42 research outputs found
Topological superconducting phase in helical Shiba chains
Recently, it has been suggested that topological superconductivity and
Majorana end states can be realized in a chain of magnetic impurities on the
surface of an s-wave superconductor when the magnetic moments form a spin helix
as a result of the RKKY interaction mediated by the superconducting substrate.
Here, we investigate this scenario theoretically by developing a tight-binding
Bogoliubov-de Gennes description starting from the Shiba bound states induced
by the individual magnetic impurities. While the resulting model Hamiltonian
has similarities with the Kitaev model for one-dimensional spinless p-wave
superconductors, there are also important differences, most notably the
long-range nature of hopping and pairing as well as the complex hopping
amplitudes. We use both analytical and numerical approaches to explore the
consequences of these differences for the phase diagram and the localization
properties of the Majorana end states when the Shiba chain is in a topological
superconducting phase.Comment: 14 pages, 9 figures, minor changes, references added; published
versio
Unconventional topological phase transitions in helical Shiba chains
Chains of magnetic impurities placed on a superconducting substrate and
forming helical spin order provide a promising venue for realizing a
topological superconducting phase. An effective tight-binding description of
such helical Shiba chains involves long-range (power-law) hopping and pairing
amplitudes which induce an unconventional topological critical point. At the
critical point, we find exponentially localized Majorana bound states with a
short localization length unrelated to a topological gap. Away from the
critical point, this exponential decay develops a power-law tail. Our
analytical results have encouraging implications for experiment.Comment: 4+ pages, 2 figures, plus supplementary material, v3: added
references and minor refinements; published versio
Shortcuts to nonabelian braiding
Topological quantum information processing relies on adiabatic braiding of
nonabelian quasiparticles. Performing the braiding operations in finite time
introduces transitions out of the ground-state manifold and deviations from the
nonabelian Berry phase. We show that these errors can be eliminated by suitably
designed counterdiabatic correction terms in the Hamiltonian. We implement the
resulting shortcuts to adiabaticity for simple protocols of nonabelian braiding
and show that the error suppression can be substantial even for approximate
realizations of the counterdiabatic terms.Comment: 5 pages, 3 figures plus supplementary materia
Signatures of topological Josephson junctions
Quasiparticle poisoning and diabatic transitions may significantly narrow the
window for the experimental observation of the -periodic Josephson
effect predicted for topological Josephson junctions. Here, we show that
switching current measurements provide accessible and robust signatures for
topological superconductivity which persist in the presence of quasiparticle
poisoning processes. Such measurements provide access to the phase-dependent
subgap spectrum and Josephson currents of the topological junction when
incorporating it into an asymmetric SQUID together with a conventional
Josephson junction with large critical current. We also argue that pump-probe
experiments with multiple current pulses can be used to measure the
quasiparticle poisoning rates of the topological junction. The proposed
signatures are particularly robust, even in the presence of Zeeman fields and
spin-orbit coupling, when focusing on short Josephson junctions. Finally, we
also consider microwave excitations of short topological Josephson junctions
which may complement switching current measurements.Comment: 25 pages, 13 figures. Accepted by Phys. Rev.
