Edge and corner superconductivity in a 2D topological model

TL;DR

This paper explores how topological properties of a 2D model lead to localized superconductivity at edges and corners, with potential for higher transition temperatures at these sites compared to the bulk.

Contribution

It demonstrates the emergence of edge and corner superconductivity in a 2D topological model with attractive interactions, revealing a novel proximity effect and enhanced local transition temperatures.

Findings

Corner superconductivity can have higher transition temperatures than the bulk.

Localized superconducting tails extend from corners into the bulk.

Edge and corner phases depend on the filling and model parameters.

Abstract

We consider a two-dimensional generalization of the Su-Schrieffer-Heeger model which is known to possess a non-trivial topological band structure. For this model, which is characterized by a single parameter, the hopping ratio $0 \leq r\leq 1$, 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 $T_{c,bulk} < T<T_{c,corner}$, 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.