Non-Hermitian topological electric circuits with projective symmetry

Non-Hermitian topological insulators have attracted considerable attention due to their distinctive energy band characteristics and promising applications. Here, we systematically investigate non-Hermitian M\"obius insulators and graphene-like topological semimetals from the projected symmetry and realize their corresponding topological phenomena in an electric circuit-based framework. By introducing a nonreciprocal hopping term consisting of negative impedance converters into a two-dimensional electric circuit, we establish an experimental platform that effectively demonstrates that introducing non-Hermitian terms significantly enhances the energy localization of topological edge states, which originate from the non-Hermitian skin effect. Furthermore, a thorough comparison of experimental measurements with numerical simulations validates the robustness and reliability of our electric circuit structure. This work not only reveals the physical properties of non-Hermitian topological materials but also provides valuable theoretical and experimental guidance for the implementation of topological circuits and the design of radiofrequency devices in the future.