14,532 research outputs found
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
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