S-wave superconductivity near a surface

TL;DR

This paper investigates how s-wave superconductivity behaves near a surface using the Bogoliubov-de Gennes formalism within the attractive Hubbard model, revealing oscillations in the order parameter and density, with the energy gap remaining similar to the bulk except at low densities.

Contribution

It provides a detailed analysis of surface effects on s-wave superconductivity, highlighting the persistence of the energy gap and the oscillatory behavior of the order parameter near surfaces.

Findings

Order parameter exhibits Friedel-like oscillations near the surface.

Energy gap remains nearly the same as bulk in most cases.

At low density, the energy gap tends to vanish on the surface.

Abstract

We study the superconducting order parameter near a surface with the Bogoliubov-de Gennes formalism. For definiteness we use the attractive Hubbard model. Near a surface, the order parameter and the density distribution exhibit ``Friedel-like'' oscillations. Although the local density of states is quite different from that in the bulk, the energy gap in the spectrum on a surface is almost the same as the bulk value. In the low-density limit, however, the energy gap tends to vanish on a surface.