Topological Protection of Majorana Qubits

We study the stability of the topological quantum computation proposals involving Majorana fermions against thermal fluctuations. We use a minimal realistic model of a spinless px+ipy superconductor and consider effect of excited midgap states localized in the vortex core as well as of transitions above the bulk superconducting gap on the quasiparticle braiding, interferometry-based qubit read-out schemes, and quantum coherence of the topological qubits. We find that thermal occupation of the midgap states does not affect adiabatic braiding operations but leads to a reduction in the visibility of the interferometry measurements. We also consider quantum decoherence of topological qubits at finite temperatures and calculate their decay rate which is associated with the change of the fermion parity and, as such, is exponentially suppressed at temperatures well below the bulk excitation gap. Our conclusion is that the Majorana-based topological quantum computing schemes are indeed protected by the virtue of the quantum non-locality of the stored information and the presence of the bulk superconducting gap.Comment: 8 pages, 1 figur

Search for Majorana fermions in multiband semiconducting nanowires

We study multiband semiconducting nanowires proximity-coupled with an s-wave superconductor. We show that when odd number of subbands are occupied the system realizes non-trivial topological state supporting Majorana modes localized at the ends. We study the topological quantum phase transition in this system and analytically calculate the phase diagram as a function of the chemical potential and magnetic field. Our key finding is that multiband occupancy not only lifts the stringent constraint of one-dimensionality but also allows to have higher carrier density in the nanowire and as such multisubband nanowires are better-suited for observing the Majorana particle. We study the robustness of the topological phase by including the effects of the short- and long-range disorder. We show that in the limit of strong interband mixing there is an optimal regime in the phase diagram ("sweet spot") where the topological state is to a large extent insensitive to the presence of disorder.Comment: 4 pages, 3 figures, expanded version includes new results; accepted for publication in PR

Spontaneous interlayer superfluidity in bilayer systems of cold polar molecules

Quantum degenerate cold-atom gases provide a remarkable opportunity to study strongly interacting systems. Recent experimental progress in producing ultracold polar molecules with a net electric dipole moment opens up new possibilities to realize novel quantum phases governed by the long-range and anisotropic dipole-dipole interactions. In this work we predict the existence of experimentally observable novel broken-symmetry states with spontaneous interlayer coherence in cold polar molecules. These exotic states appear due to strong repulsive interlayer interactions and exhibit properties of superfluids, ferromagnets and excitonic condensates.Comment: 7 pages, 5 figures, final versio

Interplay of disorder and interaction in Majorana quantum wires

We study the interplay between disorder and interaction in one-dimensional topological superconductors which carry localized Majorana zero-energy states. Using Abelian bosonization and the perturbative renormalization group (RG) approach, we obtain the RG-flow and the associated scaling dimensions of the parameters and identify the critical points of the low-energy theory. We predict a quantum phase transition from a topological superconducting phase to a non-topological localized phase, and obtain the phase boundary between these two phases as a function of the electron-electron interaction and the disorder strength in the nanowire. Based on an instanton analysis which incorporates the effect of disorder, we also identify a large regime of stability of the Majorana-carrying topological phase in the parameter space of the model.Comment: New version includes a section and an appendix with a detailed study on the effect of interaction and disorder on the stability of Majorana end-states. 6 pages, 1 figur

Soft superconducting gap in semiconductor-based Majorana nanowires

We develop a theory for the proximity effect in superconductor-semiconductor-normal metal tunneling structures, which have recently been extensively studied experimentally, leading to the observation of transport signatures consistent with the predicted zero-energy Majorana bound states. We show that our model for the semiconductor nanowire having multiple occupied subbands with different transmission probabilities through the barrier reproduces the observed "soft-gap" behavior associated with substantial subgap tunneling conductance. We study the manifestations of the soft gap phenomenon both in the tunneling conductance and in local density of states measurements and discuss the correlations between these two quantities. We emphasize that the proximity effect associated with the hybridization between low-lying states in the multiband semiconductor and the normal metal states in the lead is an intrinsic effect leading to the soft gap problem. In addition to the intrinsic contribution, there may be extrinsic effects, such as, for example, interface disorder, exacerbating the soft gap problem. Our work establishes the generic possibility of an ubiquitous presence of an intrinsic soft gap in the superconductor-semiconductor-normal metal tunneling transport conductance induced by the inverse proximity effect of the normal metal.Comment: published version, 11+ pages, 8 figure

Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures

We propose and analyze theoretically an experimental setup for detecting the elusive Majorana particle in semiconductor-superconductor heterostructures. The experimental system consists of one-dimensional semiconductor wire with strong spin-orbit Rashba interaction embedded into a superconducting quantum interference device. We show that the energy spectra of the Andreev bound states at the junction are qualitatively different in topologically trivial (i.e., not containing any Majorana) and nontrivial phases having an even and odd number of crossings at zero energy, respectively. The measurement of the supercurrent through the junction allows one to discern topologically distinct phases and observe a topological phase transition by simply changing the in-plane magnetic field or the gate voltage. The observation of this phase transition will be a direct demonstration of the existence of Majorana particles.Comment: 4 pages, 3 figures, final version published in Phys. Rev. Let

Dimensional crossover in spin-orbit-coupled semiconductor nanowires with induced superconducting pairing

We show that the topological Majorana modes in nanowires much longer than the superconducting coherence length are adiabatically connected with discrete zero-energy states generically occurring in short nanowires. We demonstrate that these zero-energy crossings can be tuned by an external magnetic field and are protected by the particle-hole symmetry. We study the evolution of the low-energy spectrum and the splitting oscillations as a function of magnetic field, wire length, and chemical potential, manifestly establishing that the low-energy physics of short wires is related to that occurring in long wires. This physics, which represents a hallmark of spinless p-wave superconductivity, can be observed in tunneling conductance measurements.Comment: published version, 7 pages, 7 color figure