Light propagation in binary kagome ribbons with evolving disorder

Abstract

By introducing evolving disorder in the binary kagome ribbons, we study the establishment of diffusive spreading of flat band states characterized by diffractionless propagation in regular periodic ribbons. Our numerical analysis relies on controlling strength and rate of change of disorder during light propagation while tailoring binarism of the kagome ribbons in order to isolate the flat band with the gap from the rest of the ribbon's eigenvalue spectrum and study systematically its influence on diffusion. We show that the flat band plays a dominant role in the establishment of the diffusion for a given strength and rate of change of disorder, whereas the rest of the ribbon's eigenvalue spectrum induces only quantitative differences in the light spreading regimes. Due to the universality of studied phenomena, our findings may be of interest in various disordered physical systems with flat spectral bands, ranging from photonics to ultracold matter systems and plasmonics.

Artificial flat band systems: from lattice models to experiments

“…Such localization-delocalization-localization behaviour as a function of the disorder strength also occurs in the level spacing statistics of certain twodimensional flat bands [55]. In the past year flat bands under non-quenched (evolving) disorder [56], disorderinduced topological phase transitions [57], and the temporal dynamics of disordered flat band states [58] started to attract attention too.…”

Lifetime of flatband states

“…While an ideal flatband allows the distortion-free storage of compact localized states of tailorable shape, a disorder potential causes distortion and, in the vicinity of intersections (yellow areas), to a coupling into the dispersive band, limiting the state's reliable storage sojourn in the flatband. studies on the impact of perturbations in flatband scenarios [26,[28][29][30][31][32][33][34][35][36][37], e.g., describing the flatband-modified propagation in dispersive bands. We identify and characterize a generic, disorder-induced decay mechanism for flatband states, lifting their static nature and causing their effective diffusion, despite the absence of a kinetic term.…”

Influence of different disorder types on Aharonov-Bohm caging in the diamond chain

“…These equations are obtained by averaging over high frequency modulation in z and can thus host both QDs and NQDs. The jn terms describe the on-site disorder potential, which we model as [29]…”

“…The consequences of mixing between the FB and DB states in the presence of weak disorder were the appearance of heavy tailed statistics and multiple localization length scales generically related to the existence of sparse, multi-peaked modes. In the case of gapped FB states weak disorder was not strong enough to cause mixing of FB and DB states, so the localization length was independent of the disorder strength [29]. However, disorder affected the mode behavior via appearance of tails in the FB states' profiles, and finally in the presence of strong disorder the mode profiles resembled those of ordinary Anderson localization.…”

“…We can understand the effect of the periodic disorder on the wavepacket spreading following the approach in Refs. [29,30]. Based on perturbation theory for linear systems in the presence of time-dependent perturbations, we expect to see transitions between different static eigenstates.…”