Twist-angle dependent proximity induced spin-orbit coupling in graphene/transition-metal dichalcogenide heterostructures

TL;DR

This study explores how the twist angle in graphene/TMDC heterostructures influences proximity-induced spin-orbit coupling, revealing key strain effects and the dependence of coupling magnitudes on twist angle and electric fields.

Contribution

It provides a first-principles analysis of twist-angle and strain effects on spin-orbit coupling in graphene/TMDC heterostructures, introducing a method to extract coupling parameters from corrected band structures.

Findings

Spin-orbit couplings are relatively insensitive to twist angle, except at specific angles like 30° and around 20° for Mo-based stacks.

Strain linearly affects band offsets, enabling correction for strain effects in the analysis.

Rashba coupling is generally weaker than valley-Zeeman coupling, but varies with twist angle and electric field.

Abstract

We investigate the proximity-induced spin-orbit coupling in heterostructures of twisted graphene and monolayers of transition-metal dichalcogenides (TMDCs) MoS$_2$, WS$_2$, MoSe$_2$, and WSe$_2$ from first principles. We identify strain, which is necessary to define commensurate supercells, as the key factor affecting the band offsets and thus magnitudes of the proximity couplings. We establish that for biaxially strained graphene the band offsets between the Dirac point and conduction (valence) TMDC bands vary linearly with strain, regardless of the twist angle. This relation allows to identify the apparent zero-strain band offsets and find a compensating transverse electric field correcting for the strain. The resulting corrected band structure is then fitted around the Dirac point to an established spin-orbit Hamiltonian. This procedure yields the dominant, valley-Zeeman and Rashba spin-orbit couplings. The magnitudes of these couplings do not vary much with the twist angle, although the valley-Zeeman coupling vanishes for 30$^{\circ}$ and Mo-based heterostructures exhibit a maximum of the coupling at around 20$^{\circ}$. The maximum for W-based stacks is at 0$^{\circ}$. The Rashba coupling is in general weaker than the valley-Zeeman coupling, except at angles close to 30$^{\circ}$. We also identify the Rashba phase angle which measures the deviation of the in-plane spin texture from tangential, and find that this angle is very sensitive to the applied transverse electric field. We further discuss the reliability of the supercell approach with respect to atomic relaxation (rippling of graphene), relative lateral shifts of the atomic layers, and transverse electric field.