Graphene with Structure-Induced Spin-Orbit Coupling: Spin-Polarized States, Spin Zero Modes, and Quantum Hall Effect

TL;DR

This paper explores how structure-induced spin-orbit coupling in graphene leads to unique spin-polarized states, zero modes in magnetic fields, and an unconventional quantum Hall effect, revealing new magnetic and electronic phenomena.

Contribution

It demonstrates that eigenstates in spin-orbit coupled graphene are in-plane polarized with zero polarization at zero momentum, and uncovers novel zero modes and quantum Hall effects under magnetic fields.

Findings

Eigenstates are in-plane polarized and vanish at zero momentum.

Two zero modes appear in the Landau level spectrum under magnetic field.

Unconventional quantum Hall effect observed in the system.

Abstract

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 perpendicular to electron momentum $\bf k$; the magnitude of spin polarization $\bf S$ vanishes when $k \to 0$. In a perpendicular magnetic field $\bf B$, $\bf S$ is parallel to $\bf B$, and two zero modes emerge in the Landau level spectrum. Singular $\bf B$-dependence of their magnetization suggests existence of a novel magnetic instability. They also manifest themselves in a new unconventional quantum Hall effect.