Anomalous Hall effect, magneto-optical properties, and nonlinear optical properties of twisted graphene systems

Jianpeng Liu,Xi Dai

doi:10.1038/s41524-020-0299-4

Abstract

We study the anomalous Hall effect, magneto-optical properties, and nonlinear optical properties of twisted bilayer graphene aligned with hexagonal boron nitride substrate, as well as twisted double bilayer graphene systems. We show that non-vanishing valley polarizations in twisted graphene systems would give rise to the anomalous Hall effect, which can be tuned by in-plane magnetic fields. The valley polarized states are also associated with giant Faraday and Kerr rotations in the terahertz frequency regime. Moreover, we propose that the twisted graphene systems exhibit colossal nonlinear optical responses by virtue of the inversion-symmetry breaking, the small bandwidth, and the small excitation gaps of the systems. In twisted double bilayer graphene, we find that certain components of the nonlinear photo-conductivity tensor are directly proportional to the orbital magnetization of the system, which would exhibit remarkable hysteresis behavior in response to perpendicular magnetic fields.

Highlights

Twisted bilayer graphene (TBG) has drawn significant attention recently due to the observations of the correlated insulating phases, anomalous Hall effect, and unconventional superconductivity[1,2,3,4,5,6,7,8,9,10]
We have studied the dependence of anomalous Hall conductivity (AHC) on the valley and spin splittings in hexagonal boron nitride (hBN)-aligned TBG, and found that the anomalous Hall effect (AHE) can be engineered using in-plane magnetic npj Computational Materials (2020) 57
In additional to AHE, we show that there exists giant magneto-optical effect by virtue of the valley-symmetry breaking and orbital magnetizations

Summary

INTRODUCTION

Twisted bilayer graphene (TBG) has drawn significant attention recently due to the observations of the correlated insulating phases, anomalous Hall effect, and unconventional superconductivity[1,2,3,4,5,6,7,8,9,10]. The orbital ferromagnetic states are believed to exist in TBG aligned with hBN substrate[4,9,35], in which (quantum) anomalous Hall effect has been observed at 3/4 filling of the flat bands around the magic angle[4,10]. It is intriguing to ask whether the orbital magnetization and valley polarization in hBN-aligned TBG and TDBG can be probed by nonlinear optical responses. We study the nonlinear optical responses such as the shift current and second harmonic generation (SHG) in hBN-aligned TBG and TDBG. We find that both systems exhibit colossal nonlinear optical responses by virtue of the small bandwidths and the small excitation gaps of the twisted graphene systems. Nonlinear photoconductivities that are generated and/or enhanced by the orbital magnetizations may be considered as where Ev and Es are positive real numbers denoting the valley and spin splittings, and μ 1⁄4 ±1 and s 1⁄4 ±1 represent the valley and strong experimental evidence for the valley polarization and orbital ferromagnetism in the twisted graphene systems

RESULTS

DISCUSSION

METHODS

CODE AVAILABILITY