Topological phases in gated bilayer graphene: Effects of Rashba spin-orbit coupling and exchange field

TL;DR

This paper explores how Rashba spin-orbit coupling, interlayer potential difference, and exchange field influence the topological phases of bilayer graphene, revealing tunable phase transitions and various topological states.

Contribution

It provides a systematic analysis of topological phase transitions in bilayer graphene under multiple external influences, including the derivation of effective Hamiltonians and phase diagrams.

Findings

Identification of a $Z_2$ topological insulator phase in AB-stacked bilayer graphene.

Discovery of a quantum valley Hall phase under certain conditions.

Observation of a quantum anomalous Hall phase when exchange field is introduced.

Abstract

We present a systematic study on the influence of Rashba spin-orbit coupling, interlayer potential difference and exchange field on the topological properties of bilayer graphene. In the presence of only Rashba spin-orbit coupling and interlayer potential difference, the band gap opening due to broken out-of-plane inversion symmetry offers new possibilities of realizing tunable topological phase transitions by varying an external gate voltage. We find a two-dimensional $Z_2$ topological insulator phase and a quantum valley Hall phase in $AB$-stacked bilayer graphene and obtain their effective low-energy Hamiltonians near the Dirac points. For $AA$ stacking, we do not find any topological insulator phase in the presence of large Rashba spin-orbit coupling. When the exchange field is also turned on, the bilayer system exhibits a rich variety of topological phases including a quantum anomalous Hall phase, and we obtain the phase diagram as a function of the Rashba spin-orbit coupling, interlayer potential difference, and exchange field.