66 research outputs found
Nonlocal conductance reveals helical superconductors
Helical superconductors form a two dimensional, time-reversal invariant
topological phase characterized by a Kramers pair of Majorana edge modes
(helical Majorana modes). Existing detection schemes to identify this phase
rely either on spin transport properties, which are quite difficult to measure,
or on local charge transport, which allows only a partial identification. Here
we show that the presence of helical Majorana modes can be unambiguously
revealed by measuring the nonlocal charge conductance. Focusing on a
superconducting ring, we suggest two experiments that provide unique and robust
signatures to detect the helical superconductor phase.Comment: 4 pages, 2 figure
Majorana-Klein hybridization in topological superconductor junctions
We present a powerful and general approach to describe the coupling of
Majorana fermions to external leads, of interacting or non-interacting
electrons. Our picture has the Klein factors of bosonization appearing as extra
Majoranas hybridizing with the physical ones. We demonstrate the power of this
approach by solving a highly nontrivial SO(M) Kondo problem arising in
topological superconductors with M Majorana-lead couplings, allowing for
arbitrary M and for conduction electron interactions. We find that these
topological Kondo problems give rise to robust non-Fermi liquid behavior, even
for Fermi liquid leads, and to a quantum phase transition between insulating
and Kondo regimes when the leads form Luttinger liquids. In particular, for M=4
we find a long sought-after stable realization of the two-channel Kondo fixed
point
Z_2 Topological Insulators in Ultracold Atomic Gases
We describe how optical dressing can be used to generate bandstructures for
ultracold atoms with non-trivial Z_2 topological order. Time reversal symmetry
is preserved by simple conditions on the optical fields. We first show how to
construct optical lattices that give rise to Z_2 topological insulators in two
dimensions. We then describe a general method for the construction of
three-dimensional Z_2 topological insulators. A central feature of our approach
is a new way to understand Z_2 topological insulators starting from the
nearly-free electron limit
Symmetry classes, many-body zero modes, and supersymmetry in the complex Sachdev-Ye-Kitaev model
The complex Sachdev-Ye-Kitaev (cSYK) model is a charge-conserving model of
randomly interacting fermions. The interaction term can be chosen such that the
model exhibits chiral symmetry. Then, depending on the charge sector and the
number of interacting fermions, level spacing statistics suggests a fourfold
categorization of the model into the three Wigner-Dyson symmetry classes. In
this work, inspired by previous findings for the Majorana Sachdev-Ye-Kitaev
model, we embed the symmetry classes of the cSYK model in the Altland-Zirnbauer
framework and identify consequences of chiral symmetry originating from
correlations across different charge sectors. In particular, we show that for
an odd number of fermions, the model hosts exact many-body zero modes that can
be combined into a generalized fermion that does not affect the system's
energy. This fermion directly leads to quantum-mechanical supersymmetry that,
unlike explicitly supersymmetric cSYK constructions, does not require
fine-tuned couplings, but only chiral symmetry. Signatures of the generalized
fermion, and thus supersymmetry, include the long-time plateau in
time-dependent correlation functions of fermion-parity-odd observables: The
plateau may take nonzero value only for certain combinations of the fermion
structure of the observable and the system's symmetry class. We illustrate our
findings through exact diagonalization simulations of the system's dynamics.ERC Starting Grant No. 678795 TopInS
The effect of symmetry class transitions on the shot noise in chaotic quantum dots
Using the random matrix theory (RMT) approach, we calculated the weak
localization correction to the shot noise power in a chaotic cavity as a
function of magnetic field and spin-orbit coupling. We found a remarkably
simple relation between the weak localization correction to the conductance and
to the shot noise power, that depends only on the channel number asymmetry of
the cavity. In the special case of an orthogonal-unitary crossover, our result
coincides with the prediction of Braun et. al [J. Phys. A: Math. Gen. {\bf 39},
L159-L165 (2006)], illustrating the equivalence of the semiclassical method to
RMT.Comment: 4 pages, 1 figur
Topological Kondo effect with Majorana fermions
The Kondo effect is a striking consequence of the coupling of itinerant
electrons to a quantum spin with degenerate energy levels. While degeneracies
are commonly thought to arise from symmetries or fine-tuning of parameters, the
recent emergence of Majorana fermions has brought to the fore an entirely
different possibility: a "topological degeneracy" which arises from the
nonlocal character of Majorana fermions. Here we show that nonlocal quantum
spins formed from these degrees of freedom give rise to a novel "topological
Kondo effect". This leads to a robust non-Fermi liquid behavior, known to be
difficult to achieve in the conventional Kondo context. Focusing on mesoscopic
superconductor devices, we predict several unique transport signatures of this
Kondo effect, which would demonstrate the non-local quantum dynamics of
Majorana fermions, and validate their potential for topological quantum
computation
Generalization of the Poisson kernel to the superconducting random-matrix ensembles
We calculate the distribution of the scattering matrix at the Fermi level for
chaotic normal-superconducting systems for the case of arbitrary coupling of
the scattering region to the scattering channels. The derivation is based on
the assumption of uniformly distributed scattering matrices at ideal coupling,
which holds in the absence of a gap in the quasiparticle excitation spectrum.
The resulting distribution generalizes the Poisson kernel to the nonstandard
symmetry classes introduced by Altland and Zirnbauer. We show that unlike the
Poisson kernel, our result cannot be obtained by combining the maximum entropy
principle with the analyticity-ergodicity constraint. As a simple application,
we calculate the distribution of the conductance for a single-channel chaotic
Andreev quantum dot in a magnetic field.Comment: 7 pages, 2 figure
Topologically stable gapless phases of time-reversal invariant superconductors
We show that time-reversal invariant superconductors in d=2 (d=3) dimensions
can support topologically stable Fermi points (lines), characterized by an
integer topological charge. Combining this with the momentum space symmetries
present, we prove analogs of the fermion doubling theorem: for d=2 lattice
models admitting a spin X electron-hole structure, the number of Fermi points
is a multiple of four, while for d=3, Fermi lines come in pairs. We show two
implications of our findings for topological superconductors in d=3: first, we
relate the bulk topological invariant to a topological number for the surface
Fermi points in the form of an index theorem. Second, we show that the
existence of topologically stable Fermi lines results in extended gapless
regions in a generic topological superconductor phase diagram.Comment: 7 pages, 1 figure; v3: expanded versio
- …