Topological circuit: a playground for exotic topological physics

Abstract

Exploring topological phases of matter and their exotic physics appeared as a rapidly growing field of study in solid-state electron systems in the past decade. In recent years, there has been a trend on the emulation of topological insulators/semimetals in many other systems, including ultracold quantum gases, trapped ions, photonic, acoustic, mechanical, and electrical circuit systems. Among these platforms, topological circuits made of simple capacitive and inductive circuit elements emerged as a very competitive platform because of its highly controllable degrees of freedom, lowercost, easy implementation, and great flexibility for integration. Owing to the unique advantages of electrical circuits such as arbitrary engineering of long-range hopping, convenient realization of nonlinear, nonreciprocal, and gain effects, highly flexible measurement, many of the nonlinear, non-abelian, and non-Hermitian physics can be potentially realized and investigated using the electrical circuit platform. In this review, we provide the first short overview of the main achievements of topological circuits developed in the past six years, primarily focusing on their theoretical modeling, circuit construction, experimental characterization, and their distinction from their counterparts in quantum electronics and photonics. The scope of this review covers a wide variety of topological circuits, including Hermitian topological circuits hosting nontrivial edge state, higher-order corner state, Weyl particles; higher dimensional topological circuits exhibiting nodal link and nodal knot states; non-Hermitian topological circuits showing skin effects, gain and loss induced nontrivial edge state; self-induced topological edge state in nonlinear topological circuit; topological circuit having non-Abelian gauge potential.