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

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.

15 pages, 17figures, and 1 table

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• Interplay between Rashba interaction and electromagnetic field in the edge states of a 2D topological insulator
• Topological Corner States in Graphene by Bulk and Edge Engineering
• A new phenomenon in graphene: The pseudospinorial Zitterbewegung
• Topological phase transition from trigonal warping in van der Waals multilayers
• Interaction Driven Topological Phase Transition in Monolayer CrCl${}_2$(pyrazine)${}_2$
• Rashba spin splitting based on trilayer graphene systems
• Zigzag nanoribbon of gated bilayer hexagonal crystals with spontaneous edge magnetism
• A Quantized Interband Topological Index in Two-Dimensional Systems
• Layered Opposite Rashba Spin-Orbit Coupling in Bilayer Graphene: Loss of Spin Chirality, Symmetry Breaking and Topological Transition
• Valley-Polarized Quantum Anomalous Hall Phase in Bilayer Graphene with Layer-Dependent Proximity Effects