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

摘要

We report an intriguing transition from the quantum spin Hall phase to thespin Hall effect upon segregation of thallium adatoms adsorbed onto a graphenesurface. Landauer-B\"uttiker and Kubo-Greenwood simulations are used to accessboth edge and bulk transport physics in disordered thallium-functionalizedgraphene systems of realistic sizes. Our findings not only quantify thedetrimental effects of adatom clustering in the formation of the topologicalstate, but also provide evidence for the emergence of spin accumulation atopposite sample edges driven by spin-dependent scattering induced by thalliumislands, which eventually results in a minimum bulk conductivity $\sim4e^{2}/h$, insensitive to localization effects.