Transport by helical edge states of a quantum spin Hall insulator is experimentally characterized by a weakly temperature-dependent mean free path of a few microns and by reproducible conductance oscillations, challenging proposed theoretical explanations. We consider a model where edge electrons experience spatially random Rashba spin-orbit coupling and couple to a magnetic impurity with spin S 1/2. In a finite bias steady state, we find for S > 1/2 an impurity induced resistance with a temperature dependence in agreement with experiments. Since backscattering is elastic, interference between different scatterers possibly explains conductance fluctuations. DOI: 10.1103/PhysRevB.93.081301 Introduction. During the last decade, the quantum spin Hall effect (QSHE) [1][2][3] has become an important example of a topologically ordered state with time-reversal invariance. One of its key features is the existence of helical edge states [4] with a quantized conductance of e 2 /h per edge, as edge electrons are protected from elastic single particle backscattering by time-reversal symmetry [1,4,5]. Soon after the theoretical prediction [6], the QSHE was realized in HgTe/CdTe quantum wells [7], and the quantized conductance [7] as well as the demonstration of nonlocal transport [8] were crucial signatures for this first-time experimental observation. However, already in this first as well as in subsequent experiments [7][8][9][10][11][12], deviations from the quantized conductance with a weak temperature dependence were found for edges longer than approximately 1 μm. Moreover, in short samples, where the conductance is essentially quantized, small conductance fluctuations are observed as the back-gate voltage is tuned [7,8,12,13]. After the prediction [14] of the QSHE in InAs/GaSb/AlSb quantum wells, the same qualitative behavior of the conductance as in HgTe/CdTe was observed also in these devices [15][16][17][18].A multitude of other mechanisms beyond elastic single particle backscattering have been proposed as possible explanations for the relatively short mean free path [19]: inelastic single particle [20][21][22][23] and two-particle backscattering [1,4,5,[23][24][25] which can be caused by electron-electron or electron-phonon interactions, both of which are usually considered in combination with other time-reversal invariant perturbations; tunneling of electrons into charge puddles caused by inhomogeneous doping, giving rise to inelastic single particle backscattering [26,27]; coupling of edge electrons to a spin bath which gets dynamically polarized [28], thus effectively breaking time-reversal symmetry and giving rise to elastic backscattering in conjunction with Rashba disorder [29]; time-reversal symmetry breaking by an exciton condensate [30]; and coupling of edge electrons to a single Kondo impurity [4,31,32], to a lattice of Kondo impurities [33], to a single Kondo impurity in the presence of homogeneous Rashba spin-orbit coupling [34,35], or to several Kondo impurities with random anisotropies [36]. Althou...

Existence of zero-energy impurity states in different classes of topological insulators and superconductors and their relation to topological phase transitions Kimme, Lukas; Hyart, Timo Kimme, L., & Hyart, T. (2016 We consider the effects of impurities on topological insulators and superconductors. We start by identifying the general conditions under which the eigenenergies of an arbitrary Hamiltonian H belonging to one of the Altland-Zirnbauer symmetry classes undergo a robust zero energy crossing as a function of an external parameter which can be, for example, the impurity strength. We define a generalized root of det H and use it to predict or rule out robust zero-energy crossings in all symmetry classes. We complement this result with an analysis based on almost degenerate perturbation theory, which allows a derivation of the asymptotic low-energy behavior of the ensemble averaged density of states ρ ∼ E α for all symmetry classes and makes it transparent that the exponent α does not depend on the choice of the random matrix ensemble. Finally, we show that a lattice of impurities can drive a topologically trivial system into a nontrivial phase, and in particular we demonstrate that impurity bands carrying extremely large Chern numbers can appear in different symmetry classes of two-dimensional topological insulators and superconductors. We use the generalized root of det H (k) to reveal a spiderweblike momentum space structure of the energy gap closings that separate the topologically distinct phases in p x + ip y superconductors in the presence of an impurity lattice.

We address the question of whether individual nonmagnetic impurities can induce zero-energy states in time-reversal-invariant topological superconductors, and define a class of symmetries which guarantee the existence of such states for a specific value of the impurity strength. These symmetries allow the definition of a position-space topological Z2 invariant, which is related to the standard bulk topological Z2 invariant. Our general results are applied to the time-reversal-invariant p-wave phase of the doped Kitaev-Heisenberg model, where we demonstrate how a lattice of impurities can drive a topologically trivial system into the nontrivial phase.