Edge and corner superconductivity in a two-dimensional topological model

Abstract

We consider a two-dimensional generalization of the Su-Schrieffer-Heeger model which is known to possess a nontrivial topological band structure. For this model, which is characterized by a single parameter, the hopping ratio $0\ensuremath{\le}r\ensuremath{\le}1$, the inhomogeneous superconducting phases induced by an attractive-$U$ Hubbard interaction are studied using mean-field theory. We show, analytically and by numerical diagonalization, that in lattices with open boundaries, phases with enhanced superconducting order on the corners or the edges can appear, depending on the filling. For finite samples at half filling, the corner site superconducting transition temperature can be much larger than that of the bulk. A novel proximity effect thus arises for ${T}_{c,\mathrm{bulk}}<T<{T}_{c,\mathrm{corner}}$, in which the corner site creates a nonzero tail of the superconducting order in the bulk. We show that such tails should be observable for a range of $r$ and $U$ values.