Abstract
We investigate the influence of different spin–orbit couplings on topological phase transitions in the bilayer Kane–Mele model. We find that the competition between intrinsic spin–orbit coupling and Rashba spin–orbit coupling can lead to two dimensional topological metallic states with nontrivial topology. Such phases, although having a metallic bulk, still possess edge states with well defined topological invariants. Specifically, we show that with preserved time reversal symmetry the system can exhibit a -metallic phase with spin helical edge states and a nontrivial invariant. When time reversal symmetry is broken, a Chern metallic phase could appear with chiral edge states and a nontrivial Chern invariant.
Highlights
Study of the effects of spin–orbit coupling (SOC) has been a central theme in condensed matter physics in the past decade
In this work, motivated by the above mentioned progress, we study the effects of different SOCs in a bilayer Kane–Mele model, focusing on its topological properties
We have studied the topological phases of a bilayer Kane–Mele model in detail
Summary
Study of the effects of spin–orbit coupling (SOC) has been a central theme in condensed matter physics in the past decade. When the layer potential U is finite, a topological state with nontrivial topological invariant can appear [32,33,34] As another example, it has been found that the Rashba SOC, which tends to destroy the QSH phase in a single layer turns out to favor the QSH phase in bilayer graphene [35]. We discover novel 2D topological metallic phases in this system due to the competition between the intrinsic SOC and the Rashba SOC: the 2D 2-metallic phase and the Chern metallic phase, depending on whether time reversal symmetry is broken In such phases, the bulk band gap is closed indirectly, a topological invariant can still be well defined, and the state is adiabatically connected to a topologically nontrivial insulator.
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