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

Abstract

We employ electric circuit networks to study topological states of matter in non-Hermitian systems enriched by parity-time symmetry $\mathcal{P}\mathcal{T}$ and chiral symmetry anti-$\mathcal{P}\mathcal{T}$ ($\mathcal{A}\mathcal{P}\mathcal{T}$). The topological structure manifests itself in the complex admittance bands which yields excellent measurability and signal to noise ratio. We analyze the impact of $\mathcal{P}\mathcal{T}$ 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 $\mathcal{A}\mathcal{P}\mathcal{T}$ 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 $\mathcal{P}\mathcal{T}$ 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 $\mathcal{P}\mathcal{T}$ symmetric, the topological defect state disappears and only reemerges when $\mathcal{A}\mathcal{P}\mathcal{T}$ 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.

4 pages, 3 figures, 6 pages supplement (separate file)

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• Hyperbolic Matter in Electrical Circuits with Tunable Complex Phases
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• Fourth-Order Exceptional Points in Correlated Quantum Many-Body Systems
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• Symmetry-protected exceptional and nodal points in non-Hermitian systems
• Observation of Large-Number Corner Modes in $\mathbb{Z}$-class Higher-Order Topolectrical Circuits
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• Observation of flat-band localization and topological edge states induced by effective strong interactions in electrical circuit networks
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• Scaling laws of the out-of-time-order correlators at the transition to the spontaneous $\mathcal{P}\mathcal{T}$-symmetry breaking in a Floquet system
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