Competing topological phases in few-layer graphene

TL;DR

This paper explores how spin-orbit coupling influences topological phases in monolayer and bilayer graphene, revealing conditions for transitions between quantum Hall and quantum spin Hall states driven by gate voltage and symmetry breaking.

Contribution

It demonstrates that tuning Fermi level can induce topological phase transitions in monolayer graphene and identifies methods to realize quantum spin Hall phases in bilayer graphene through symmetry breaking.

Findings

Gate voltage can switch monolayer graphene between quantum Hall and quantum spin Hall phases.

Spin-orbit coupling alone does not induce topological phases in bilayer graphene.

Breaking layer inversion symmetry can enable topological phases in bilayer graphene.

Abstract

We investigate the effect of spin-orbit coupling on the band structure of graphene-based two-dimensional Dirac fermion gases in the quantum Hall regime. Taking monolayer graphene as our first candidate, we show that a quantum phase transition between two distinct topological states -- the quantum Hall and the quantum spin Hall phases -- can be driven by simply tuning the Fermi level with a gate voltage. This transition is characterized by the existence of a chiral spin-polarized edge state propagating along the interface separating the two topological phases. We then apply our analysis to the more difficult case of bilayer graphene. Unlike in monolayer graphene, spin-orbit coupling by itself has indeed been predicted to be unsuccessful in driving bilayer graphene into a topological phase, due to the existence of an even number of pairs of spin-polarized edge states. While we show that this remains the case in the quantum Hall regime, we point out that by additionally breaking the layer inversion symmetry, a non-trivial quantum spin Hall phase can re-emerge in bilayer graphene at low energy. We consider two different symmetry-breaking mechanisms: inducing spin-orbit coupling only in the upper layer, and applying a perpendicular electric field. In both cases, the presence at low energy of an odd number of pairs of edge states can be driven by an exchange field. The related situation in trilayer graphene is also discussed.