Graphene with structure-induced spin-orbit coupling: Spin-polarized states, spin zero modes, and quantum Hall effect

Spin splitting of the energy spectrum of single-layer graphene on Au/Ni(111) substrate has been recently reported. I show that eigenstates of spin-orbit coupled graphene are polarized in-plane and are perpendicular to electron momentum k; the magnitude of spin polarization S vanishes when k→0. In a perpendicular magnetic field B, S is parallel to B, and two zero modes emerge in the Landau level spectrum. Singular B dependence of their magnetization suggests existence of a new variety of magnetic instability. They also manifest themselves in a new variety of unconventional quantum Hall effect.