Twist-angle dependent proximity induced spin-orbit coupling in graphene/topological insulator heterostructures

TL;DR

This study investigates how twist angles in graphene/topological insulator heterostructures influence proximity-induced spin-orbit coupling, revealing angle-dependent SOC types, sign changes, and potential electrical tuning of SOC parameters.

Contribution

It provides a first-principles analysis of twist-angle dependent SOC in graphene/TI heterostructures, including effects of gating and structural variations.

Findings

Valley-Zeeman and Rashba SOC dominate at small twist angles

Sign change in valley-Zeeman SOC around 10°

Electrical tuning can invert Kane-Mele SOC sign

Abstract

The proximity-induced spin-orbit coupling (SOC) in heterostructures of twisted graphene and topological insulators (TIs) Bi$_2$Se$_3$ and Bi$_2$Te$_3$ is investigated from first principles. To build commensurate supercells, we strain graphene and correct thus resulting band offsets by applying a transverse electric field. We then fit the low-energy electronic spectrum to an effective Hamiltonian that comprises orbital and spin-orbit terms. For twist angles 0$^\circ\leq\Theta \lessapprox 20^\circ$, we find the dominant spin-orbit couplings to be of the valley-Zeeman and Rashba types, both a few meV strong. We also observe a sign change in the induced valley-Zeeman SOC at $\Theta\approx 10^\circ$. Additionally, the in-plane spin structure resulting from the Rashba SOC acquires a non-zero radial component, except at $0^\circ$ or $30^\circ$. At $30^\circ$ the graphene Dirac cone interacts directly with the TI surface state. We therefore explore this twist angle in more detail, studying the effects of gating, TI thicknesses, and lateral shifts on the SOC parameters. We find, in agreement with previous results, the emergence of the proximitized Kane-Mele SOC, with a change in sign possible by electrically tuning the Dirac cone within the TI bulk band gap.