Localization-Delocalization Transitions in Non-Hermitian Aharonov-Bohm Cages

TL;DR

This paper investigates how non-Hermitian effects, flat bands, and correlated disorder influence localization-delocalization transitions in a one-dimensional rhombic lattice with Aharonov-Bohm cages, revealing conditions for the emergence of the non-Hermitian skin effect.

Contribution

It demonstrates the interplay of point-gap topology, flat bands, and correlated disorder in inducing localization-delocalization transitions and the non-Hermitian skin effect in a rhombic lattice.

Findings

Hermitian lattice shows coexistence of localization and delocalization with disorder.

Non-Hermitian lattice exhibits complete delocalization and NHSE emergence.

Similar NHSE effects are observed due to Bernoulli anti-symmetric disorder.

Abstract

A unique feature of non-Hermitian systems is the extreme sensitivity of the eigenspectrum to boundary conditions with the emergence of the non-Hermitian skin effect (NHSE). A NHSE originates from the point-gap topology of complex eigenspectrum, where an extensive number of eigenstates are anomalously localized at the boundary driven by nonreciprocal dissipation. Two different approaches to create localization are disorder and flat-band spectrum, and their interplay can lead to the anomalous inverse Anderson localization, where the Bernoulli anti-symmetric disorder induce mobility in a full-flat band system in the presence of Aharonov-Bohm (AB) Cage. In this work, we study the localization-delocalization transitions due to the interplay of the point-gap topology, flat band and correlated disorder in the one-dimensional rhombic lattice, where both its Hermitian and non-Hermitian structures show AB cage in the presence of magnetic flux. Although it remains the coexistence of localization and delocalization for the Hermitian rhombic lattice in the presence of the random anti-symmetric disorder, it surprisingly becomes complete delocalization, accompanied by the emergence of NHSE. To further study the effects from the Bernoulli anti-symmetric disorder, we found the similar NHSE due to the interplay of the point-gap topology, correlated disorder and flat bands. Our anomalous localization-delocalization property can be experimentally tested in the classical physical platform, such as electrical circuit.