# Proximity effects in bilayer graphene on monolayer WSe$_2$: Field-effect spin-valley locking, spin-orbit valve, and spin transistor

## TL;DR

This paper investigates how bilayer graphene on monolayer WSe2 exhibits tunable proximity-induced spin-orbit effects, enabling a field-effect spin transistor through electric field control of spin-valley locking.

## Contribution

It demonstrates the first-principles prediction of electric-field-controlled spin-valley locking and spin-orbit valve effects in bilayer graphene on WSe2, proposing a new spin transistor platform.

## Key findings

- Built-in electric field induces a 10 meV orbital band gap in bilayer graphene.
- Proximity spin-orbit splitting for holes is about 2 meV, much larger than for electrons.
- External electric field can reverse spin-valley locking, enabling a spin transistor.

## Abstract

Proximity orbital and spin-orbit effects of bilayer graphene on monolayer WSe$_2$ are investigated from first-principles. We find that the built-in electric field induces an orbital band gap of about 10 meV in bilayer graphene. Remarkably, the proximity spin-orbit splitting for holes is two orders of magnitude---the spin-orbit splitting of the valence band at K is about 2 meV---more than for electrons. Effectively, holes experience spin-valley locking due to the strong proximity of the lower graphene layer to WSe$_2$. However, applying an external transverse electric field of some 1 V/nm, countering the built-in field of the heterostructure, completely reverses this effect and allows, instead for holes, electrons to be spin-valley locked with 2 meV spin-orbit splitting. Such a behavior constitutes a highly efficient field-effect spin-orbit valve, making bilayer graphene on WSe$_2$ a potential platform for a field-effect spin transistor.