Solitons in one-dimensional lattices with a flat band

TL;DR

This paper explores the spectral properties of two dimerisation configurations in a quasi-one-dimensional lattice with a flat band, revealing their topological differences and potential for soliton formation.

Contribution

It compares two lattice configurations with identical spectra but different topological and symmetry properties, highlighting their implications for solitons and topological phases.

Findings

Both configurations have a flat band at zero energy.

One configuration exhibits symmetry similar to the SSH model.

The other configuration shows non-trivial topology only with chiral-symmetry breaking.

Abstract

We investigate the spectral properties of a quasi-one-dimensional lattice in two possible dimerisation configurations. Both configurations are characterized by the same lattice topology and the identical spectra containing a flat band at zero energy. We find that one of the dimerised configuration has similar symmetry to a one-dimensional chain proposed by Su-Schrieffer-Heeger for studying solitons in conjugated polymers. Whereas, the other dimerised configuration only shows non-trivial topological properties in the presence of chiral-symmetry breaking adiabatic pumping.