Solitons in one-dimensional three-band model with a central flat band

Abstract

Defect formation in the one-dimensional topological three-band model, spanned by the generators of SU(2) and containing a central flat band, is examined within both lattice and continuum theories. Classic results of Jackiw-Rebbi and Rice-Mele for the soliton charge are generalized. The charge is twice the value obtained for the two-band case with the corresponding parameters. A sudden jump in the soliton charge from zero to one as the soliton state passes through the central flat band is predicted, and confirmed by numerical calculation on a lattice model. The quantum field-theoretical calculation of Goldstone and Wilczek is generalized as well, to obtain the same soliton charge. The diamond-chain lattice is argued to be an ideal structure to host a topological three-band we examine.