Inverse Anderson Transition Caused by Flatbands

Abstract

We propose a new disorder-induced insulator-metal transition of one-electron states, which may be called the "inverse Anderson transition." We first make a highly degenerated localized states by constructing a three-dimensional periodic system possessing only flat dispersion relations. When we introduce a disorder into it, a finite-size scaling of the level statistics shows two clear (localization-delocalization and delocalization-localization) transitions for a wide range of the energy, with increasing the degree of disorder. These transitions are confirmed also by finding the system-size-independent characteristic of the wave function.

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 .…”

Anomalous Minimum and Scaling Behavior of Localization Length Near an Isolated Flat Band

“…A quantity strongly influenced by DOS is the the localization length in a disordered system, and it displays quite different properties depending on whether a flat band is present. For example, previous studies in flat band systems have shown inverse Anderson transition [19], localization with unconventional critical exponents and multi-fractal behavior [20], mobility edges with algebraic singularities [21], and unusual scaling behaviors [22,23].…”

Bosonic Condensation and Disorder-Induced Localization in a Flat Band

“…Another important class of emerging phenomena in flat band systems originates from the effects of disorder, which are enhanced by the very large mass [9] and can significantly deviate from conventional Anderson localization. Examples include the inverse Anderson transition (delocalization transition) [10], localization with unconventional critical exponents and multi-fractal behavior [11], and mobility edges with algebraic singularities [12].…”