Multiple Quantum Phases in Graphene with Enhanced Spin-Orbit Coupling: From the Quantum Spin Hall Regime to the Spin Hall Effect and a Robust Metallic State

TL;DR

This study explores the transition from quantum spin Hall to spin Hall effects in graphene with thallium adatoms, revealing how adatom clustering affects topological states and leads to a robust metallic phase with spin accumulation.

Contribution

It demonstrates the impact of adatom segregation on topological phases in graphene and uncovers a stable metallic state with spin accumulation driven by spin-dependent scattering.

Findings

Adatom clustering diminishes the quantum spin Hall phase.

Spin accumulation occurs at sample edges due to spin-dependent scattering.

Bulk conductivity stabilizes around 4e^2/h, unaffected by localization.

Abstract

We report an intriguing transition from the quantum spin Hall phase to the spin Hall effect upon segregation of thallium adatoms adsorbed onto a graphene surface. Landauer-B\"uttiker and Kubo-Greenwood simulations are used to access both edge and bulk transport physics in disordered thallium-functionalized graphene systems of realistic sizes. Our findings not only quantify the detrimental effects of adatom clustering in the formation of the topological state, but also provide evidence for the emergence of spin accumulation at opposite sample edges driven by spin-dependent scattering induced by thallium islands, which eventually results in a minimum bulk conductivity $\sim 4e^{2}/h$, insensitive to localization effects.