Spontaneous edge current in a small chiral superconductor with a rough surface

TL;DR

This paper theoretically investigates the behavior of spontaneous edge currents in small chiral superconductors with surface roughness, revealing their dependence on pairing symmetry and robustness under surface imperfections.

Contribution

It provides self-consistent solutions for edge current distributions considering surface roughness across different chiral pairing symmetries, highlighting their distinct robustness.

Findings

Edge currents in chiral p- and d-wave superconductors are robust against surface roughness.

Surface roughness can reverse the direction of edge current in chiral d-wave superconductors.

Edge current in chiral f-wave superconductors is fragile under surface roughness.

Abstract

We study theoretically the spontaneous edge current in a small chiral superconductor with surface roughness. We obtained self-consistent solutions of the pair potential and the vector potential by solving the quasiclassical Eilenberger equation and the Maxwell equation simultaneously. We then employed them to calculate numerically the spatial distribution of the chiral edge current in a small superconductor. The characteristic behavior of the spontaneous edge current depends strongly on the symmetries of the order parameters such as chiral $p$-, chiral $d$- and chiral $f$-wave pairing. The edge current is robust under the surface roughness in the chiral $p$- and chiral $d$-wave superconductors. In the chiral $d$-wave case, the surface roughness tends to flip the direction of the chiral current. On the other hand, the edge current in a chiral $f$-wave superconductor is fragile when there is surface roughness. We also discuss the temperature dependence of a spontaneous magnetization, which is a measurable value in standard experiments.