Dynamical robustness of topological end states in nonreciprocal Su-Schrieffer-Heeger models with open boundary conditions

TL;DR

This paper demonstrates that non-Hermitian skin effects can enhance the dynamical robustness of topological end states in nonreciprocal SSH models, and proposes a classical electric circuit to study these effects experimentally.

Contribution

It reveals the dynamical robustness of topological end states due to the non-Hermitian skin effect and introduces a classical circuit implementation for experimental observation.

Findings

Non-Hermitian skin effect suppresses leakage of end states to bulk.

End states in nonreciprocal models are more robust dynamically than in Hermitian models.

A classical electric circuit can simulate non-Hermitian quantum dynamics.

Abstract

For non-Hermitian quantum models, the dynamics is apparently not reflected by the static properties, e.g., the complex energy spectrum, because of the nonorthogonality of the right eigenvectors, the nonunitarity of the time evolution, the breakdown of the adiabatic theory, etc., but in experiments the time evolution of an initial state is commonly used. Here, we pay attention to the dynamics of an initial end state in nonreciprocal Su-Schrieffer-Heeger models under open boundary conditions, and we find that it is dynamically more robust than its Hermitian counterpart, because the non-Hermitian skin effect can suppress the part leaking to the bulk sites. To observe this, we propose a classical electric circuit with only a few passive inductors and capacitors, the mapping of which to the quantum model is established. This work explains how the non-Hermitian skin effect enhances the robustness of the topological end state, and it offers an easy way, via the classical electric circuit, of studying the nonreciprocal quantum dynamics, which may stimulate more dynamical studies of non-Hermitian models in other platforms.