Manipulation of topological edge states in two-dimensional lattice circuits

Abstract Edge states typically appear at the boundaries of physical systems and are closely related to the topological structure of the system’s lattice. Achieving localized edge states within the bulk lattice structure is of significance in condensed matter physics, especially in the design of low-energy consumption devices. A topological circuit lattice structure was established in this paper for achieving edge states in the lattice array, and proposed a mechanism for controlling the path of edge state in the system by adjusting the transition strength between lattice sites. The alternating inductors were used in the circuit lattice structure to simulate the transition strengths both inside and outside the lattice, while grounding capacitors were adopted to simulate the lattice sites. The model of the relationship between the lattice band structure and circuit topological parameters was developed. By logically combining RF switches to simulate the transition strength between lattice sites, equivalent topological edge state features of periodic array lattices were obtained within the pseudo-periodic array. Both simulation and experimental results verified the energy band structure and the edge states in the corresponding frequency range. By adjusting the logical combination of the switch array, the realization of edge state phenomena within the required path in the bulk region were further validated. The robustness of the edge state characteristics under certain random defects and the universality of the proposed method were also discussed.