings

Spin-valley polarized state shows a two-peak optical conductivity.

Berry curvature dipole varies with chemical potential for different states.

Results can help determine the insulating state in TBG experimentally.

Abstract

In this work, we calculate the optical response and the nonlinear Hall response of twisted bilayer graphene (TBG) in the insulating states. Different insulating states, including spin-valley polarized (SPVP) state, spin-polarized quantum Hall(SPQH) state, spin-polarized valley Hall (SPVH) state, and spin polarized Kramers-intervalley coherence (SPKIVC) state, are considered. We calculate the optical conductivity ($\sigma_{xx}$) of these four states and we find that the spin-valley polarized state shows a two-peak feature which is different from the other three states. In order to distinguish the other three states, we calculate the nonlinear Hall response which is proportional to Berry curvature dipole, and we find the chemical potential dependence of the Berry curvature dipole can distinguish these three states. Our result can be tested in the spectroscopy and transport experiments and may be helpful to determine the nature of insulating state in TBG.