Effects of surface roughness on the paramagnetic response of small unconventional superconductors

Abstract

We theoretically study the effects of surface roughness on the magnetic response of small unconventional superconductors by solving the Eilenberger equation for the quassiclassical Green function and the Maxwell equation for the vector potential simultaneously and self-consistently. The paramagnetic phase of spin-singlet d-wave superconducting disks is greatly suppressed by the surface roughness, whereas that of spin-triplet p-wave disks is robust even in the presence of the roughness. This difference derives from the orbital symmetry of paramagnetic odd-frequency Cooper pairs appearing at the surface of the disks. The orbital part of the paramagnetic pairing correlation has p-wave symmetry in the d-wave disks, whereas it has s-wave symmetry in the p-wave disks. Calculating the free energy, we also confirm that the paramagnetic state is more stable than the normal state, which indicates a possibility of detecting the paramagnetic effect in experiments. Indeed, our results are consistent with an experimental finding on high-Tc thin films.

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