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arXiv · 1807.09555

Band structure engineering and reconstruction in electric circuit networks

Tobias Helbig·Tobias Hofmann·Ching Hua Lee·Ronny Thomale·Stefan Imhof·Laurens W. Molenkamp·Tobias Kiessling
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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.

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Tobias Helbig, Tobias Hofmann, Ching Hua Lee, Ronny Thomale, Stefan Imhof, Laurens W. Molenkamp, Tobias Kiessling. 2018-07-25. Band structure engineering and reconstruction in electric circuit networks. https://doi.org/10.1103/physrevb.99.161114

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