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Register a new userDisorder effects in topological insulator nanowires
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Three-dimensional topological insulator (TI) nanowires with quantized surface subband spectra are studied as a main component of Majorana bound states (MBS) devices. However, such wires are known to have large concentration $N sim 10^{19}$ cm$^{-3}$ of Coulomb impurities. It is believed that a MBS device can function only if the amplitude of long-range fluctuations of the random Coulomb potential $Gamma$ is smaller than the subband gap $Delta$. Here we calculate $Gamma$ for recently experimentally studied large-dielectric-constant (Bi$_{1-x}$Sb$_x$)$_2$Te$_{3}$ wires in a small-dielectric-constant environment (no superconductor). We show that provided by such a dielectric-constant contrast, the confinement of electric field of impurities within the wire allows more distant impurities to contribute into $Gamma$, leading to $Gamma sim 3Delta$. We also calculate a TI wire resistance as a function of the Fermi level and carrier concentration due to scattering on Coulomb and neutral impurities, and do not find observable discrete subband-spectrum related oscillations at $N gtrsim 10^{18}$ cm$^{-3}$.
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Thin films of topological insulators (TI) attract large attention because of expected topological effects from the inter-surface hybridization of Dirac points. However, these effects may be depleted by unexpectedly large energy smearing $Gamma$ of surface Dirac points by the random potential of abundant Coulomb impurities. We show that in a typical TI film with large dielectric constant $sim 50$ sandwiched between two low dielectric constant layers, the Rytova-Chaplik-Entin-Keldysh modification of the Coulomb potential of a charge impurity allows a larger number of the film impurities to contribute to $Gamma$. As a result, $Gamma$ is large and independent of the TI film thickness $d$ for $d > 5$ nm. In thinner films $Gamma$ grows with decreasing $d$ due to reduction of screening by the hybridization gap. We study the surface conductivity away from the neutrality point and at the neutrality point. In the latter case, we find the maximum TI film thickness at which the hybridization gap is still able to make a TI film insulating and allow observation of the quantum spin Hall effect, $d_{max} sim 7$ nm.
Disorder inevitably exists in realistic samples, manifesting itself in various exotic properties for the topological states. In this paper, we summarize and briefly review work completed over the last few years, including our own, regarding recent developments in several topics about disorder effects in topological states. For weak disorder, the robustness of topological states is demonstrated, especially for both quantum spin Hall states with $Z_2=1$ and size induced nontrivial topological insulators with $Z_2=0$. For moderate disorder, by increasing the randomness of both the impurity distribution and the impurity induced potential, the topological insulator states can be created from normal metallic or insulating states. These phenomena and their mechanisms are summarized. For strong disorder, the disorder causes a metal-insulator transition. Due to their topological nature, the phase diagrams are much richer in topological state systems. Finally, the trends in these areas of disorder research are discussed.
In this chapter we review our work on the theory of quantum transport in topological insulator nanowires. We discuss both normal state properties and superconducting proximity effects, including the effects of magnetic fields and disorder. Throughout we assume that the bulk is insulating and inert, and work with a surface-only theory. The essential transport properties are understood in terms of three special modes: in the normal state, half a flux quantum along the length of the wire induces a perfectly transmitted mode protected by an effective time reversal symmetry; a transverse magnetic field induces chiral modes at the sides of the wire, with different chiralities residing on different sides protecting them from backscattering; and, finally, Majorana zero modes are obtained at the ends of a wire in a proximity to a superconductor, when combined with a flux along the wire. Some parts of our discussion have a small overlap with the discussion in the review [Bardarson and Moore, Rep. Prog. Phys., 76, 056501, (2013)]. We do not aim to give a complete review of the published literature, instead the focus is mainly on our own and directly related work.
Recent studies of disorder or non-Hermiticity induced topological insulators inject new ingredients for engineering topological matter. Here we consider the effect of purely non-Hermitian disorders, a combination of these two ingredients, in a 1D chiral symmetric lattice with disordered gain and loss. The increasing disorder strength can drive a transition from trivial to topological insulators, characterizing by the change of topological winding number defined by localized states in the gapless and complex bulk spectra. The non-Hermitian critical behaviors are characterized by the biorthogonal localization length of zero energy edge modes, which diverges at the critical transition point and establishes the bulk-edge correspondence. Furthermore, we show that the bulk topology may be experimentally accessed by measuring the biorthogonal chiral displacement $mathcal{C}$, which converges to the winding number through time-averaging and can be extracted from proper Ramsey-interference sequences. We propose a scheme to implement and probe such non-Hermitian disorder driven topological insulators using photons in coupled micro-cavities.
Finding a clear signature of topological superconductivity in transport experiments remains an outstanding challenge. In this work, we propose exploiting the unique properties of three-dimensional topological insulator nanowires to generate a normal-superconductor junction in the single-mode regime where an exactly quantized $2e^2/h$ zero-bias conductance can be observed over a wide range of realistic system parameters. This is achieved by inducing superconductivity in half of the wire, which can be tuned at will from trivial to topological with a parallel magnetic field, while a perpendicular field is used to gap out the normal part, except for two spatially separated chiral channels. The combination of chiral mode transport and perfect Andreev reflection makes the measurement robust to moderate disorder, and the quantization of conductance survives to much higher temperatures than in tunnel junction experiments. Our proposal may be understood as a variant of a Majorana interferometer which is easily realizable in experiments.
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