Topological defect engineering and PT-symmetry in non-Hermitian electrical circuits

TL;DR

This paper demonstrates how electric circuit networks can be used to explore topological states in non-Hermitian systems with PT and anti-PT symmetries, revealing new topological phenomena and invariants.

Contribution

It introduces a method to study topological states in non-Hermitian circuits with PT and anti-PT symmetry, including measurement of admittance spectra and discovery of a novel PT symmetric Z2 invariant.

Findings

Realization of all three symmetry phases, including anti-PT symmetry.

Measurement of admittance spectrum and eigenstates under various boundary conditions.

Observation of the disappearance and reemergence of defect states depending on symmetry regime.

Abstract

We employ electric circuit networks to study topological states of matter in non-Hermitian systems enriched by parity-time symmetry $\mathcal{PT}$ and chiral symmetry anti-$\mathcal{PT}$ ($\mathcal{APT}$). The topological structure manifests itself in the complex admittance bands which yields excellent measurability and signal to noise ratio. We analyze the impact of $\mathcal{PT}$ symmetric gain and loss on localized edge and defect states in a non-Hermitian Su--Schrieffer--Heeger (SSH) circuit. We realize all three symmetry phases of the system, including the $\mathcal{APT}$ symmetric regime that occurs at large gain and loss. We measure the admittance spectrum and eigenstates for arbitrary boundary conditions, which allows us to resolve not only topological edge states, but also a novel $\mathcal{PT}$ symmetric $\mathbb{Z}_2$ invariant of the bulk. We discover the distinct properties of topological edge states and defect states in the phase diagram. In the regime that is not $\mathcal{PT}$ symmetric, the topological defect state disappears and only reemerges when $\mathcal{APT}$ symmetry is reached, while the topological edge states always prevail and only experience a shift in eigenvalue. Our findings unveil a future route for topological defect engineering and tuning in non-Hermitian systems of arbitrary dimension.