Abstract

The transformations of the topological phase and the edge modes of a double-bilayer bismuthene were investigated with first-principles calculations and Green’s function as the inter-bilayer spacing increased from 0 Å to 10 Å. At a critical spacing of 2 Å, a topological phase transition from a topological insulator to a band insulator resulting from a band inversion between the highest valence band and the second lowest conduction band, was observed, and this was understood based on the particular orbital characters of the band inversion involved states. The edge modes of double-bilayer bismuthene survived the phase transition. When d was 2 Å < d < 4 Å, the interaction between the edge modes of two separated bismuthene bilayers induced an anti-crossing gap and resulted in a trivial band connection. At and beyond 4 Å, the two bilayers behavior decoupled entirely. The results demonstrate the transformability of the topological phase and the edge modes with the inter-bilayer spacing in double-bilayer bismuthene, which may be useful for spintronic applications.

Highlights

  • Topological insulators have attracted much attention over the past decade for their fundamental physics interests and promising applications in spintronics [1]

  • A topological insulator is different from a band insulator in regard to band topology, which can be characterized by a topological invariant [2]

  • Our findings demonstrate the transformability of the topological phase and the dispersion of edge modes with inter-bilayer spacing of double-bilayer bismuthene

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Summary

Introduction

Topological insulators have attracted much attention over the past decade for their fundamental physics interests and promising applications in spintronics [1]. The nontrivial topology of the band structure of a topological insulator gives rise to metallic boundary modes [1], which are robust and cannot be destroyed by altering the boundary conditions [3,4]. The edge modes are highly spin polarized because of the prominent spin-orbit coupling effect associated with the heavy elements commonly found in topological insulators [5]. The spin polarized boundary modes can host spin currents, which can be utilized to transmit and process information with little energy dissipation [6]. The topological edge modes cannot be eliminated their properties can be tuned by factors such as strain [7], composition [8] and chemical adsorption [9]

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