Entanglement entropy and entanglement spectrum of Bi${}_{1-x}$Sb${}_x$ (111) bilayers

Abstract

We investigate topological properties of Bi${}_{1-x}$Sb${}_x$ bilayers in the (111) plane using entanglement measures. Electronic structures are studied using multi-orbital tight-binding model, with structural stability confirmed through first-principles calculations. Topologically non-trivial nature of Bi bilayer is proved by the presence of spectral flow in the entanglement spectrum. We consider topological phase transitions driven by a composition change $x$, an applied external electric field in pure Bi, and strain in pure Sb. Composition- and strain-induced phase transitions reveal a finite discontinuity in the entanglement entropy. However, this quantity remains a continuous function of electric field strength, but shows a discontinuity in the first derivative. We relate the difference in behavior of the entanglement entropy to breaking of the inversion symmetry in the last case.

8 pages, 8 figures

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Cited by in corpus (2)

• Topological phases in Bi/Sb planar and buckled honeycomb monolayers
• Entanglement as a topological marker in harmonically confined attractive Fermi-Hubbard chains