533 research outputs found
Quantized conductance at the Majorana phase transition in a disordered superconducting wire
Superconducting wires without time-reversal and spin-rotation symmetries can
be driven into a topological phase that supports Majorana bound states. Direct
detection of these zero-energy states is complicated by the proliferation of
low-lying excitations in a disordered multi-mode wire. We show that the phase
transition itself is signaled by a quantized thermal conductance and electrical
shot noise power, irrespective of the degree of disorder. In a ring geometry,
the phase transition is signaled by a period doubling of the magnetoconductance
oscillations. These signatures directly follow from the identification of the
sign of the determinant of the reflection matrix as a topological quantum
number.Comment: 7 pages, 4 figures; v3: added appendix with numerics for long-range
disorde
Geodesic scattering by surface deformations of a topological insulator
We consider the classical ballistic dynamics of massless electrons on the
conducting surface of a three-dimensional topological insulator, influenced by
random variations of the surface height. By solving the geodesic equation and
the Boltzmann equation in the limit of shallow deformations, we obtain the
scattering cross section and the conductivity {\sigma}, for arbitrary
anisotropic dispersion relation. At large surface electron densities n this
geodesic scattering mechanism (with {\sigma} propto sqrt{n}) is more effective
at limiting the surface conductivity than electrostatic potential scattering.Comment: 9 pages, 5 figure
Seismic monitoring and verification for the Co2CRC Ottway Basin project
The Otway Project conducted under the Australian Cooperative Research Centre for Greenhouse Gas Technologies (CO2CRC) is the first of its kind, where CO2 is injected into a depleted gas reservoir. The use of depleted fields for CO2 storage is likely to become widely adopted globally and, therefore, the project will provide important experience for monitoring under these conditions. However, such scenario is not favorable for the application of geophysical techniques for the purpose of CO2 monitoring and verification (M&V) because the injection of CO2 into a CH4 depleted reservoir is modeled to produce very subtle changes in elastic properties of the reservoir rock which may be very difficult to measure. Consequently geophysical program for the Otway site was design according to the expected time-lapse effects. It combines both surface and borehole seismic methods. Surface seismic should provide a global vision of the underground and an indirect confirmation of the CO2 containment by recording no differences between the successive time-lapse experiments. Vertical Seismic Profile (VSP) surveys are expected to provide an improved characterization of the reservoir and hopefully a direct indication of the fluid distribution and/or its potential upward migration along the reservoir bounding fault pattern. Indeed the results of the current analysis of both pre-base line (test) and base-line 2D and 3D VSP data are encouraging. The availability of vector wave field (three-component) data recorded in VSP surveys should significantly improve the outcomes of M&V program at Naylor site
Quantum point contact as a probe of a topological superconductor
We calculate the conductance of a ballistic point contact to a
superconducting wire, produced by the s-wave proximity effect in a
semiconductor with spin-orbit coupling in a parallel magnetic field. The
conductance G as a function of contact width or Fermi energy shows plateaus at
half-integer multiples of 4e^2/h if the superconductor is in a topologically
nontrivial phase. In contrast, the plateaus are at the usual integer multiples
in the topologically trivial phase. Disorder destroys all plateaus except the
first, which remains precisely quantized, consistent with previous results for
a tunnel contact. The advantage of a ballistic contact over a tunnel contact as
a probe of the topological phase is the strongly reduced sensitivity to finite
voltage or temperature.Comment: 6 pages, 6 figures; corrected App.
Covering problems in edge- and node-weighted graphs
This paper discusses the graph covering problem in which a set of edges in an
edge- and node-weighted graph is chosen to satisfy some covering constraints
while minimizing the sum of the weights. In this problem, because of the large
integrality gap of a natural linear programming (LP) relaxation, LP rounding
algorithms based on the relaxation yield poor performance. Here we propose a
stronger LP relaxation for the graph covering problem. The proposed relaxation
is applied to designing primal-dual algorithms for two fundamental graph
covering problems: the prize-collecting edge dominating set problem and the
multicut problem in trees. Our algorithms are an exact polynomial-time
algorithm for the former problem, and a 2-approximation algorithm for the
latter problem, respectively. These results match the currently known best
results for purely edge-weighted graphs.Comment: To appear in SWAT 201
Dependence Logic with Generalized Quantifiers: Axiomatizations
We prove two completeness results, one for the extension of dependence logic
by a monotone generalized quantifier Q with weak interpretation, weak in the
meaning that the interpretation of Q varies with the structures. The second
result considers the extension of dependence logic where Q is interpreted as
"there exists uncountable many." Both of the axiomatizations are shown to be
sound and complete for FO(Q) consequences.Comment: 17 page
Zero-voltage conductance peak from weak antilocalization in a Majorana nanowire
We show that weak antilocalization by disorder competes with resonant Andreev
reflection from a Majorana zero-mode to produce a zero-voltage conductance peak
of order e^2/h in a superconducting nanowire. The phase conjugation needed for
quantum interference to survive a disorder average is provided by particle-hole
symmetry - in the absence of time-reversal symmetry and without requiring a
topologically nontrivial phase. We identify methods to distinguish the Majorana
resonance from the weak antilocalization effect.Comment: 13 pages, 8 figures. Addendum, February 2014: Appendix B shows
results for weak antilocalization in the circular ensemble. (This appendix is
not in the published version.
Random-matrix theory of Andreev reflection from a topological superconductor
We calculate the probability distribution of the Andreev reflection
eigenvalues R_n at the Fermi level in the circular ensemble of random-matrix
theory. Without spin-rotation symmetry, the statistics of the electrical
conductance G depends on the topological quantum number Q of the
superconductor. We show that this dependence is nonperturbative in the number N
of scattering channels, by proving that the p-th cumulant of G is independent
of Q for p<N/d (with d=2 or d=1 in the presence or in the absence of
time-reversal symmetry). A large-N effect such as weak localization cannot,
therefore, probe the topological quantum number. For small N we calculate the
full distribution P(G) of the conductance and find qualitative differences in
the topologically trivial and nontrivial phases.Comment: 13 pages, 4 figures (published version
Advances on Testing C-Planarity of Embedded Flat Clustered Graphs
We show a polynomial-time algorithm for testing c-planarity of embedded flat
clustered graphs with at most two vertices per cluster on each face.Comment: Accepted at GD '1
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