Abstract
We employ electric circuit networks to study topological states of matter in non-Hermitian systems enriched by parity-time symmetry and chiral symmetry anti- (). The topological structure manifests itself in the complex admittance bands which yields excellent measurability and signal to noise ratio. We analyze the impact of -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 -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 -symmetric 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 symmetric, the topological defect state disappears and only reemerges when 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.
- Received 10 November 2020
- Accepted 21 April 2021
DOI:https://doi.org/10.1103/PhysRevLett.126.215302
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