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 (14)

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• Enhanced chiral edge currents and orbital magnetic moment in chiral $d$-wave superconductors from mesoscopic finite-size effects
• Odd-frequency pairs and anomalous proximity effect in nematic and chiral states of superconducting topological insulators
• Vortex supercurrent inversion by frequency-symmetry conversion of Cooper pairs
• Quasiparticle spectrum in mesoscopic superconducting junctions with weak magnetization
• Impurity strength-temperature phase diagram with phase crystals and competing time-reversal symmetry breaking states in nodal $d$-wave superconductors
• Supercurrent reversal in Zeeman-split Josephson junctions
• $\eta$-pairing on bipartite and non-bipartite lattices
• Fulde-Ferrell-Larkin-Ovchinnikov state in a superconducting thin film attached to a ferromagnetic cluster
• Chiral Current Inversion Induced by Flat-Band Andreev Bound States