Tuning correlated states of twisted mono-bilayer graphene with proximity-induced spin-orbit coupling

TL;DR

This paper investigates how proximity-induced spin-orbit coupling influences the correlated and topological ground states of twisted mono-bilayer graphene, revealing SOC-dependent transitions in spin order and symmetry breaking.

Contribution

It introduces a comprehensive Hartree-Fock analysis of twisted mono-bilayer graphene with SOC, highlighting the impact of SOC on symmetry breaking and spin configurations at various fillings.

Findings

Interaction-induced insulators at integer fillings retain translational symmetry.

Small SOC significantly alters the spin nature of correlated states.

Different types of SOC induce distinct spin order transitions.

Abstract

We study the correlated ground states of twisted mono-bilayer graphene with and without proximity-induced spin-orbit coupling (SOC) from a transition-metal dichalcogenide layer placed on top. We perform self-consistent Hartree-Fock calculations that allow the variational space to include multi-$Q$ translational symmetry broken states for all integer and half-integer fillings of the conduction bands, where signatures of correlated, topological states have been reported experimentally. We find interaction-induced insulators that retain moir\'e translational symmetry at integer fillings, but that break this symmetry at half-integer fillings. We argue that translational symmetry breaking arises from half-filled polarized bands, even when SOC is present. Yet, we find that small SOC can already crucially affect the spin nature of correlated states. Generally, Ising SOC favors out-of-plane spin polarization and spin-valley locking, while Rashba SOC favors in-plane spin order. If only one of these two terms is present, we find that, depending on the type of SOC, it drives a transition from a tetrahedal antiferromagnet to either a coplanar, non-coplanar, or collinear spin-density wave state for half-integer fillings. The frustration associated with the simultaneous presence of both types of SOC can induce chiral, non-coplanar order in parameter ranges where the ground state in the absence of SOC is collinear.