3,943 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
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
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
Weak localization in mesoscopic hole transport: Berry phases and classical correlations
We consider phase-coherent transport through ballistic and diffusive
two-dimensional hole systems based on the Kohn-Luttinger Hamiltonian. We show
that intrinsic heavy-hole light-hole coupling gives rise to clear-cut
signatures of an associated Berry phase in the weak localization which renders
the magneto-conductance profile distinctly different from electron transport.
Non-universal classical correlations determine the strength of these Berry
phase effects and the effective symmetry class, leading even to
antilocalization-type features for circular quantum dots and Aharonov-Bohm
rings in the absence of additional spin-orbit interaction. Our semiclassical
predictions are quantitatively confirmed by numerical transport calculations
One-loop surface tensions of (supersymmetric) kink domain walls from dimensional regularization
We consider domain walls obtained by embedding the 1+1-dimensional
-kink in higher dimensions. We show that a suitably adapted dimensional
regularization method avoids the intricacies found in other regularization
schemes in both supersymmetric and non-supersymmetric theories. This method
allows us to calculate the one-loop quantum mass of kinks and surface tensions
of kink domain walls in a very simple manner, yielding a compact d-dimensional
formula which reproduces many of the previous results in the literature. Among
the new results is the nontrivial one-loop correction to the surface tension of
a 2+1 dimensional N=1 supersymmetric kink domain wall with chiral domain-wall
fermions.Comment: 23 pages, LATeX; v2: 25 pages, 2 references added, extended
discussion of renormalization schemes which dispels apparent contradiction
with previous result
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
Visual Experience Shapes Orthographic Representations in the Visual Word Form Area
Current neurocognitive research suggests that the efficiency of visual word recognition rests on abstract memory representations of written letters and words stored in the visual word form area (VWFA) in the left ventral occipitotemporal cortex. These representations are assumed to be invariant to visual characteristics such as font and case. In the present functional MRI study, we tested this assumption by presenting written words and varying the case format of the initial letter of German nouns (which are always capitalized) as well as German adjectives and adverbs (both usually in lowercase). As evident from a Word Type Ă— Case Format interaction, activation in the VWFA was greater to words presented in unfamiliar case formats relative to familiar case formats. Our results suggest that neural representations of written words in the VWFA are not fully abstract and still contain information about the visual format in which words are most frequently perceived
- …