# Twist-angle dependence of the proximity spin-orbit coupling in graphene on transition-metal dichalcogenides

## TL;DR

This paper theoretically investigates how the twist angle between graphene and transition-metal dichalcogenides affects proximity-induced spin-orbit coupling, revealing significant enhancement and tunability of spin splitting with potential for twist-angle engineering.

## Contribution

It introduces a theoretical method applicable to incommensurate bilayers, demonstrating twist-angle control over spin-orbit coupling in graphene on TMDCs.

## Key findings

- Spin splitting is enhanced by a factor of 3-10 with twist angles.
- Maximum spin splitting occurs around 20° twist angle.
- The type of SOC can be switched from Zeeman to Rashba by rotation.

## Abstract

We theoretically study the proximity spin-orbit coupling in graphene on transition-metal dichalcogenides monolayer stacked with arbitrary twist angles. We find that the relative rotation greatly enhances the spin splitting of graphene, typically by a few to ten times compared to the non-rotated geometry,and the maximum splitting is achieved around $20^\circ$. The induced SOC can be changed from the Zeeman-type to the Rashba-type by rotation. The spin-splitting is also quite sensitive to the gate-induced potential, and it sharply rises when the graphene's Dirac point is shifted toward the TMDC band. The theoretical method does not need the exact lattice matching and it is applicable to any incommensurate bilayer systems. It is useful for the twist-angle engineering of a variety of van der Waals proximity effects.