Transport effects in non-Hermitian nonreciprocal systems: General approach

TL;DR

This paper introduces a universal analytical framework for understanding transport phenomena like reflectionless transmission, lasing, and absorption in complex non-Hermitian, nonreciprocal systems, applicable to higher-dimensional and multi-degree models.

Contribution

It develops a generalized transfer matrix method that unifies the analysis of transport effects in diverse non-Hermitian nonreciprocal systems, extending beyond simple one-dimensional models.

Findings

Analytical conditions for reflectionless and transparent transport.

Identification of signatures of non-Hermitian, nonreciprocal, and topological behaviors.

Demonstration of the framework on a tunable ladder model.

Abstract

In this paper, we present a unifying analytical framework for identifying conditions for transport effects such as reflectionless and transparent transport, lasing, and coherent perfect absorption in non-Hermitian nonreciprocal systems using a generalized transfer matrix method. This provides a universal approach to studying the transport of tight-binding platforms, including higher-dimensional models and those with an internal degree of freedom going beyond the previously studied case of one-dimensional chains with nearest-neighbor couplings. For a specific class of tight-binding models, the relevant transport conditions and their signatures of non-Hermitian, nonreciprocal, and topological behavior are analytically tractable from a general perspective. We investigate this class and illustrate our formalism in a paradigmatic ladder model where the system's parameters can be tuned to adjust the transport effect and topological phases.