Band structure engineering and reconstruction in electric circuit networks

We develop an approach to design, engineer, and measure band structures in a synthetic crystal composed of electric circuit elements. Starting from the nodal analysisof a circuit lattice in terms of currents and voltages, our Laplacian formalism for synthetic matter allows us to investigate arbitrary tight-bindingmodels in terms of wave number resolved Laplacian eigenmodes, yielding an admittanceband structure of the circuit. For illustration, we model and measure a honeycomb circuit featuring a Dirac cone admittancebulk dispersion as well as flat band admittanceedge modes at its bearded and zigzag terminations. We further employ our circuit band analysis to measure a topological phase transition in the topolectrical Su-Schrieffer-Heeger circuit.