Topological Edge State Nucleation in Frequency Space and its Realization with Floquet Electrical Circuits

TL;DR

This paper demonstrates how Floquet-driven capacitive circuits can realize topological states in frequency space, with edge modes nucleating at frequency boundaries, providing a new platform for topological matter simulation.

Contribution

The study introduces a Floquet circuit network approach to realize and observe topological edge states in the frequency domain, combining circuit design with topological physics.

Findings

Topological edge modes nucleate at frequency boundaries in Floquet circuits.

Implementation of a Su-Schrieffer-Heeger Floquet lattice model in circuits.

Measurement of circuit Laplacian reveals topological state signatures.

Abstract

We build Floquet-driven capactive circuit networks to realize topological states of matter in the frequency domain. We find the Floquet circuit network equations of motion to reveal a potential barrier which effectively acts as a boundary in frequency space. By implementing a Su-Shrieffer-Heeger Floquet lattice model and measuring the associated circuit Laplacian and characteristic resonances, we demonstrate how topological edge modes can nucleate at such a frequency boundary.