Compact Localized States in Electric Circuit Flatband Lattices

TL;DR

This paper demonstrates the generation and analysis of compact localized states in electric circuit flatband lattices, revealing their properties, limitations, and nonlinear extensions, advancing flatband physics applications in circuit dynamics.

Contribution

It introduces a method to generate and study compact localized states in electric circuits, including nonlinear states, and compares experimental results with simulations.

Findings

Successful generation of localized states in circuit lattices

Local driving cannot isolate single states in non-orthogonal flatbands

Nonlinear localized states can be realized in the circuit

Abstract

We generate compact localized states in an electrical diamond lattice, comprised of only capacitors and inductors, via local driving near its flatband frequency. We compare experimental results to numerical simulations and find very good agreement. We also examine the stub lattice, which features a flatband of a different class where neighboring compact localized states share lattice sites. We find that local driving, while exciting the lattice at that flatband frequency, is unable to isolate a single compact localized state due to their non-orthogonality. Finally, we introduce lattice nonlinearity and showcase the realization of nonlinear compact localized states in the diamond lattice. Our findings pave the way of applying flatband physics to complex electric circuit dynamics.