Multi-Band Superconductivity in One-Dimensional Topological Models

We study the one-dimensional Su-Schrieffer-Heeger (SSH) model in the presence of topological defects. When periodic topological defects are applied to the SSH model, the number of bands within the electronic spectrum is tuned by the periodicity of topological defects. We study the electronic band structure of the non-interacting system as the number of such defects is tuned; in particular, we calculate the real-space winding numbers and reveal a rich topological phase diagram for the resulting multi-band structures. When turning on an attractive-U Hubbard interaction, superconducting gaps open within each of these bands, with band-dependent superconducting gaps. We analyze the scaling relationships between the superconducting properties, such as the superconducting order parameter, superconducting gap width, and the critical temperature, as functions of the attraction strength U and the chemical potential.