Disorder perturbed flat bands. II. Search for criticality

Abstract

We present a common mathematical formulation of the level statistics of a disordered tightbinding lattice, with one or many flat bands in clean limit, in which system specific details enters through a single parameter. The formulation, applicable to both single as well as many particle flat bands, indicates the possibility of two different types of critical statistics: one in weak disorder regime (below a system specific disorder strength) and insensitive of the disorder-strength, another in strong disorder regime and occurs at specific critical disorder strengths. The single parametric dependence however relates the statistics in the two regimes (notwithstanding different scattering conditions therein). This also helps in revealing an underlying universality of the statistics in weakly disordered flat bands, shared by a wide-range of other complex systems irrespective of the origin of their complexity.

Flat-band many-body localization and ergodicity breaking in the Creutz ladder

“…Calculations for μ=6 and μ=30 shown in figure 2(a) clearly exhibit this behavior: Poisson→GUE→Poisson. The above behavior of the Creutz ladder model is similar to that in other flat-band models in [60][61][62]. The previous studies focus on a .…”

Flat-band engineering in tight-binding models: Beyond the nearest-neighbor hopping

“…Although the exact flatness will be spoiled by the additional hoppings in the real solid-state systems, our method will serve as a good starting point to search the materials with nearly flat bands penetrating the dispersive bands, which also show the intriguing physics. Studying the properties of those models, such as correlation effects, superconductivity, topological physics, and effects of disorders 58,59,[70][71][72][73] , will be an interesting future problem.…”

Localization, phases, and transitions in three-dimensional extended Lieb lattices

“…Systems that exhibit flat-band physics correspond usually to specially "engineered" lattice structures such as quasi-1D lattices [6,17,18], diamond-type lattices [19], and so-called Lieb lattices, [7,[20][21][22][23][24]. Indeed, the Lieb lattice, a two-dimensional (2D) extension of a simple cubic lattice, was the first where the flat band structure was recognized and used to enhance magnetic effects in model studies [2, 25,26].…”

“…Less attention has been given to 3D flat-band systems [19] or extended Lieb lattices [24,28]. Furthermore, while disorder in quasi-1D [29][30][31][32] and 2D [33] has previously received some attention, comparatively little work has investigated the influence of disorder on 3D flat-band systems [17,34,35]. Recently, instead of concentrating on the properties of flatband states, we investigated how the localization properties in the neighboring dispersive bands are changed by the disorder for 2D flat-band systems [28].…”