Stability of Z2 topological 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 insulators. It is shown that even though a vacancy is not classified as a topological defect in the KM model, it generally induces a pair of degenerate mid-gap bound states only in the TI phase. Hence mid-gap bound states due to vacancies arise from the same Z2 classification of topological insulators. Furthermore, we show that in the presence of many vacancies, an impurity band is induced and coexists with edge states until a phase transition occurs when the spectral weights of Dirac cones near Dirac points are depleted. Our analyses indicate that the same scenario holds for point vacancies or lines of vacancies in 3D TIs as well.