Supersymmetric correspondence in spectra on a graph and its line graph: From circuit theory to spoof plasmons on metallic lattices

TL;DR

This paper explores the supersymmetry-based spectral correspondence between circuit networks on graphs and their line graphs, and demonstrates this phenomenon in metallic lattices through simulations and terahertz spectroscopy.

Contribution

It establishes a theoretical connection between spectra of circuit networks and their line graphs via supersymmetry, and experimentally verifies this in metallic lattices.

Findings

Spectral coincidence between graph and line graph circuits due to SUSY

Predicted band correspondence in metallic lattices

Experimental verification using terahertz spectroscopy

Abstract

We investigate the supersymmetry (SUSY) structures for inductor-capacitor circuit networks on a simple regular graph and its line graph. We show that their eigenspectra must coincide (except, possibly, for the highest eigenfrequency) due to SUSY, which is derived from the topological nature of the circuits. To observe this spectra correspondence in the high-frequency range, we study spoof plasmons on metallic hexagonal and kagom\'e lattices. The band correspondence between them is predicted by a simulation. Using terahertz time-domain spectroscopy, we demonstrate the band correspondence of fabricated metallic hexagonal and kagom\'e lattices.