Tuning Topological Superconductivity in Phase-Controlled Josephson Junctions with Rashba and Dresselhaus Spin-Orbit Coupling
Recently, topological superconductors based on Josephson junctions in
two-dimensional electron gases with strong Rashba spin-orbit coupling have been
proposed as attractive alternatives to wire-based setups. Here, we elucidate
how phase-controlled Josephson junctions based on quantum wells with [001]
growth direction and an arbitrary combination of Rashba and Dresselhaus
spin-orbit coupling can also host Majorana bound states for a wide range of
parameters as long as the magnetic field is oriented appropriately. Hence,
Majorana bound states based on Josephson junctions can appear in a wide class
of two-dimensional electron gases. We study the effect of spin-orbit coupling,
the Zeeman energies, and the superconducting phase difference to create a full
topological phase diagram and find the optimal stability region to observe
Majorana bound states in narrow junctions. Surprisingly, for equal Rashba and
Dresselhaus spin-orbit coupling, well localized Majorana bound states can
appear only for phase differences as the topological gap
protecting the Majorana bound states vanishes at . Our results show
that the ratio between Rashba and Dresselhaus spin-orbit coupling or the choice
of the in-plane crystallographic axis along which the superconducting phase
bias is applied offer additional tunable knobs to test Majorana bound states in
these systems. Finally, we discuss signatures of Majorana bound states that
could be probed experimentally by tunneling conductance measurements at the
edge of the junction.Comment: 21 pages, 12 figure
Signatures of topological phase transitions in mesoscopic superconducting rings
We investigate Josephson currents in mesoscopic rings with a weak link which
are in or near a topological superconducting phase. As a paradigmatic example,
we consider the Kitaev model of a spinless p-wave superconductor in one
dimension, emphasizing how this model emerges from more realistic settings
based on semiconductor nanowires. We show that the flux periodicity of the
Josephson current provides signatures of the topological phase transition and
the emergence of Majorana fermions situated on both sides of the weak link even
when fermion parity is not a good quantum number. In large rings, the Majorana
fermions hybridize only across the weak link. In this case, the Josephson
current is h/e periodic in the flux threading the loop when fermion parity is a
good quantum number but reverts to the more conventional h/2e periodicity in
the presence of fermion-parity changing relaxation processes. In mesoscopic
rings, the Majorana fermions also hybridize through their overlap in the
interior of the superconducting ring. We find that in the topological
superconducting phase, this gives rise to an h/e-periodic contribution even
when fermion parity is not conserved and that this contribution exhibits a peak
near the topological phase transition. This signature of the topological phase
transition is robust to the effects of disorder. As a byproduct, we find that
close to the topological phase transition, disorder drives the system deeper
into the topological phase. This is in stark contrast to the known behavior far
from the phase transition, where disorder tends to suppress the topological
phase.Comment: 14 pages, 9 figures, minor changes in the text, published versio
The universal shear conductivity of Fermi liquids and spinon Fermi surface states and its detection via spin qubit noise magnetometry
We demonstrate a remarkable property of metallic Fermi liquids: the transverse conductivity
assumes a universal value in the quasi-static (ω → 0) limit for wavevectors q in the regime
l
−1
mfp q pF, where lmfp is the mean free path and pF is the Fermi momentum. This value is
(e2/h)RFS/q in two dimensions (2D), where RFS measures the local radius of curvature of the
Fermi surface (FS) in momentum space. Even more surprisingly, we find that U(1) spin liquids
with a spinon FS have the same universal transverse conductivity. This means such spin liquids
behave effectively as metals in this regime, even though they appear insulating in standard
transport experiments. Moreover, we show that transverse current fluctuations result in a universal
low-frequency magnetic noise that can be directly probed by a spin qubit, such as a
nitrogen-vacancy (NV) center in diamond, placed at a distance z above of the 2D metal or spin
liquid. Specifically the magnetic noise is given by CωPFS/z, where PFS is the perimeter of the FS in
momentum space and C is a combination of fundamental constants of nature. Therefore these
observables are controlled purely by the geometry of the FS and are independent of kinematic
details of the quasi-particles, such as their effective mass and interactions. This behavior can be
used as a new technique to measure the size of the FS of metals and as a smoking gun probe to
pinpoint the presence of the elusive spinon FS in two-dimensional systems. We estimate that this
universal regime is within reach of current NV center spectroscopic techniques for several spinon
FS candidate materials
Enhanced zero-bias Majorana peak in disordered multi-subband quantum wires
A recent experiment [Mourik et al., Science 336, 1003 (2012)] on InSb quantum
wires provides possible evidence for the realization of a topological
superconducting phase and the formation of Majorana bound states. Motivated by
this experiment, we consider the signature of Majorana bound states in the
differential tunneling conductance of multi-subband wires. We show that the
weight of the Majorana-induced zero-bias peak is strongly enhanced by mixing of
subbands, when disorder is added to the end of the quantum wire. We also
consider how the topological phase transition is reflected in the gap structure
of the current-voltage characteristic.Comment: 4+ pages, 5 figures, minor changes in the text and Fig. 5, references
added; published versio