37 research outputs found
Majorana fermion chain at the Quantum Spin Hall edge
We study a realization of a 1d chain of Majorana bound states at the
interfaces between alternating ferromagnetic and superconducting regions at a
quantum spin Hall insulator edge. In the limit of well separated Majoranas, the
system can be mapped to the transverse field Ising model. The disordered
critical point can be reached by tuning the relative magnitude or phases of the
ferromagnetic and superconducting order parameters. We compute the voltage
dependence of the tunneling current from a metallic tip into the Majorana chain
as a direct probe of the random critical state.Comment: 5 pages, 3 figure
Majorana Fermions Signatures in Macroscopic Quantum Tunneling
Thermodynamic measurements of magnetic fluxes and I-V characteristics in
SQUIDs offer promising paths to the characterization of topological
superconducting phases. We consider the problem of macroscopic quantum
tunneling in an rf-SQUID in a topological superconducting phase. We show that
the topological order shifts the tunneling rates and quantum levels, both in
the parity conserving and fluctuating cases. The latter case is argued to
actually enhance the signatures in the slowly fluctuating limit, which is
expected to take place in the quantum regime of the circuit. In view of recent
advances, we also discuss how our results affect a -junction loop.Comment: 10 pages, 11 figure
Winterberg's conjectured breaking of the superluminal quantum correlations over large distances
We elaborate further on a hypothesis by Winterberg that turbulent
fluctuations of the zero point field may lead to a breakdown of the
superluminal quantum correlations over very large distances. A phenomenological
model that was proposed by Winterberg to estimate the transition scale of the
conjectured breakdown, does not lead to a distance that is large enough to be
agreeable with recent experiments. We consider, but rule out, the possibility
of a steeper slope in the energy spectrum of the turbulent fluctuations, due to
compressibility, as a possible mechanism that may lead to an increased
lower-bound for the transition scale. Instead, we argue that Winterberg
overestimated the intensity of the ZPF turbulent fluctuations. We calculate a
very generous corrected lower bound for the transition distance which is
consistent with current experiments.Comment: 7 pages, submitted to Int. J. Theor. Phy
Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
Superconductivity is a phenomenon where the macroscopic quantum coherence
appears due to the pairing of electrons. This offers a fascinating arena to
study the physics of broken gauge symmetry. However, the important symmetries
in superconductors are not only the gauge invariance. Especially, the symmetry
properties of the pairing, i.e., the parity and spin-singlet/spin-triplet,
determine the physical properties of the superconducting state. Recently it has
been recognized that there is the important third symmetry of the pair
amplitude, i.e., even or odd parity with respect to the frequency. The
conventional uniform superconducting states correspond to the even-frequency
pairing, but the recent finding is that the odd-frequency pair amplitude arises
in the spatially non-uniform situation quite ubiquitously. Especially, this is
the case in the Andreev bound state (ABS) appearing at the surface/interface of
the sample. The other important recent development is on the nontrivial
topological aspects of superconductors. As the band insulators are classified
by topological indices into (i) conventional insulator, (ii) quantum Hall
insulator, and (iii) topological insulator, also are the gapped
superconductors. The influence of the nontrivial topology of the bulk states
appears as the edge or surface of the sample. In the superconductors, this
leads to the formation of zero energy ABS (ZEABS). Therefore, the ABSs of the
superconductors are the place where the symmetry and topology meet each other
which offer the stage of rich physics. In this review, we discuss the physics
of ABS from the viewpoint of the odd-frequency pairing, the topological
bulk-edge correspondence, and the interplay of these two issues. It is
described how the symmetry of the pairing and topological indices determines
the absence/presence of the ZEABS, its energy dispersion, and properties as the
Majorana fermions.Comment: 91 pages, 38 figures, Review article, references adde