Generating isolated CLSs in stub lattices and engineering more complex flatband circuit architectures

Investigate the feasibility of generating well-defined (isolated) compact localized eigenstates in one-dimensional stub electrical lattices via local sinusoidal driving at the flatband frequency, despite the non-orthogonality of neighboring CLSs; and develop electric-circuit implementations of more intricate quasi-one-dimensional and two-dimensional flatband architectures (e.g., Lieb lattices) that support the generation of linear and nonlinear flatband states.

Background

The experimental work demonstrates local driving of diamond and stub electrical lattices. In the diamond lattice, orthogonal compact localized states (CLSs) are resonantly excited at the flatband frequency, and this robustness persists even under nonlinear varactor-based driving. In the stub lattice, CLSs are non-orthogonal and share sites with neighbors, and local driving excites exponentially localized resonant modes rather than isolated CLSs.

The authors explicitly raise open questions about whether isolated CLSs can be generated in stub lattices and about extending circuit implementations to more complex geometries, including quasi-one-dimensional architectures and two-dimensional Lieb lattices, with an emphasis on realizing both linear and nonlinear flatband states.