Intrinsic anomalous, spin and valley Hall effects in ex-so-tic van-der-Waals structures

TL;DR

This paper investigates various Hall effects in a novel graphene-based van-der-Waals heterostructure, deriving analytical expressions for Hall conductivities and revealing conditions for quantized valley conductivity.

Contribution

It provides a theoretical analysis of anomalous, spin, valley, and valley spin Hall effects in a specific heterostructure, deriving analytical formulas for Hall conductivities based on an effective Hamiltonian.

Findings

Quantized valley conductivity depending on Fermi level and gate voltage.

Analytical expressions for Hall conductivities derived.

Identification of conditions for anomalous Hall effects.

Abstract

We consider the anomalous, spin, valley, and valley spin Hall effects in a pristine ex-so-tic graphene-based van-der-Waals (vdW) heterostructure consisting of a bilayer graphene (BLG) between semiconducting van-der-Waals material with strong SOC (e.g., WS$_2$) and ferromagnetic and insulating vdW material (e.g. Cr$_2$Ge$_2$Te$_6$). Reducing the effective Hamiltonian derived by Zollner et al [Phys. Rev. Lett. 125(19), 196402 (2020)] to low-energy states, and using the Green function formalism, we derived analytical results for the Hall conductivities as a function of the Fermi level and gate voltage. Depending on these parameters, we found quantized valley conductivity.