Compact Localized States in Electronic Circuit Flat Band Diamond Lattices

One-dimensional lattices of certain geometries which enable pathways of destructive interference are known to feature flat bands – a band structure where the frequency of a Bloch wave is entirely independent of its wavenumber - and support compact localized states (CLS). A well-known lattice in this class is often called the diamond (or rhombic) chain featuring one flat band and two dispersive bands. We have constructed an electrical lattice of this geometry from LC oscillators and show that a CLS can be generated therein. Furthermore, we experimentally demonstrate that this CLS can be continued into the nonlinear regime. Finally, we prove that all bands can be made flat in this electronic system via a suitable circuit modification, and we investigate the resulting transport properties of such a chain.