High-order corner state in two-dimensional face-centered square lattice topological circuit

High-order topological states typically refer to a subclass of topological states where the insulation bound-ary is 2 or more orders lower than the bulk phase dimension. In contrast to the traditional bulk-boundary correspondence, it possesses edge states with lower dimensions. These edge states are topologically pro-tected and stable against perturbations.The symmetry of the high-order topological insulator will not be destroyed. In this paper, a circuit topology with high-order corner state based on the face-centered square (FCS) lattice is constructed. The description model for the energy band of the circuit topology of the lat-tice is established. Factors influencing the topological properties of the lattice circuit are analyzed, and the energy bands of the lattice circuit are calculated. The structure of the energy band changes as the frequen-cy increasing, which indicates the occurrence of a topological phase transition in the system. The numeri-cal calculations and experiments are conducted to verify the existence of high-order corner states in the system, and the occurrence of the phase transition corresponded to the change in the topological structure of the bands. The proposed FCS lattice circuit model distinguishes from conventional square lattices by its unique symmetry-protected corner states. This work demonstrates, for the first time, the realization of high-order topological corner states in an FCS structure, expanding the design paradigm for low-dimensional topological materials. This study also provides a novel scheme for realizing high-order corner states in FCS lattice structures in condensed matter systems. Due to its topologically protected edge state, it has potential application in guiding the design of related low-power devices, high-sensitivity sensors, and other corresponding aspects.