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

## TL;DR

This paper investigates the anomalous Hall effect, magneto-optical, and nonlinear optical properties of twisted graphene systems, revealing tunable valley polarization effects, giant Faraday/Kerr rotations, and colossal nonlinear responses driven by symmetry breaking and small gaps.

## Contribution

It provides a comprehensive analysis of the nonlinear optical responses and magneto-optical effects in twisted graphene systems, highlighting the role of valley polarization and orbital magnetization.

## Key findings

- Valley polarization induces anomalous Hall effect tunable by magnetic fields.
- Giant Faraday/Kerr rotations observed in terahertz regime.
- Colossal nonlinear optical responses with specific tensor components linked to magnetization.

## Abstract

We study the anomalous Hall effect, magneto-optical properties, and nonlinear optical properties of twisted bilayer graphene (TBG) aligned with hexagonal boron nitride (hBN) substrate as well as twisted double bilayer graphene systems. We show that non-vanishing valley polarizations in twisted graphene systems would give rise to anomalous Hall effect which can be tuned by in-plane magnetic fields. The valley polarized states are also associated with giant Faraday/Kerr rotations in the terahertz frequency regime. Moreover, both hBN-aligned TBG and TDBG exhibit colossal nonlinear optical responses by virtue of the inversion-symmetry breaking, the small bandwidth, and the small excitation gaps of the systems. Our calculations indicate that in both systems the nonlinear optical conductivities of the shift currents are on the order of $10^3\,\mu$A/V$^2$; and the second harmonic generation (SHG) susceptibilities are on the order of $10^6\,$pm/V in the terahertz frequency regime. Moreover, in TDBG with $AB\textrm{-}BA$ stacking, we find that a finite orbital magnetization would generate a new component $\sigma^{x}_{xx} $ of the nonlinear photoconductivity tensor; while in $AB$-$AB$ stacked TDBG with vertical electric fields, the valley polarization and orbital magnetization would make significant contributions to the $\sigma^{y}_{xx}$ component of the photoconductivity tensor. These nonlinear photo-conductivities are proportional to the orbital magnetizations of the systems, thus they are expected to exhibit hysteresis behavior in response to out-of-plane magnetic fields.