Fate of topological-insulator surface states under strong disorder

Abstract

Three-dimensional topological insulators feature Dirac-like surface states which are topologically protected against the influence of weak quenched disorder. Here we investigate the effect of surface disorder beyond the weak-disorder limit using large-scale numerical simulations. We find two qualitatively distinct regimes: Moderate disorder destroys the Dirac cone and induces diffusive metallic behavior at the surface. Even more remarkably, for strong surface disorder a Dirac cone reappears, as new weakly disordered "surface" states emerge in the sample beneath the disordered surface layer, which can be understood in terms of an interface between a topological and an Anderson insulator. Together, this demonstrates the drastic effect of disorder on topological surface states, which cannot be captured within effective two-dimensional models for the surface states alone.Topological insulators (TIs) are a novel form of insulators, where topological properties of the band structure lead to the formation of metallic states at the surface [1,2]. Two-dimensional (2d) TIs were predicted [3,4] and then realized in quantum-well heterostructures [5]. Subsequently, three-dimensional (3d) generalizations were discussed theoretically [6][7][8] and realized afterwards, primarily in Bi-based compounds [9,10]. 3d TIs are characterized by a set of topological quantum numbers, which lead to a classification into strong and weak TIs.Strong TIs possess low-energy surface states which can be described in terms of massless 2d Dirac electrons, with an odd number of Dirac cones per surface. Remarkably, these surface states are topologically protected against the influence of disorder due to their helical nature: The spin-momentum locking of the Dirac theory implies that the states k and − k have opposite spin. This in turn suppresses the lowest-order matrix element for backscattering, k → − k, leading to the absence of weak localization for weak potential disorder. What about strong disorder? Theoretical results obtained within 2d continuum Dirac models suggest that such states remain metallic even for arbitrarily large disorder: The beta-function describing the renormalization-group flow of the conductivity is always positive [11][12][13]. However, by construction the applicability of these effective theories to TI surface states is restricted to energies much smaller than the bulk gap, ∆, and the effect of surface disorder with a strength γ ∆ can therefore not be captured. Intuitively, this is because strong impurities will influence both surface and bulk states, causing a non-trivial coupling between the two which cannot be described by a theory for surface states alone.To the best of our knowledge, the effect of strong surface disorder has only been discussed locally for isolated impurities [14], but the global fate of TI surface states under moderate or strong disorder is not known. This issue is not only of fundamental interest in order to understand the range and limitations of "topological protection", but is also of enormous pra...

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

“…Indeed, surface states or edge states are shown to persist in the presence of weak disorders [5]. However, it is also found that in the presence of disorders, anomalous transmutation between TI and insulators with trivial topology may happen [9,10,12]. In particular, in computer simulations of a HgTe quantum well, it is discovered that an ordinary insulating state can be transformed into a topological insulator, called topological Anderson insulator [10,11].…”

“…Since topological order is protected by associated symmetries [4], surface states and edge states in TIs are considered to be robust against bulk disorders that do not break the time-reversal symmetry that is associated with Z 2 topological order. The robustness against disorders is the key to potential technological applications and hence a great effort has been dedicated to understanding the behavior of the topological materials in the presence of disorders [5][6][7][8][9][10]12]. Indeed, surface states or edge states are shown to persist in the presence of weak disorders [5].…”

Kondo holes in topological Kondo insulators: Spectral properties and surface quasiparticle interference

“…Kondo holes on the surface of TKIs promise to be interesting also because they represent strong scatterers for which the simplest arguments of topological protection no longer apply. 29,30 Here we will employ a fully self-consistent mean-field description of the Kondo insulator, taking into account the local modification of Kondo screening by defects. Applying this methodology to both the weak topological insulator (WTI) and strong topological insulator (STI) phases, we will calculate the electronic structure and the surface QPI patterns for dilute surface Kondo holes as well as for other types of impurities.…”

Holographic treatment of boundary disorder in a topological insulator

“…5) on the surface of as-grown topological insulator Bi 2−x Cu x Se 3 which is necessary to prevent the surface band bending caused by the adsorption of residual atoms present in the vacuum chamber. As the manifestations of topological systems -such as the protected surface states or Majorana fermions -are localized near the surface or the edge of the system [11][12][13][14][15] , the effect of surface impurities on the surface spectral and transport properties are of both theoretical and practical interest [16][17][18] . Impurity effects could be apparent through the Local density of states (LDOS), and spectral functions.…”

“…The only general analysis of surface impurities was given recently, when an exact diagonalization (ED) approach has been applied to non-interacting TIs with surface disorder 16,19 (recent additional work was dedicated to surface Kondo effects in 3D TI's 20,21 ). This study found evidence for a crossover between a nearly ballistic response of the surface electrons at weak disorder, localization physics at intermediate disorder, and then a restored nearly ballistic surface state hiding in the second layer when disorder is very strong.…”