Gain- and Loss-Induced Topological Insulating Phase in a Non-Hermitian Electrical Circuit

Abstract

© 2020 American Physical Society. There have been considerable efforts devoted to the study of topological phases in certain non-Hermitian systems that possess real eigenfrequencies in the presence of gain and loss. However, it is challenging to experimentally realize such non-Hermitian topological insulators in either quantum or photonic systems, due to difficulties in introducing controlled gain and loss. On the other hand, the wide choices of active circuit components provide us with unprecedented convenience and flexibility in engineering non-Hermitian topological insulators in electrical circuits. Here, we report on the experimental realization of a one-dimensional non-Hermitian topological circuit that exhibits topologically protected edge states purely induced by gain and loss. We show that, by tuning the value of the positive and negative resistors in the circuit, our system can switch between different topological phase regions. The topological edge states and interface states are observed at the circuit edge and at the interface between a trivial and nontrivial circuit; these states are manifested by a prominent impedance peak at the midgap frequency, which is topologically robust to variations of circuit parameters. Our work opens up an alternative gateway towards actively controllable topological systems.