Two-point spectroscopy of Fibonacci topoelectrical circuits

TL;DR

This paper presents a fast, single-measurement method to determine the spectral properties of topoelectrical circuits, demonstrated on a Fibonacci chain with a fractal spectrum, simplifying the analysis of complex topological systems.

Contribution

It introduces a novel experimental approach using two-point impedance measurements to efficiently extract the full spectrum of topoelectrical circuits, reducing complexity compared to traditional methods.

Findings

Successfully recovered eigenvalues of a fractal spectrum Fibonacci circuit

Demonstrated the method's effectiveness on complex, non-periodic systems

Showed topoelectrical circuits as ideal platforms for spectral measurements

Abstract

Topoelectrical circuits are meta-material realizations of topological features of condensed matter systems. In this work, we discuss experimental methods that allow a fast and straightforward detection of the spectral features of these systems from the two-point impedance of the circuit. This allows to deduce the full spectrum of a topoelectrical circuit consisting of N sites from a single two-point measurement of the frequency resolved impedance. In contrast, the standard methods rely on $N^2$ measurements of admittance matrix elements with a subsequent diagonalization on a computer. We experimentally test our approach by constructing a Fibonacci topoelectrical circuit. Although the spectrum of this chain is fractal, i.e., more complex than the spectra of periodic systems, our approach is successful in recovering its eigenvalues. Our work promotes the topoelectrical circuits as an ideal platform to measure spectral properties of various (quasi)crystalline systems.