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We study theoretically the spontaneous edge current in a small chiralsuperconductor with surface roughness. We obtained self-consistent solutions ofthe pair potential and the vector potential by solving the quasiclassicalEilenberger equation and the Maxwell equation simultaneously. We then employedthem to calculate numerically the spatial distribution of the chiral edgecurrent in a small superconductor. The characteristic behavior of thespontaneous edge current depends strongly on the symmetries of the orderparameters such as chiral $p$-, chiral $d$- and chiral $f$-wave pairing. Theedge current is robust under the surface roughness in the chiral $p$- andchiral $d$-wave superconductors. In the chiral $d$-wave case, the surfaceroughness 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 issurface roughness. We also discuss the temperature dependence of a spontaneousmagnetization, which is a measurable value in standard experiments.

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