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Register a new userEffects of electron scattering on the topological properties of nanowires: Majorana fermions from disorder and superlattices
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We focus on inducing topological state from regular, or irregular scattering in (i) p-wave superconducting wires and (ii) Rashba wires proximity coupled to an s-wave superconductor. We find that contrary to common expectations the topological properties of both systems are fundamentally different: In p-wave wires, disorder generally has a detrimental effect on the topological order and the topological state is destroyed beyond a critical disorder strength. In contrast, in Rashba wires, which are relevant for recent experiments, disorder can {it induce} topological order, reducing the need for quasiballistic samples to obtain Majorana fermions. Moreover, we find that the total phase space area of the topological state is conserved for long disordered Rashba wires, and can even be increased in an appropriately engineered superlattice potential.
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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$^{-3}$.
Developing a gate-tunable, scalable, and topologically-protectable supercurrent qubit and integrating it into a quantum circuit are crucial for applications in the fields of quantum information technology and topological phenomena. Here we propose that the nano-hybrid supercurrent transistors, a superconducting quantum analogue of a transistor, made of topological insulator nanowire would be a promising platform for unprecedented control of both the supercurrent magnitude and the current-phase relation by applying a voltage on a gate electrode. We believe that our experimental design will help probing Majorana state in topological insulator nanowire and establishing a solid-state platform for topological supercurrent qubit.
Recent experiments have produced mounting evidence of Majorana zero modes in nanowire-superconductor hybrids. Signatures of an expected topological phase transition accompanying the onset of these modes nevertheless remain elusive. We investigate a fundamental question concerning this issue: Do well-formed Majorana modes necessarily entail a sharp phase transition in these setups? Assuming reasonable parameters, we argue that finite-size effects can dramatically smooth this putative transition into a crossover, even in systems large enough to support well-localized Majorana modes. We propose overcoming such finite-size effects by examining the behavior of low-lying excited states through tunneling spectroscopy. In particular, the excited-state energies exhibit characteristic field and density dependence, and scaling with system size, that expose an approaching topological phase transition. We suggest several experiments for extracting the predicted behavior. As a useful byproduct, the protocols also allow one to measure the wires spin-orbit coupling directly in its superconducting environment.
The idea of topological quantum computation (TQC) is to store and manipulate quantum information in an intrinsically fault-tolerant manner by utilizing the physics of topologically ordered phases of matter. Currently, one of the most promising platforms for a topological qubit is in terms of Majorana fermion zero modes (MZMs) in spin-orbit coupled superconducting nanowires. However, the topologically robust operations that are possible with MZMs can be efficiently simulated on a classical computer and are therefore not sufficient for realizing a universal gate set for TQC. Here, we show that an array of coupled semiconductor-superconductor nanowires with MZM edge states can be used to realize a more sophisticated type of non-Abelian defect: a genon in an Ising $times$ Ising topological state. This leads to a possible implementation of the missing topologically protected $pi/8$ phase gate and thus universal TQC based on semiconductor-superconductor nanowire technology. We provide detailed numerical estimates of the relevant energy scales, which we show to lie within accessible ranges.
Multiple zero-energy Majorana fermions (MFs) with spatially overlapping wave functions can survive only if their splitting is prevented by an underlying symmetry. Here we show that, in quasi-one-dimensional (Q1D) time reversal invariant topological superconductors (class DIII), a realistic model for superconducting lithium molybdenum purple bronze and certain families of organic superconductors, multiple Majorana-Kramers pairs with strongly overlapping wave functions persist at zero energy even in the absence of an easily identifiable symmetry. We find that similar results hold in the case of Q1D semiconductor-superconductor heterostructures (class D) with transverse hopping t_{perp} much smaller than longitudinal hopping t_x. Our results, explained in terms of special properties of the Hamiltonian and wave functions, underscore the importance of hidden accidental symmetries in topological superconductors.
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