Related papers: Disorder effects in the two-dimensional Lieb latti…
We investigate the propagation of waves in one-dimensional systems with L\'evy-type disorder. We perform a complete analysis of non-relativistic and relativistic wave transmission submitted to potential barriers whose width, separation or…
The collective electronic properties of various types of pseudospin-$1$ Dirac-cone materials with a flat band and finite bangaps in their energy spectra are the subject of our reported investigation. Specifically, we have calculated the…
Recently, several experiments have illustrated that metal surface electrons can be manipulated to form a two dimensional (2D) lattice by depositing a designer molecule lattice on metal surface. This offers a promising new technique to…
We present, theoretically and experimentally, amorphous photonic lattices exhibiting a band-gap yet completely lacking Bragg diffraction: 2D waveguides distributed randomly according to a liquid-like model responsible for the absence of…
We consider a disordered two-dimensional system of independent lattice electrons in a perpendicular magnetic field with rigid confinement in one direction and generalized periodic boundary conditions (GPBC) in the other direction. The…
The paper investigates localized deformation patterns resulting from the onset of instabilities in lattice structures. The study is motivated by previous observations on discrete hexagonal lattices, where the onset of non-uniform,…
We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of…
We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of…
The behavior of extended states is quantitatively analyzed for two dimensional lattice models. A levitation picture is established for both white-noise and correlated disorder potentials. In a continuum limit window of the lattice models we…
We present a numerical study on the light transport properties which are modulated by the disorder strength in quasi-one-dimensional disordered waveguide which consists of periodically arranged scatterers with random dielectric constant.…
The spectral approach to infinite disordered crystals is applied to an Anderson-type Hamiltonian to demonstrate the existence of extended states for nonzero disorder in 2D lattices of different geometries. The numerical simulations shown…
We study two coupled 3D lattices, one of them featuring uncorrelated on-site disorder and the other one being fully ordered, and analyze how the interlattice hopping affects the localization-delocalization transition of the former and how…
This paper extends an earlier analytical scattering matrix treatment of conductance and localization in coupled two- and three Anderson chain systems for weak disorder when evanescent states are present at the Fermi level. Such states exist…
Light localization by scattering is a fundamental mechanism driving phase transitions of wave transport in disordered systems. Characterizing the localization length in scattering systems is crucial yet challenging. In this Letter, we…
We address the issue of nonlinear modes in a two-dimensional waveguide array, spatially distributed in the Lieb lattice geometry, and modeled by a saturable nonlinear Schr\"odinger equation. In particular, we analyze the existence and…
Photonic lattices facilitate band structure engineering, supporting both localized and extended modes through their geometric design. However, greater control over these modes can be achieved by taking advantage of the interference effect…
We have studied the peculiarities of electron transport in one-dimensional (1D) disordered chain at the presence of correlations between on-site interaction and tunneling integrals. In the considered models the disorder in host-lattice…
The exploration of flatband in photonics is fundamentally important, aiming to control the localization of light for potential applications in optical communications. We study the flatband physics in a synthetic space including the…
The flat band localization, as an important phenomenon in solid state physics, is fundamentally interesting in the exploration of exotic ground property of many-body system. Here we demonstrate the appearance of a flat band in a general…
We study the effect of weak disorder on the delocalization properties of gapped graphene superlattice (SL) formed by periodically located rectangular potential barriers. We consider two types of the SLs: the SLs with uniform and nonuniform…