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

Bimodal conductance distribution of Kitaev edge modes in topological superconductors

A two-dimensional superconductor with spin-triplet p-wave pairing supports chiral or helical Majorana edge modes with a quantized (length $L$-independent) thermal conductance. Sufficiently strong anisotropy removes both chirality and helicity, doubling the conductance in the clean system and imposing a super-Ohmic $1/\sqrt{L}$ decay in the presence of disorder. We explain the absence of localization in the framework of the Kitaev Hamiltonian, contrasting the edge modes of the two-dimensional system with the one-dimensional Kitaev chain. While the disordered Kitaev chain has a log-normal conductance distribution peaked at an exponentially small value, the Kitaev edge has a bimodal distribution with a second peak near the conductance quantum. Shot noise provides an alternative, purely electrical method of detection of these charge-neutral edge modes.Comment: 11 pages, 13 figure

Extended topological group structure due to average reflection symmetry

We extend the single-particle topological classification of insulators and superconductors to include systems in which disorder preserves average reflection symmetry. We show that the topological group structure of bulk Hamiltonians and topological defects is exponentially extended when this additional condition is met, and examine some of its physical consequences. Those include localization-delocalization transitions between topological phases with the same boundary conductance, as well as gapless topological defects stabilized by average reflection symmetry.Comment: 8 pages, 5 figures, 1 table; improved section 4 "Extended topological classification" incl. example of stacked QSH layer

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

Pilot study of vegetation in the Alchichica-Perote region by remote sensing

A study of the application of satellite images to the identification of vegetation in a small area corresponding to the arid zone of Veracruz and part of Puebla is presented. This study is accomplished by means of images from the LANDSAT satellite obtained on January 19 and May 23, 1973. The interpretation of the different maps is made on the basis of information from the data bank of the Flora de Veracruz program, and various surveys made by land and air

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

Topologically protected charge transfer along the edge of a chiral p\textit{p}-wave superconductor

The Majorana fermions propagating along the edge of a topological superconductor with $p_x+ip_y$ pairing deliver a shot noise power of $\frac{1}{2}\times e^2/h$ per eV of voltage bias. We calculate the full counting statistics of the transferred charge and find that it becomes trinomial in the low-temperature limit, distinct from the binomial statistics of charge-$e$ transfer in a single-mode nanowire or charge-$2e$ transfer through a normal-superconductor interface. All even-order correlators of current fluctuations have a universal quantized value, insensitive to disorder and decoherence. These electrical signatures are experimentally accessible, because they persist for temperatures and voltages large compared to the Thouless energy.Comment: 5 pages, 4 figures. v3 [post-publication]: added an appendix on the effect of a tunnel barrier at the normal-superconductor contac