Chiral Bloch states in single layer graphene with Rashba spin-orbit coupling: Spectrum and spin current density

TL;DR

This paper investigates the unique electronic and spin transport properties of single-layer graphene with Rashba spin-orbit coupling under a periodic potential, revealing novel band structures and spin current behaviors.

Contribution

It uncovers the existence of two Dirac points and finite spin current densities with perpendicular polarization, advancing understanding of graphene spintronics with spin-orbit effects.

Findings

Two Dirac points at non-zero momenta in the band structure

Finite off-diagonal spin current density components increase with spin-orbit strength

Space-dependent spin currents with associated spin torque densities

Abstract

We study the Bloch spectrum and spin physics of 2D massless Dirac electrons in single layer graphene subject to a one dimensional periodic Kronig-Penney potential and Rashba spin-orbit coupling. The Klein paradox exposes novel features in the band dispersion and in graphene spintronics. In particular it is shown that: (1) The Bloch energy dispersion $\veps(p)$ has unusual structure: There are {\it two Dirac points} at Bloch momenta $\pm p \ne 0$ and a narrow band emerges between the wide valence and conduction bands. (2) The charge current and the spin density vector vanish. (3) Yet, all the non-diagonal elements of the spin current density tensor are finite and their magnitude increases linearly with the spin-orbit strength. In particular, there is a spin density current whose polarization is perpendicular to the graphene plane. (4) The spin density currents are space-dependent, hence their continuity equation includes a finite spin torque density.