Melting line of the vortex lattice in superconductors with pinning

Abstract

The vortex-lattice melting line in three-dimensional type-II superconductors with pinning by point defects is derived from an energy balance. We account for the elastic and pinning energies of the vortex system and the entropy change due to the disappearance of the phonon shear modes in the liquid. The pinning is assumed to be caused by point defects and to be not too strong so that the melting line lies inside the so-called bundle-pinning region. Estimating the effect of pinning on the entropy jump at melting, we find the upper critical point of the melting line.