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

Stagnation Temperature Recording

The present report deals with the development of a thermometer for recording stagnation temperature in compressible mediums in turbulent flow within 1 to 2 percent error of the adiabatic temperature in the stagnation point, depending upon the speed. This was achieved by placing the junction of a thermocouple near the stagnation point of an aerodynamically beneficial body, special care being taken to assure an uninterrupted supply of fresh compressed air on the junction together with the use of metals of low thermal conductivity, thus keeping heat-transfer and heat-dissipation losses to a minimum. In other experiments the use of the plate thermometer was proved unsuitable for practical measurements by reason of its profound influence in the reading by the Reynolds number and by the direction of flow

Fibroblast growth factor receptor 4 single nucleotide polymorphism Gly388Arg in head and neck carcinomas

BACKGROUND Head and neck squamous cell carcinoma (HNSCC) is considered to be a progressive disease resulting from alterations in multiple genes regulating cell proliferation and differentiation like receptor tyrosine kinases (RTKs) and members of the fibroblast growth factor receptors (FGFR)-family. Single-nucleotide polymorphism (SNP) Arg388 of the FGFR4 is associated with a reduced overall survival in patients with cancers of various types. We speculate that FGFR4 expression and SNP is associated with worse survival in patients with HSNCC. AIM To investigate the potential clinical significance of FGFR4 Arg388 in the context of tumors arising in HNSCC, a comprehensive analysis of FGFR4 receptor expression and genotype in tumor tissues and correlated results with patients' clinical data in a large cohort of patients with HNSCC was conducted. METHODS Surgical specimens from 284 patients with HNSCC were retrieved from the Institute of Pathology at the Ludwig-Maximilian-University in Germany. Specimens were analyzed using immunohistochemistry and polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP). The expression of FGFR4 was analyzed in 284 surgical specimens of HNSCC using immunohistochemstry. FGFR4 polymorphism was detected by PCR-RFLP. Patients' clinical data with a minimum follow-up of 5 syears were statistically evaluated with a special emphasis on survival analysis employing Kaplan-Meier estimator and Cox regression analysis. RESULTS Concerning the invasive tumor areas the intensity of the FGFR4 expression was evaluated in a four-grade system: no expression, low expression, intermediate and high expression. FGFR4 expression was scored as "high" (+++) in 74 (26%), "intermediate" (++) in 103 (36.3%), and "low" (+) in 107 (36.7%) cases. Analyzing the FGFR4 mutation it was found in 96 tumors (33.8%), 84 of them (29.6%) having a heterozygous and 12 (4.2%) homozygous mutated Arg388 allele. The overall frequency concerning the mutant alleles demonstrated 65% vs 34% mutated alleles in general. FGFR4 Arg388 was significantly associated with advanced tumor stage (P < 0.004), local metastasis (P < 0.0001) and reduced disease-free survival (P < 0.01). Furthermore, increased expression of FGFR4 correlated significantly with worse overall survival (P < 0.003). CONCLUSION In conclusion, the FGFR4 Arg388 genotype and protein expression of FGFR4 impacts tumor progression in patients with HNSCC and may present a useful target within a multimodal therapeutic intervention

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

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

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

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

Barrier transmission of Dirac-like pseudospin-one particles

We address the problem of barrier tunneling in the two-dimensional T_3 lattice (dice lattice). In particular we focus on the low-energy, long-wavelength approximation for the Hamiltonian of the system, where the lattice can be described by a Dirac-like Hamiltonian associated with a pseudospin one. The enlarged pseudospin S = 1 (instead of S = 1/2 as for graphene) leads to an enhanced "super" Klein tunneling through rectangular electrostatic barriers. Our results are confirmed via numerical investigation of the tight-binding model of the lattice. For a uniform magnetic field, we discuss the Landau levels and we investigate the transparency of a rectangular magnetic barrier. We show that the latter can mainly be described by semiclassical orbits bending the particle trajectories, qualitatively similar as it is the case for graphene. This makes it possible to confine particles with magnetic barriers of sufficient width