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 PT and chiral symmetry anti-PT (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 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 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 PT-symmetric 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 PT symmetric, the topological defect state disappears and only reemerges when 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.