Solitons in One‐Dimensional Lattices with a Flat Band

Abstract 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.