Spin-orbit gap of graphene: First-principles calculations

TL;DR

This paper presents first-principles calculations showing that graphene's spin-orbit interaction opens a very small energy gap, implying the quantum spin Hall effect in graphene would only occur at extremely low temperatures.

Contribution

The study provides the first ab initio calculation of the spin-orbit gap in graphene and explains its implications for the quantum spin Hall effect.

Findings

Spin-orbit gap in graphene is about 10^{-3} meV.

Quantum spin Hall effect in graphene is only feasible at very low temperatures.

Spin-orbit interaction in graphene is approximately 4 meV.

Abstract

Even though graphene is a low energy system consisting of the two dimensional honeycomb lattice of carbon atoms, its quasi-particle excitations are fully described by the 2+1 dimensional relativistic Dirac equation. In this paper we show that while the spin-orbit interaction in graphene is of the order of $4 meV$, it opens up a gap of the order of $10^{-3} meV$ at the Dirac points. We present the first principle calculation of the spin-orbit gap, and explain the behavior in terms of a simple tight-binding model. Our result also shows that the recently predicted quantum spin Hall effect in graphene can only occur at unrealistically low temperature.