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

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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-Büttiker 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 ~4e2/h, insensitive to localization effects.
S. R. acknowledges the Spanish Ministry of Economy and Competitiveness for funding (MAT2012-33911), the Severo Ochoa Program (MINECO SEV-2013-0295), and the Secretaria de Universidades e Investigación del Departamento de Economía y Conocimiento de la Generalidad de Cataluña. The research leading to these results has received funding from the European Union Seventh Framework Programme under Grant Agreement No. 604391 Graphene Flagship.