Influence of diffuse surface scattering on the stability of superconducting phases with spontaneous surface current generated by Andreev bound states

TL;DR

This study theoretically investigates how surface roughness affects the phase transition temperature of superconducting states with surface currents, revealing that diffuse scattering suppresses the transition in d-wave but not in p-wave superconductors.

Contribution

It introduces a systematic quasiclassical approach to analyze the impact of surface roughness on surface phase transitions in unconventional superconductors.

Findings

Diffuse scattering reduces the transition temperature in d-wave superconductors.

P-wave superconductors' transition temperature is insensitive to surface roughness.

Andreev bound states in p-wave are robust against diffuse scattering due to symmetry considerations.

Abstract

We report a theoretical study on the phase transition between superconducting states with and without spontaneous surface current. The phase transition takes place due to the formation of surface Andreev bound states in unconventional superconductors. Based on the quasiclassical theory of superconductivity, we examine the influence of atomic-scale surface roughness on the surface phase transition temperature $T_s$. To describe the surface effect, the boundary condition for the quasiclassical Green's function is parameterized in terms of specularity (the specular reflection probability in the normal state at the Fermi level). This boundary condition allows systematic study of the surface effect ranging from the specular limit to the diffuse limit. We show that diffuse quasiparticle scattering at a rough surface causes substantial reduction of $T_s$ in the d-wave pairing state of high-$T_c$ cuprate superconductors. We also consider a p-wave pairing state in which Andreev bound states similar to those in the d-wave state are generated. In contrast to the d-wave case, $T_s$ in the p-wave state is insensitive to the specularity. This is because the Andreev bound states in the p-wave superconductor are robust against diffuse scattering, as implied from symmetry consideration for odd-frequency Cooper pairs induced at the surface; the p-wave state has odd-frequency pairs with s-wave symmetry, while the d-wave state does not.