Elementary vortex pinning potential in superconductors with unconventional order parameter

The elementary vortex pinning potential is studied in unconventional superconductors within the framework of the quasiclassical theory of superconductivity. Numerical results are presented for d-, anisotropic s-, and isotropic s-wave superconductors to show explicitly that in unconventional superconductors the vortex pinning potential is determined mainly by the loss of the condensation energy in bulk due to the presence of the pinning center, i.e., by the breakdown of the Anderson’s theorem. It is found that the vortex pinning energy in the d-wave pairing case is 4 – 13 times larger than those in the s-wave pairing cases. This means that an enhancement of pinning effect in unconventional superconductors occurs due to the breakdown of the Anderson’s theorem. The case of a chiral p-wave superconductor is also investigated in terms of the vortex core states subject to the Andreev reflection, where important is whether the vorticity and chirality are parallel or antiparallel.