Stability of Z₂topological order in the presence of vacancy-induced impurity band

Abstract

Although topological insulators (TIs) are known to be robust against non-magnetic perturbations and exhibit edge or surface states as their distinct feature, experimentally it is known that vacancies often occur in these materials and impose strong perturbations. Here we investigate effects of vacancies on the stability of Z2 topological order using the Kane-Mele (KM) model as a prototype of topological insulator. It is shown that even though a vacancy is not classified as a topological defect in KM model, it generally induces a pair of degenerate midgap states only in the TI phase. We show that these midgap states results from edge states that fit into vacancies and are characterized by the same Z2 topological order. Furthermore, in the presence of many vacancies, an impurity band that is degenerate with edge states in energy is induced and mixes directly with edge states. However, the Z2 topological order persists and edge states exist between the impurity band and perturbed bulk bands until a phase transition occurs when Dirac cones near Dirac points are depleted. Our analyses indicate that the same scenario holds for point vacancies or line of vacancies in 3D TIs as well.

Anderson localization and topological transition in Chern insulators

“…Similar behavior has been found in Ref. 37 although the critical density reported there is a bit different.…”

“…14 A similar behavior has been reported in Ref. 37 for the case of vacancies. This mechanism is also supported by the analysis of the DOS depicted in Fig.…”

“…As shown by many authors, a single vacancy induces a midgap bound state in the Haldane or Kane Mele model, [28][29][30][31][32][33] while a density of vacancies induces an impurity band inside the gap. 33 Increasing the density of vacancies enhances the spectral weight inside the gap, which eventually closes for high enough vacancy density. In contrast, potential disorder localizes states near the band edges and generate a mobility edge.…”

“…But the sensitivity of the localization transition to the sublattice selection has only been addressed more recently. 21,37 Reference 37 discusses the topological transition in the case of the time reversal symplectic class (Kane-Mele model). Our findings are qualitatively similar in the equally diluted case but differ in the selected dilution case.…”

Robustness of topological insulating phase against vacancy, vacancy cluster, and grain boundary bulk defects

“…Therefore, an intriguing and important question is how robust a TI phase can be against bulk defects? While the bulk defects have been studied in arsenene [3][4][5], antimonene [4,6], bismuthene [7][8][9], and 3D Bichalcogenide [10][11][12][13], their influence on topological properties, especially how different bulk defects would destroy topological order, are still under-studied [6,7,14]. In this Rapid Communication, we attempt to address this outstanding question for the most typical defects of vacancy (VA), vacancy cluster (VC), and grain boundary (GB), first in general within the theoretical framework of tight-binding (TB) model of 2D TI [15][16][17][18], and then in specific for a prototypical large-gap 2D TI, SiC-supported monolayer Bi, based on first-principles calculation.…”