Related papers: Random edge states on a finite lattice
We calculate the effect of two kinds of randomness on the hopping of an excitation through a nearly regular Rydberg gas. We present calculations for how fast the excitation can hop away from its starting position for different dimensional…
Random fluctuations of the shot-noise power in disordered graphene nanoribbons are studied. In particular, we calculate the distribution of the shot noise of nanoribbons with zigzag and armchair edge terminations. We show that the shot…
We study a class of periodic Schr\"odinger operators, which in distinguished cases can be proved to have linear band-crossings or "Dirac points". We then show that the introduction of an "edge", via adiabatic modulation of these periodic…
By using two ab initio numerical methods we study the effects that disorder has on the spectral gaps and on wave localization in two-dimensional photonic band gap materials. We find that there are basically two different responses depending…
Bond-disordered Anderson model in two dimensions on a square lattice is studied numerically near the band center by calculating density of states (DoS), multifractal properties of eigenstates and the localization length. DoS divergence at…
We investigate the properties of magnon edge states in a ferromagnetic honeycomb lattice with armchair boundaries. In contrast with fermionic graphene, we find novel edge states due to the missing bonds along the boundary sites. After…
We consider the one-dimensional Dirac equation with the most general relativistic contact interaction supported on two points symmetrically located with respect to the origin. In order to determine the shape of the interaction, we use a…
Tight-binding 1D random system with long-range correlations is studied numerically using the localisation criterium, which represents the number of sites, covered by the wave function. At low degrees of disorder the signs of a mobility…
We study the effects of extended and localized potentials and a magnetic field on the Dirac electrons residing at the surface of a three-dimensional topological insulator. We use a lattice model to numerically study the various states; we…
Topological behavior has been observed in quantum systems including ultracold atoms. However, background harmonic traps for cold-atoms hinder direct detection of topological edge states arising at the boundary because the distortion fuses…
Edge states of photonic crystals have attracted much attention for the potential applications such as high transmission waveguide bends, spin dependent splitters and one-way photonic circuits. Here, we theoretically discuss and…
We investigate experimentally the light evolution inside a two-dimensional finite periodic array of weakly- coupled optical waveguides with a disordered boundary. For a completely localized initial condition away from the surface, we find…
Diffusion of electrons in a two-dimensional system in static random magnetic fields is studied by solving the time-dependent Schr\"{o}dinger equation numerically. The asymptotic behaviors of the second moment of the wave packets and the…
Robust states emerging at the boundary of a system constitute a hallmark for topological band structures. Other than in closed systems, topologically protected states can occur even in systems with a trivial band structure, if exposed to…
We construct and investigate a family of two-band unitary systems living on a cylinder geometry and presenting localized edge states. Using the transfer matrix formalism, we solve and investigate in details such states in the thermodynamic…
We study the localization properties of the two-dimensional Lieb lattice and its extensions in the presence of disorder using transfer matrix method and finite-size scaling. We find that all states in the Lieb lattice and its extensions are…
Flat bands are of significant interest due to their potential for energy confinement and their ability to enable strongly correlated physics. Incorporating topology into flatband systems further enhances flatband mode robustness against…
Particle beam scattering is a conventional technique for detecting the nature of matter. We studied the scattering problem of a cluster connected to multiple leads. We established the connection between the eigenstate of the topological…
An effective-mass theory with a deformation-induced (an axial) gauge field is proposed as a theoretical framework to study graphene edge. Though the gauge field is singular at edge, it can represent the boundary condition and this framework…
Properties of the boundary of two conductors in a quantizing magnetic field are studied: with conventional Dirac charge carriers and so-called pseudospin-1 fermions, which are realized in graphene-like and Lieb lattices respectively. It is…