Invisibility in non-Hermitian tight-binding lattices

TL;DR

This paper demonstrates that certain non-Hermitian tight-binding lattices with complex hopping amplitudes can host defects that are completely invisible to external observation, unlike Hermitian lattices.

Contribution

It introduces a class of non-Hermitian lattices with invisible defects that have real spectra but do not require PT symmetry, expanding the understanding of defect invisibility.

Findings

Invisible defects in non-Hermitian lattices with complex hopping amplitudes.

Real-valued energy spectrum of these non-Hermitian lattices.

Invisibility achieved without PT symmetry.

Abstract

Reflectionless defects in Hermitian tight-binding lattices, synthesized by the intertwining operator technique of supersymmetric quantum mechanics, are generally not invisible and time-of-flight measurements could reveal the existence of the defects. Here it is shown that, in a certain class of non-Hermitian tight-binding lattices with complex hopping amplitudes, defects in the lattice can appear fully invisible to an outside observer. The synthesized non-Hermitian lattices with invisible defects possess a real-valued energy spectrum, however they lack of parity-time (PT) symmetry, which does not play any role in the present work.