Thermodynamics of a d-wave Superconductor Near a Surface

TL;DR

This paper investigates the thermodynamic behavior of a d-wave superconductor near a surface, focusing on how surface effects influence the order parameter and free energy, which are crucial for understanding surface properties.

Contribution

It provides a self-consistent calculation of the order parameter and surface free energy for a d-wave superconductor near a surface, considering order parameter mixing and surface orientation effects.

Findings

Order parameter components of different symmetries can appear near the surface.

Surface free energy depends on the degree of order parameter mixing.

Surface orientation influences the order parameter behavior near the boundary.

Abstract

We study the properties of an anisotropically paired superconductor in the presence of a specularly reflecting surface. The bulk stable phase of the superconducting order parameter is taken to have $d_{x^2-y^2}$ symmetry. Contributions by order parameter components of different symmetries vanish in the bulk, but may enter in the vicinity of a wall. We calculate the self-consistent order parameter and surface free energy within the quasiclassical formulation of superconductivity. We discuss, in particular, the dependence of these quantities on the degree of order parameter mixing and the surface to lattice orientation. Knowledge of the thermodynamically stable order parameter near a surface is a necessary precondition for calculating measurable surface properties which we present in a companion paper.