Robustness of chiral surface current and subdominant s-wave Cooper pairs

The robustness of the chiral surface current of chiral superconductors against surface roughness is studied utilizing the quasiclassical Eilenberger theory. We consider the general chiral superconductors where the pair potential is given by the spherical harmonics ${Y}_{l}^{m}$ such that the $(l,m)=(1,\ifmmode\pm\else\textpm\fi{}1)$ state corresponds to a $({p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y})$-wave superconductor. The self-consistent calculations demonstrate that the robustness of the chiral current is determined by whether subdominant $s$-wave Cooper pairs are induced by disorder. The induced $s$-wave pairs act as an effective pair potential. As a result, the spontaneous chiral current of $({p}_{x}+i{p}_{y})$- and $({d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{d}_{xy})$-wave superconductors is robust against the roughness because the subdominant $s$-wave Cooper pairs are present.