Solitons in One-Dimensional Lattices with a Flat Band

We investigate the spectral properties of a quasi-one-dimensional lattice in two possible dimerisation configurations. Both configurations are characterised 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.