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The conventional bulk-boundary correspondence directly connects the number of topological edge states in a finite system with the topological invariant in the bulk band structure with periodic boundary condition (PBC). However, recent studies show that this principle fails in certain non-Hermitian systems with broken reciprocity, which stems from the non-Hermitian skin effect (NHSE) in the finite system where most of the eigenstates decay exponentially from the system boundary. In this work, we experimentally demonstrate a 1D non-Hermitian topological circuit with broken reciprocity by utilizing the unidirectional coupling feature of the voltage follower module. The topological edge state is observed at the boundary of an open circuit through an impedance spectra measurement between adjacent circuit nodes. We confirm the inapplicability of the conventional bulk-boundary correspondence by comparing the circuit Laplacian between the periodic boundary condition (PBC) and open boundary condition (OBC). Instead, a recently proposed non-Bloch bulk-boundary condition based on a non-Bloch winding number faithfully predicts the number of topological edge states.

Topological circuits, an exciting field just emerged over the last two years, have become a very accessible platform for realizing and exploring topological physics, with many of their physical phenomena and potential applications as yet to be discovered. In this work, we design and experimentally demonstrate a topologically nontrivial band structure and the associated topologically protected edge states in an RF circuit, which is composed of a collection of grounded capacitors connected by alternating inductors in the x and y directions, in analogy to the Su–Schrieffer–Heeger model. We take full control of the topological invariant (i.e., Zak phase) as well as the gap width of the band structure by simply tuning the circuit parameters. Excellent agreement is found between the experimental and simulation results, both showing obvious nontrivial edge state that is tightly bound to the circuit boundaries with extreme robustness against various types of defects. The demonstration of topological properties in circuits provides a convenient and flexible platform for studying topological materials and the possibility for developing flexible circuits with highly robust circuit performance.

A hybrid structure based on a planar waveguide (PWG) mode coupling a long-range surface plasmon resonance (LRSPR) mode is proposed to enhance the GH shift. Both the PWG mode and LRSPR mode can be in strong resonance, and these two modes can be coupled together due to the normal-mode splitting. The largest GH shift of PWG-coupled LRSPR structure is 4156 times that of the incident beam, which is 23 times and 3.6 times that of the surface plasmon resonance (SPR) structure and the LRSPR structure, respectively. As a GH shift sensor, the highest sensitivity of 4.68 × 107λ is realized in the coupled structure. Compared with the sensitivity of the traditional SPR structure, the sensitivity of our structure is increased by more than 2 orders, which theoretically indicates that the proposed configuration can be applied to the field of high-sensitivity sensors in the future. [ABSTRACT FROM AUTHOR]