Tailoring flat bands and topological phases in a multi-strand Creutz network

TL;DR

This paper analytically demonstrates how to induce topological phase transitions and flat bands in a multi-strand Creutz ladder network through parameter tuning, with potential applications in photonics and ultracold atoms.

Contribution

It introduces an exact analytical method to control topological phases and flat bands in a multi-strand Creutz network by parameter correlation and basis transformation.

Findings

Topological phase transitions can be triggered by parameter correlation.

Flat bands and their degeneracy can be analytically extracted.

The model maps to decoupled SSH chains depending on the number of strands.

Abstract

We prove that, a suitable correlation between the system parameters can trigger topological phase transition and flat bands in a multi strand 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 1 decoupled Su Schrieffer Heeger chains, depending onNeven 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 the same. Our results are analytically exact, and may inspire experiments in photonics and ultracold atomic systems.