Tailoring flat bands and topological phases in a multistrand Creutz network

Abstract

We prove that a suitable correlation between system parameters can trigger topological phase transitions and flat bands in a multistrand Creutz ladder network when a staggered second neighbor interaction is included along the $x$ axis. An appropriate change of basis maps such a finite $N$-strand mesh into $N$ or $N\ensuremath{-}1$ decoupled Su-Schrieffer-Heeger chains, depending on $N$ even or odd. A simple intuitive method, using a real-space decimation scheme, turns out to be very powerful in analytically extracting the flat bands, explaining their degeneracy, or a lifting of same. Our results are analytically exact and may inspire experiments in photonics and ultracold atomic systems.