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

Abstract

We theoretically study 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 drastically suppressed by the surface roughness, whereas that of spin-triplet $p$-wave disks is robust even in the presence of the roughness. Such difference derives from the orbital symmetry of paramagnetic odd-frequency Cooper pairs appearing at the surface of disks. The orbital part of the paramagnetic pairing correlation is $p$-wave symmetry in the $d$-wave disks, whereas it is $s$-wave symmetry in the $p$-wave ones. 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-$T_c$ thin films.

11 pages, 10 figures

References in corpus (5)

• Theory of the proximity effect in junctions with unconventional superconductors
• Odd-frequency pairing in normal metal/superconductor junctions
• Anomalous Proximity Effect and Theoretical Design for its Realization
• Consequences of bulk odd-frequency superconducting states for the classification of Cooper pairs
• Modification of Born impurity scattering near the surface of d-wave superconductors and influence of external magnetic field

Cited by in corpus (3)

• Spontaneous symmetry-breaking at surfaces of $d$-wave superconductors: influence of geometry and surface ruggedness
• Effects of the phase coherence on the local density of states in superconducting proximity structures
• Enhanced chiral edge currents and orbital magnetic moment in chiral $d$-wave superconductors from mesoscopic finite-size effects