Flatbands under Correlated Perturbations

Abstract

Flatband networks are characterized by the coexistence of dispersive and flatbands. Flatbands (FBs) are generated by compact localized eigenstates (CLSs) with local network symmetries, based on destructive interference. Correlated disorder and quasiperiodic potentials hybridize CLSs without additional renormalization, yet with surprising consequences: (i) states are expelled from the FB energy E_{FB}, (ii) the localization length of eigenstates vanishes as ξ∼1/ln(E-E_{FB}), (iii) the density of states diverges logarithmically (particle-hole symmetry) and algebraically (no particle-hole symmetry), and (iv) mobility edge curves show algebraic singularities at E_{FB}. Our analytical results are based on perturbative expansions of the CLSs and supported by numerical data in one and two lattice dimensions.

Localized gap modes in nonlinear dimerized Lieb lattices

“…Seminal papers showed that interesting effects in condensed matter systems [14][15][16] are observed. Additionally, the influence of the singularity of flat band systems was investigated in the frame of the fractional quantum and magnon Hall effect [17,18] and energy localization in the presence of magnetic fields [19], spin-orbit coupling [20,21], or disorder [22,23]. Recently this topic attracted a lot of attention.…”

Interdimensional optical isospectrality inspired by graph networks

“…The fragile degeneracy guarantees the presence of a connected 1D structure that has an identical spectral response to that of a 3D disordered structure. Our results thus extend the field of correlated disorder [1,2,8,10,14,32] into network-like level statistics.Our approach utilizing the Hamiltonian transformation allows the finding of 1D isospectral structures from random networks deterministically, in contrast to numerical searching techniques, e.g. genetic algorithm.…”

“…Due to the critical needs in light harvesting [6], robust bandgaps [7,8], and ultrafast optics [9], disordered optical materials have also been intensively studied to exploit their broadband responses. Although one-(1D) [8,10], two-(2D) [1,11,12], and three-dimensional (3D) [13] disordered structures have been considered promising candidates for broadband and omnidirectional operations, the deliberate control of disordered structures [1,3,7,8,14] has been achieved only in 1D or 2D structures, owing to the difficulty of manipulating 3D randomness.To understand the role of the 'dimension' in optics, we can employ the interdisciplinary viewpoint from network theory. For the structures composed of coupled resonances, light flows inside those can be interpreted as signal transport over graph networks [14][15][16][17].…”

“…Although one-(1D) [8,10], two-(2D) [1,11,12], and three-dimensional (3D) [13] disordered structures have been considered promising candidates for broadband and omnidirectional operations, the deliberate control of disordered structures [1,3,7,8,14] has been achieved only in 1D or 2D structures, owing to the difficulty of manipulating 3D randomness.…”

Nonlinear localized flat-band modes with spin-orbit coupling

“…The CLS existence has been experimentally probed in the same settings where FB lattices may be realized, as mentioned above: waveguiding arrays [7][8][9], exciton-polariton condensates [10], and atomic BECs [4]. The impact of various perturbations, such as disorder [5,11], correlated potentials [12,13], and external magnetic and electric fields [14], on FB lattices and the corresponding CLSs was studied too.…”