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

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 Ts. 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 Ts in the d-wave pairing state of high-Tc 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, Ts 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.

Spontaneous symmetry breaking at surfaces of d -wave superconductors: Influence of geometry and surface ruggedness

“…The zero-energy states in such a p-wave superconductor will thus be completely robust against surface diffusivity and backscattering, as was shown in Ref. 52 . However, since the sign change in the order parameter in that case comes from reflected trajectories, the robustness might be lost at interfaces with finite transmission into other systems, e.g.…”

“…However, the results and the analysis presented in this paper can be extended to other phases and systems that host surface Andreev states, e.g. p-wave superconductors [48][49][50][51][52] .…”

“…Due to the results of Refs. 20,52 , the translational symmetry-breaking phase is expected to survive considerable atomic surface roughness, but more research is required.…”

“…1), but other order parameters that enable surface Andreev bound states are also of relevance (e.g. polar p-wave superconductors [48][49][50][51][52] ). In the present system, the angle between the sample interface and the crystal abaxes (hence the d-wave order parameter lobes) directly influences the spectral weight of midgap Andreev states.…”

Tunnelling conductance of $d+ip$-wave superconductor

“…other possibilities have been pointed out such as surface ferromagnetism 39 , spin density wave 40 , staggered flux phase 41,42 , and translational symmetry breaking [43][44][45][46][47][48][49][50] .…”