Quantum Spin Hall Effect in Graphene

TL;DR

Graphene is converted from an ideal two-dimensional semimetallic state to a quantum spin Hall insulator and the spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder, and symmetry breaking fields are discussed.

Abstract

We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime the symmetry allowed spin orbit potential converts graphene from an ideal two dimensional semimetallic state to a quantum spin Hall insulator. This novel electronic state of matter is gapped in the bulk and supports the quantized transport of spin and charge in gapless edge states that propagate at the sample boundaries. The edge states are non chiral, but they are insensitive to disorder because their directionality is correlated with spin. The spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder and symmetry breaking fields are discussed.

Figures (3)

• Figure 1: (a) One dimensional energy bands for a strip of graphene (shown in inset) modeled by (7) with $t_2/t=.03$. The bands crossing the gap are spin filtered edge states.
• Figure 2: Schematic diagrams showing (a) two terminal and (b) four terminal measurement geometries. In (a) a charge current $I=(2e^2/h)V$ flows into the right lead. In (b) a spin current $I^s=(e/4\pi)V$ flows into the right lead. The diagrams to the right indicate the population of the edge states.
• Figure 3: Feynman diagram describing the renormalization of the SO potential by the Coulomb interaction. The solid line represents the electron propagator and the wavy line is the Coulomb interaction.