Compact localized states in electric circuit flat-band lattices

Abstract

We generate compact localized states (CLSs) in an electrical diamond lattice, comprised of only capacitors and inductors, via local driving near its flat-band frequency. We compare experimental results to numerical simulations and find very good agreement. We also examine the stub lattice, which features a flat band of a different class where neighboring compact localized states share lattice sites. We find that local driving, while exciting the lattice at that flat-band frequency, is unable to isolate a single compact localized state due to their nonorthogonality. Finally, we introduce lattice nonlinearity and showcase the realization of nonlinear compact localized states in the diamond lattice. We induce an instability in the nonlinear CLS when it is shifted into resonance with a dispersive (optical) band. Our findings pave the way of applying flat-band physics to complex electric circuit dynamics. © 2024 American Physical Society.