292 research outputs found
Non-Abelian gauge potentials in graphene bilayers
We study the effect of spatial modulations in the interlayer hopping of
graphene bilayers, such as those that arise upon shearing or twisting. We show
that their single-particle physics, characterized by charge accumulation and
recurrent formation of zero-energy bands as the pattern period L increases, is
governed by a non-Abelian gauge potential arising in the low-energy electronic
theory due to the coupling between layers. We show that such gauge-type
couplings give rise to a potential that, for certain discrete values of L,
spatially confines states at zero energy in particular regions of the Moir\'e
patterns. We also draw the connection between the recurrence of the flat
zero-energy bands and the non-Abelian character of the potential.Comment: 5 pages, 3 figures, published versio
AC Josephson effect in finite-length nanowire junctions with Majorana modes
It has been predicted that superconducting junctions made with topological
nanowires hosting Majorana bound states (MBS) exhibit an anomalous
4\pi-periodic Josephson effect. Finding an experimental setup with these
unconventional properties poses, however, a serious challenge: for
finite-length wires, the equilibrium supercurrents are always 2\pi-periodic as
anticrossings of states with the same fermionic parity are possible. We show,
however, that the anomaly survives in the transient regime of the ac Josephson
effect. Transients are moreover protected against decay by quasiparticle
poisoning as a consequence of the quantum Zeno effect, which fixes the parity
of Majorana qubits. The resulting long-lived ac Josephson transients may be
effectively used to detect MBS.Comment: 9 pages, 4 figures, published version (with supplementary material
Quantum Hall effect in graphene with twisted bilayer stripe defects
We analyze the quantum Hall effect in single layer graphene with bilayer
stripe defects. Such defects are often encountered at steps in the substrate of
graphene grown on silicon carbide. We show that AB or AA stacked bilayer
stripes result in large Hall conductivity fluctuations that destroy the quantum
Hall plateaux. The fluctuations are a result of the coupling of edge states at
opposite edges through currents traversing the stripe. Upon rotation of the
second layer with respect to the continuous monolayer (a twisted-bilayer stripe
defect), such currents decouple from the extended edge states and develop into
long-lived discrete quasi bound states circulating around the perimeter of the
stripe. Backscattering of edge modes then occurs only at precise resonant
energies, and hence the quantum Hall plateaux are recovered as twist angle
grows.Comment: 8 pages, 7 figures, published versio
Topological -junctions from crossed Andreev reflection in the Quantum Hall regime
We consider a two-dimensional electron gas (2DEG) in the Quantum Hall regime
in the presence of a Zeeman field, with the Fermi level tuned to filling factor
. We show that, in the presence of spin-orbit coupling, contacting the
2DEG to a narrow strip of an s-wave superconductor produces a topological
superconducting gap along the contact as a result of crossed Andreev reflection
(CAR) processes across the strip. The sign of the topological gap, controlled
by the CAR amplitude, depends periodically on the Fermi wavelength and strip
width and can be externally tuned. An interface between two halves of a long
strip with topological gaps of opposite sign implements a robust
-junction, hosting a pair of Majorana zero modes that do not split despite
their overlap. We show that such a situation can be exploited to perform
protected non-Abelian tunnel-braid operations without any fine tuning.Comment: 10 pages, 5 figures. Corrected minor errors, updated figures and
reference
Mapping the Topological Phase Diagram of Multiband Semiconductors with Supercurrents
We show that Josephson junctions made of multiband semiconductors with strong
spin-orbit coupling carry a critical supercurrent that contains
information about the non-trivial topology of the system. In particular, we
find that the emergence and annihilation of Majorana bound states in the
junction is reflected in strong even-odd effects in at small junction
transparency. This effect allows for a mapping between and the
topological phase diagram of the junction, thus providing a dc measurement of
its topology.Comment: 5 pages 3 figures. Published versio
Transport spectroscopy of NS nanowire junctions with Majorana fermions
We investigate transport though normal-superconductor nanowire junctions in
the presence of spin-orbit coupling and magnetic field. As the Zeeman field
crosses the critical bulk value B_c of the topological transition, a Majorana
bound state (MBS) is formed, giving rise to a sharp zero-bias anomaly (ZBA) in
the tunneling differential conductance. We identify novel features beyond this
picture in wires with inhomogeneous depletion, like the appearance of two MBSs
inside a long depleted region for B<B_c. The resulting ZBA is in most cases
weakly split and may coexist with Andreev bound states near zero energy. The
ZBA may appear without evidence of a topological gap closing. This latter
aspect is more evident in the multiband case and stems from a smooth pinch-off
barrier. Most of these features are in qualitative agreement with recent
experiments [Mourik et al, Science 336, 1003 (2012)]. We also discuss the rich
phenomenology of the problem in other regimes which remain experimentally
unexplored.Comment: 10 pages, 12 figures. Published version, supplementary material
include
SNS junctions in nanowires with spin-orbit coupling: role of confinement and helicity on the sub-gap spectrum
We study normal transport and the sub-gap spectrum of
superconductor-normal-superconductor (SNS) junctions made of semiconducting
nanowires with strong Rashba spin-orbit coupling. We focus, in particular, on
the role of confinement effects in long ballistic junctions. In the normal
regime, scattering at the two contacts gives rise to two distinct features in
conductance, Fabry-Perot resonances and Fano dips. The latter arise in the
presence of a strong Zeeman field that removes a spin sector in the leads
(\emph{helical} leads), but not in the central region. Conversely, a helical
central region between non-helical leads exhibits helical gaps of half-quantum
conductance, with superimposed helical Fabry-Perot oscillations. These normal
features translate into distinct subgap states when the leads become
superconducting. In particular, Fabry-Perot resonances within the helical gap
become parity-protected zero-energy states (parity crossings), well below the
critical field at which the superconducting leads become topological. As
a function of Zeeman field or Fermi energy, these zero-modes oscillate around
zero energy, forming characteristic loops, which evolve continuously into
Majorana bound states as exceeds . The relation with the physics of
parity crossings of Yu-Shiba-Rusinov bound states is discussed.Comment: 12 pages main article, 14 figures + 5 pages supplementary material, 5
figures. Added new appendix. Other minor changes. Published versio
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