Realization and characterization of an all-bands-flat electrical lattice

TL;DR

This paper reports the design and experimental realization of an all-bands-flat electrical lattice using a network of capacitors, inductors, and operational amplifiers, demonstrating compact localized states and matching theoretical predictions.

Contribution

It introduces a novel electrical lattice with all flat bands and experimentally demonstrates the existence of localized states, advancing the study of flat band physics in electric networks.

Findings

Successful creation of an all-bands-flat electrical lattice

Experimental observation of compact localized states

Good agreement between experimental results and theoretical models

Abstract

We construct an electrical all-bands-flat (ABF) lattice and experimentally generate compact localized states (CLSs) therein. The lattice is a diamond (rhombic) chain and implemented as a network of capacitors and inductors, as well as voltage inverters (using operational amplifiers) in order to introduce a \(\pi\)-phase flux within each diamond. The network's normal modes split into three flat bands, and the corresponding CLSs can be excited in isolation via a two-node driving at the flat band frequencies. We also examine the role of the lattice edges and their interaction with the CLSs. Finally, we compare the experimental results to tight-binding predictions and obtain very good agreement. This analysis paves the way for further experimental implementations of ABF systems in electric networks, especially with an eye towards exploring their interplay with nonlinearity.