Spherical Orbifolds for Cosmic Topology

Harmonic analysis is a tool to infer cosmic topology from the measured astrophysical cosmic microwave background CMB radiation. For overall positive curvature, Platonic spherical manifolds are candidates for this analysis. We combine the specific point symmetry of the Platonic manifolds with their deck transformations. This analysis in topology leads from manifolds to orbifolds. We discuss the deck transformations of the orbifolds and give eigenmodes for the harmonic analysis as linear combinations of Wigner polynomials on the 3-sphere. These provide new tools for detecting cosmic topology from the CMB radiation.Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1011.427

Crossover between different regimes of inhomogeneous superconductivity in planar superconductor-ferromagnet hybrids

We studied experimentally the effect of a stripe-like domain structure in a ferromagnetic BaFe_{12}O_{19} substrate on the magnetoresistance of a superconducting Pb microbridge. The system was designed in such a way that the bridge is oriented perpendicular to the domain walls. It is demonstrated that depending on the ratio between the amplitude of the nonuniform magnetic field B_0, induced by the ferromagnet, and the upper critical field H_{c2} of the superconducting material, the regions of the reverse-domain superconductivity in the H-T plane can be isolated or can overlap (H is the external magnetic field, T is temperature). The latter case corresponds to the condition B_0/H_{c2}<1 and results in the formation of superconductivity above the magnetic domains of both polarities. We discovered the regime of edge-assisted reverse-domain superconductivity, corresponding to localized superconductivity near the edges of the bridge above the compensated magnetic domains. Direct verification of the formation of inhomogeneous superconducting states and external-field-controlled switching between normal state and inhomogeneous superconductivity were obtained by low-temperature scanning laser microscopy.Comment: 11 pages, 12 figure

Reverse-domain superconductivity in superconductor-ferromagnet hybrids: effect of a vortex-free channel on the symmetry of I-V characteristics

We demonstrate experimentally that the presence of a single domain wall in an underlying ferromagnetic BaFe_{12}O_{19} substrate can induce a considerable asymmetry in the current (I) - voltage (V) characteristics of a superconducting Al bridge. The observed diode-like effect, i.e. polarity-dependent critical current, is associated with the formation of a vortex-free channel inside the superconducting area which increases the total current flowing through the superconducting bridge without dissipation. The vortex-free region appears only for a certain sign of the injected current and for a limited range of the external magnetic field

Direct Observation of Condon Domains in Silver by Hall Probes

Using a set of micro Hall probes for the detection of the local induction, the inhomogeneous Condon domain structure has been directly observed at the surface of a pure silver single crystal under strong Landau quantization in magnetic fields up to 10 T. The inhomogeneous induction occurs in the theoretically predicted part of the H-T Condon domain phase diagram. Information about size, shape and orientation of the domains is obtained by analyzing Hall probes placed along and across the long sample axis and by tilting the sample. On a beryllium surface the induction inhomogeneity is almost absent although the expected induction splitting here is at least ten times higher than in silver.Comment: 4 pages, 6 figures, submitted to PR

Hysteresis in the de Haas-van Alphen Effect

A hysteresis loop is observed for the first time in the de Haas-van Alphen (dHvA) effect of beryllium at low temperatures and quantizing magnetic field applied parallel to the hexagonal axis of the single crystal. The irreversible behavior of the magnetization occurs at the paramagnetic part of the dHvA period in conditions of Condon domain formation arising by strong enough dHvA amplitude. The resulting extremely nonlinear response to a very small modulation field offers the possibility to find in a simple way the Condon domain phase diagram. From a harmonic analysis, the shape and size of the hysteresis loop is constructed.Comment: 4 pages, 5 figures, submitted to PR

Electron propagation in crossed magnetic and electric fields

Laser-atom interaction can be an efficient mechanism for the production of coherent electrons. We analyze the dynamics of monoenergetic electrons in the presence of uniform, perpendicular magnetic and electric fields. The Green function technique is used to derive analytic results for the field--induced quantum mechanical drift motion of i) single electrons and ii) a dilute Fermi gas of electrons. The method yields the drift current and, at the same time it allows us to quantitatively establish the broadening of the (magnetic) Landau levels due to the electric field: Level number k is split into k+1 sublevels that render the $k$th oscillator eigenstate in energy space. Adjacent Landau levels will overlap if the electric field exceeds a critical strength. Our observations are relevant for quantum Hall configurations whenever electric field effects should be taken into account.Comment: 11 pages, 2 figures, submitte

Revivals of quantum wave-packets in graphene

We investigate the propagation of wave-packets on graphene in a perpendicular magnetic field and the appearance of collapses and revivals in the time-evolution of an initially localised wave-packet. The wave-packet evolution in graphene differs drastically from the one in an electron gas and shows a rich revival structure similar to the dynamics of highly excited Rydberg states. We present a novel numerical wave-packet propagation scheme in order to solve the effective single-particle Dirac-Hamiltonian of graphene and show how the collapse and revival dynamics is affected by the presence of disorder. Our effective numerical method is of general interest for the solution of the Dirac equation in the presence of potentials and magnetic fields.Comment: 22 pages, 10 figures, 3 movies, to appear in New Journal of Physic

Crystallography on Curved Surfaces

We study static and dynamical properties that distinguish two dimensional crystals constrained to lie on a curved substrate from their flat space counterparts. A generic mechanism of dislocation unbinding in the presence of varying Gaussian curvature is presented in the context of a model surface amenable to full analytical treatment. We find that glide diffusion of isolated dislocations is suppressed by a binding potential of purely geometrical origin. Finally, the energetics and biased diffusion dynamics of point defects such as vacancies and interstitials is explained in terms of their geometric potential.Comment: 12 Pages, 8 Figure