Inhomogeneous Superconductivity due to Surfaces

Depending on competing on-site and nearest-neighbour interactions, the extended Hubbard model can host a variety of mixed s-, p- and d-wave superconducting phases. Phase transitions between these phases occur as a function of the interaction strengths, temperature and electron density, leading to a rich phase diagram. In a system with periodic boundary conditions, the order parameters are uniform in space and can be characterized by the dominant/sub-dominant components. In this work, we investigate the effect of surfaces on the mixed-symmetry phases using a real-space Bogoliubov-de Gennes method. We present the inhomogeneous order parameter profiles and show how the dominant superconducting phase can be different near the surface versus the bulk.