Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals

TL;DR

This paper investigates a non-Hermitian quasicrystal model revealing boundary-dependent self-dualities, asymmetrical localization, and topological phase transitions, with potential experimental implications in electric circuits.

Contribution

It introduces boundary-dependent self-dualities and analytically describes asymmetrical localization and topological transitions in a non-Hermitian quasicrystal.

Findings

Localization can occur independently of topological phase transitions.

States are asymmetrically localized due to the non-Hermitian skin effect.

Localized states have energy-independent localization lengths.

Abstract

We study a non-Hermitian Aubry-Andr\'e-Harper model with both nonreciprocal hoppings and complex quasiperiodical potentials, which is a typical non-Hermitian quasicrystal. We introduce boundary-dependent self-dualities in this model and obtain analytical results to describe its Asymmetrical Anderson localization and topological phase transitions. We find that the Anderson localization is not necessarily in accordance with the topological phase transitions, which are characteristics of localization of states and topology of energy spectrum respectively. Furthermore, in the localized phase, single-particle states are asymmetrically localized due to non-Hermitian skin effect and have energy-independent localization lengths. We also discuss possible experimental detections of our results in electric circuits.