Generalized Aubry-Andr\'e self-duality and Mobility edges in non-Hermitian quasi-periodic lattices

TL;DR

This paper reveals a generalized self-duality in non-Hermitian quasi-periodic lattices, deriving analytical mobility edges and proposing an optical experiment to observe coexistence of localized and extended states with complex and real energies.

Contribution

It introduces a generalized Aubry-André self-duality in non-Hermitian systems and derives analytical expressions for mobility edges, advancing understanding of localization phenomena.

Findings

Mobility edges separate localized and extended states in non-Hermitian lattices.

Mobility edges indicate coexistence of complex and real eigenenergies.

An optical scheme is proposed to experimentally realize these phenomena.

Abstract

We demonstrate the existence of generalized Aubry-Andr\'e self-duality in a class of non-Hermitian quasi-periodic lattices with complex potentials. From the self-duality relations, the analytical expression of mobility edges is derived. Compared to Hermitian systems, mobility edges in non-Hermitian ones not only separate localized from extended states, but also indicate the coexistence of complex and real eigenenergies, making it possible a topological characterization of mobility edges. An experimental scheme, based on optical pulse propagation in synthetic photonic mesh lattices, is suggested to implement a non-Hermitian quasi-crystal displaying mobility edges.