Landau levels in quasicrystals

Two-dimensional tight-binding models for quasicrystals made of plaquettes with commensurate areas are considered. Their energy spectrum is computed as a function of an applied perpendicular magnetic field. Landau levels are found to emerge near band edges in the zero-field limit. Their existence is related to an effective zero-field dispersion relation valid in the continuum limit. For quasicrystals studied here, an underlying periodic crystal exists and provides a natural interpretation to this dispersion relation. In addition to the slope (effective mass) of Landau levels, we also study their width as a function of the magnetic flux per plaquette and identify two fundamental broadening mechanisms: (i) tunneling between closed cyclotron orbits and (ii) individual energy displacement of states within a Landau level. Interestingly, the typical broadening of the Landau levels is found to behave algebraically with the magnetic field with a nonuniversal exponent.Comment: 14 pages, 9 figure

Aharonov-Bohm cages in two-dimensional structures

We present an extreme localization mechanism induced by a magnetic field for tight-binding electrons in two-dimensional structures. This spectacular phenomenon is investigated for a large class of tilings (periodic, quasiperiodic, or random). We are led to introduce the Aharonov-Bohm cages defined as the set of sites eventually visited by a wavepacket that can, for particular values of the magnetic flux, be bounded. We finally discuss the quantum dynamics which exhibits an original pulsating behaviour.Comment: 4 pages Latex, 3 eps figures, 1 ps figur

Optimum Placement of Post-1PN GW Chirp Templates Made Simple at any Match Level via Tanaka-Tagoshi Coordinates

A simple recipe is given for constructing a maximally sparse regular lattice of spin-free post-1PN gravitational wave chirp templates subject to a given minimal match constraint, using Tanaka-Tagoshi coordinates.Comment: submitted to Phys. Rev.

Quasiperiodic tilings under magnetic field

We study the electronic properties of a two-dimensional quasiperiodic tiling, the isometric generalized Rauzy tiling, embedded in a magnetic field. Its energy spectrum is computed in a tight-binding approach by means of the recursion method. Then, we study the quantum dynamics of wave packets and discuss the influence of the magnetic field on the diffusion and spectral exponents. Finally, we consider a quasiperiodic superconducting wire network with the same geometry and we determine the critical temperature as a function of the magnetic field.Comment: 6 pages, 5 EPS figure

Topological models in rotationally symmetric quasicrystals

We investigate the physics of quasicrystalline models in the presence of a uniform magnetic field, focusing on the presence and construction of topological states. This is done by using the Hofstadter model but with the sites and couplings denoted by the vertex model of the quasicrystal, giving the Hofstadter vertex model. We specifically consider two-dimensional quasicrystals made from tilings of two tiles with incommensurate areas, focusing on the five-fold Penrose and the eight-fold Ammann-Beenker tilings. This introduces two competing scales; the uniform magnetic field and the incommensurate scale of the cells of the tiling. Due to these competing scales the periodicity of the Hofstadter butterfly is destroyed. We observe the presence of topological edge states on the boundary of the system via the Bott index that exhibit two way transport along the edge. For the eight-fold tiling we also observe internal edge-like states with non-zero Bott index, which exhibit two way transport along this internal edge. The presence of these internal edge states is a new characteristic of quasicrystalline models in magnetic fields. We then move on to considering interacting systems. This is challenging, in part because exact diagonalization on a few tens of sites is not expected to be enough to accurately capture the physics of the quasicrystalline system, and in part because it is not clear how to construct topological flatbands having a large number of states. We show that these problems can be circumvented by building the models analytically, and in this way we construct models with Laughlin type fractional quantum Hall ground states.Comment: 13 pages, 16 figures, published PR

Geometrical characterization of textures consisting of two or three discrete colorings

Geometrical characterization for discretized contrast textures is realized by computing the Gaussian and mean curvatures relative to the central pixel of a clique and four neighboring pixels, these four neighbors either being first or second order neighbors. Practical formulae for computing these curvatures are presented. Curvatures based on the central pixel depend upon the brightness configuration of the clique pixels. Therefore the cliques are classified into classes by configuration of pixel contrast or coloring. To look at the textures formed by geometrically classified cliques, we create several textures using overlapping tiling of cliques belonging to a single curvature class. Several examples of hyperbolic textures, consisting of repeated hyperbolic cliques surrounded by non-hyperbolic cliques, are presented with the nonhyperbolic textures. We also introduce a system of 81 rotationally and brightness shift invariant geo-cliques that have shared curvatures and show that histograms of these 81 geo-cliques seem to be able to distinguish isotrigon textures