Soliton Defects in One-dimensional Topological Three-band Hamiltonian

TL;DR

This paper investigates defect formation and soliton charges in a one-dimensional topological three-band model, revealing unique behaviors due to the flat band and extending classical results with quantum field theory.

Contribution

It generalizes the Jackiw-Rebbi and Rice-Mele soliton charge results to a three-band model, incorporating the effects of a flat band and using quantum field theory.

Findings

Soliton charge behavior differs qualitatively from two-band models due to the flat band.

Diamond-chain lattice effectively hosts topological three-band structures.

Generalization of Goldstone-Wilczek calculation to three-band systems.

Abstract

Defect formation in the one-dimensional topological three-band model is examined within both lattice and continuum models. Classic results of Jackiw-Rebbi and Rice-Mele for the soliton charge is generalized to the three-band model. The presence of the central flat band in the three-band model makes the soliton charge as a function of energy behave in a qualitatively different way from the two-band Dirac model case. Quantum field-theoretical calculation of Goldstone and Wilczek is also generalized to the three-band model to obtain the soliton charge. Diamond-chain lattice is shown to be an ideal structure to host a topological three-band structure.