Delocalization and re-entrant localization of flat-band states in non-Hermitian disordered lattice models with flat bands

TL;DR

This study numerically investigates how non-Hermitian disorder affects flat-band states, revealing a unique double transition from localization to delocalization and back, driven by an imaginary vector potential.

Contribution

It uncovers the re-entrant localization phenomenon in flat-band states caused by the interplay of disorder and non-Hermiticity, a novel insight in non-Hermitian lattice models.

Findings

Flat-band states undergo double localization-delocalization transition.

Participation ratio and winding number indicate delocalization and re-entrant localization.

Re-entrant localization occurs at specific critical values of the imaginary vector potential.

Abstract

We present a numerical study of Anderson localization in disordered non-Hermitian lattice models with flat bands. Specifically we consider one-dimensional stub and two-dimensional kagome lattices that have a random scalar potential and a uniform imaginary vector potential and calculate the spectra of the complex energy, the participation ratio, and the winding number as a function of the strength of the imaginary vector potential, $h$. The flat-band states are found to show a double transition from localized to delocalized and back to localized states with $h$, in contrast to the dispersive-band states going through a single delocalization transition. When $h$ is sufficiently small, all flat-band states are localized. As $h$ increases above a certain critical value $h_1$, some pair of flat-band states become delocalized. The participation ratio associated with them increases substantially and their winding numbers become nonzero. As $h$ increases further, more and more flat-band states get delocalized until the fraction of the delocalized states reaches a maximum. For larger $h$ values, a re-entrant localization takes place and, at another critical value $h_2$, all flat-band states return to compact localized states with very small participation ratios and zero winding numbers. This re-entrant localization transition, which is due to the interplay among disorder, non-Hermiticity, and flat band, is a phenomenon occurring in many models having an imaginary vector potential and a flat band simultaneously. We explore the spatial characteristics of the flat-band states by calculating the local density distribution.