3,744 research outputs found
Emergence of massless Dirac fermions in graphene's Hofstadter butterfly at switches of the quantum Hall phase connectivity
The fractal spectrum of magnetic minibands (Hofstadter butterfly), induced by
the moir\'e super- lattice of graphene on an hexagonal crystal substrate, is
known to exhibit gapped Dirac cones. We show that the gap can be closed by
slightly misaligning the substrate, producing a hierarchy of conical
singularities (Dirac points) in the band structure at rational values Phi =
(p/q)(h/e) of the magnetic flux per supercell. Each Dirac point signals a
switch of the topological quantum number in the connected component of the
quantum Hall phase diagram. Model calculations reveal the scale invariant
conductivity sigma = 2qe^2 / pi h and Klein tunneling associated with massless
Dirac fermions at these connectivity switches.Comment: 4 pages, 6 figures + appendix (3 pages, 1 figure
Theory of the topological Anderson insulator
We present an effective medium theory that explains the disorder-induced
transition into a phase of quantized conductance, discovered in computer
simulations of HgTe quantum wells. It is the combination of a random potential
and quadratic corrections proportional to p^2 sigma_z to the Dirac Hamiltonian
that can drive an ordinary band insulator into a topological insulator (having
an inverted band gap). We calculate the location of the phase boundary at weak
disorder and show that it corresponds to the crossing of a band edge rather
than a mobility edge. Our mechanism for the formation of a topological Anderson
insulator is generic, and would apply as well to three-dimensional
semiconductors with strong spin-orbit coupling.Comment: 4 pages, 3 figures (updated figures, calculated DOS
Andreev reflection from a topological superconductor with chiral symmetry
It was pointed out by Tewari and Sau that chiral symmetry (H -> -H if e
h) of the Hamiltonian of electron-hole (e-h) excitations in an N-mode
superconducting wire is associated with a topological quantum number
Q\in\mathbb{Z} (symmetry class BDI). Here we show that Q=Tr(r_{he}) equals the
trace of the matrix of Andreev reflection amplitudes, providing a link with the
electrical conductance G. We derive G=(2e^2/h)|Q| for |Q|=N,N-1, and more
generally provide a Q-dependent upper and lower bound on G. We calculate the
probability distribution P(G) for chaotic scattering, in the circular ensemble
of random-matrix theory, to obtain the Q-dependence of weak localization and
mesoscopic conductance fluctuations. We investigate the effects of chiral
symmetry breaking by spin-orbit coupling of the transverse momentum (causing a
class BDI-to-D crossover), in a model of a disordered semiconductor nanowire
with induced superconductivity. For wire widths less than the spin-orbit
coupling length, the conductance as a function of chemical potential can show a
sequence of 2e^2/h steps - insensitive to disorder.Comment: 10 pages, 5 figures. Corrected typo (missing square root) in
equations A13 and A1
Majorana bound states without vortices in topological superconductors with electrostatic defects
Vortices in two-dimensional superconductors with broken time-reversal and
spin-rotation symmetry can bind states at zero excitation energy. These
socalled Majorana bound states transform a thermal insulator into a thermal
metal and may be used to encode topologically protected qubits. We identify an
alternative mechanism for the formation of Majorana bound states, akin to the
way in which Shockley states are formed on metal surfaces: An atomic-scale
electrostatic line defect can have a pair of Majorana bound states at the end
points. The Shockley mechanism explains the appearance of a thermal metal in
vortex-free lattice models of chiral p-wave superconductors and (unlike the
vortex mechanism) is also operative in the topologically trivial phase.Comment: 8 pages, 7 figures; the appendices are included as supplemental
material in the published versio
Phase-locked magnetoconductance oscillations as a probe of Majorana edge states
We calculate the Andreev conductance of a superconducting ring interrupted by
a flux-biased Josephson junction, searching for electrical signatures of
circulating edge states. Two-dimensional pair potentials of spin-singlet d-wave
and spin-triplet p-wave symmetry support, respectively, (chiral) Dirac modes
and (chiral or helical) Majorana modes. These produce h/e-periodic
magnetoconductance oscillations of amplitude \simeq (e^{2}/h)N^{-1/2}, measured
via an N-mode point contact at the inner or outer perimeter of the grounded
ring. For Dirac modes the oscillations in the two contacts are independent,
while for an unpaired Majorana mode they are phase locked by a topological
phase transition at the Josephson junction.Comment: 10 pages, 6 figures. New appendix on the gauge invariant
discretization of the Bogoliubov-De Gennes equation. Accepted for publication
in PR
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
Wigner-Poisson statistics of topological transitions in a Josephson junction
The phase-dependent bound states (Andreev levels) of a Josephson junction can
cross at the Fermi level, if the superconducting ground state switches between
even and odd fermion parity. The level crossing is topologically protected, in
the absence of time-reversal and spin-rotation symmetry, irrespective of
whether the superconductor itself is topologically trivial or not. We develop a
statistical theory of these topological transitions in an N-mode quantum-dot
Josephson junction, by associating the Andreev level crossings with the real
eigenvalues of a random non-Hermitian matrix. The number of topological
transitions in a 2pi phase interval scales as sqrt(N) and their spacing
distribution is a hybrid of the Wigner and Poisson distributions of
random-matrix theory.Comment: 12 pages, 15 figures; v2 to appear in PRL, with appendix in the
supplementary materia
Graphene Rings in Magnetic Fields: Aharonov-Bohm Effect and Valley Splitting
We study the conductance of mesoscopic graphene rings in the presence of a
perpendicular magnetic field by means of numerical calculations based on a
tight-binding model. First, we consider the magnetoconductance of such rings
and observe the Aharonov-Bohm effect. We investigate different regimes of the
magnetic flux up to the quantum Hall regime, where the Aharonov-Bohm
oscillations are suppressed. Results for both clean (ballistic) and disordered
(diffusive) rings are presented. Second, we study rings with smooth mass
boundary that are weakly coupled to leads. We show that the valley degeneracy
of the eigenstates in closed graphene rings can be lifted by a small magnetic
flux, and that this lifting can be observed in the transport properties of the
system.Comment: 12 pages, 9 figure
Ettingshausen effect due to Majorana modes
The presence of Majorana zero-energy modes at vortex cores in a topological
superconductor implies that each vortex carries an extra entropy , given
by , that is independent of temperature. By utilizing this
special property of Majorana modes, the edges of a topological superconductor
can be cooled (or heated) by the motion of the vortices across the edges. As
vortices flow in the transverse direction with respect to an external imposed
supercurrent, due to the Lorentz force, a thermoelectric effect analogous to
the Ettingshausen effect is expected to occur between opposing edges. We
propose an experiment to observe this thermoelectric effect, which could
directly probe the intrinsic entropy of Majorana zero-energy modes.Comment: 16 pages, 3 figure
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