Band structure engineering and reconstruction in electric circuit networks

TL;DR

This paper presents a method to design and analyze band structures in electric circuit networks, enabling the exploration of topological phases and edge modes in synthetic materials.

Contribution

It introduces a Laplacian formalism for synthetic matter in circuits, allowing for the engineering and measurement of complex band structures and topological transitions.

Findings

Demonstrated Dirac cone admittance dispersion in a honeycomb circuit

Observed flat band edge modes at circuit terminations

Measured a topological phase transition in a topolectrical circuit

Abstract

We develop an approach to design, engineer, and measure band structures in a synthetic crystal composed of electric circuit elements. Starting from the nodal analysis of a circuit lattice in terms of currents and voltages, our Laplacian formalism for synthetic matter allows us to investigate arbitrary tight-binding models in terms of wave number resolved Laplacian eigenmodes, yielding an admittance band structure of the circuit. For illustration, we model and measure a honeycomb circuit featuring a Dirac cone admittance bulk dispersion as well as flat band admittance edge 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.