Realizing Next-Nearest-Neighbor Coupling and Peierls Phase in Circuits

We really design the trimerized circuits for the non-Hermitian one-dimensional Su-Schrieffer-Heeger models. There are three models, the initial one just considers the nearest neighbor coupling, the enhanced one is extended to contain the next-nearest-neighbor coupling, and the final one is reenhanced by introducing the Peierls phase. We investigate the dynamics of the circuit Laplacians with respect to the models, find that the topological states appear in the initial model and the response intervals are substantially affected by the next-nearest-neighbor coupling channels and the Peierls phase. These results are practically demonstrated by numerical simulations and experimental measurements. As a conclusion, the trimerized circuits can provide an adjustable and simple platform to investigate new topological physical states.