Topological Transitions with an Imaginary Aubry-Andre-Harper Potential

TL;DR

This paper explores topological edge states in one-dimensional lattices with imaginary Aubry-Andre-Harper potentials, revealing unique non-Hermitian phenomena and potential applications in topological laser arrays.

Contribution

It introduces a novel non-Hermitian topological phase with imaginary potentials, demonstrating edge states stabilized by particle-hole symmetry and their persistence beyond real gap closures.

Findings

Edge states have purely imaginary eigenenergies.

Edge states are stabilized by non-Hermitian particle-hole symmetry.

Persistence of edge states even when the real gap closes.

Abstract

We study one-dimensional lattices with imaginary-valued Aubry-Andre-Harper (AAH) potentials. Such lattices can host edge states with purely imaginary eigenenergies, which differ from the edge states of the Hermitian AAH model and are stabilized by a non-Hermitian particle-hole symmetry. The edge states arise when the period of the imaginary potential is a multiple of four lattice constants. They are topological in origin, and can manifest on domain walls between lattices with different modulation periods and phases, as predicted by a bulk polarization invariant. Interestingly, the edge states persist and remain localized even if the real line gap closes. These features can be used in laser arrays to select topological lasing modes under spatially extended pumping.