What is the Vortex Lattice Melting, Reality or Fiction?

Abstract

The concept of the transition into the Abrikosov state as the appearance of long-range phase coherence is considered. It is shown that the famous Abrikosov solution gives qualitatively incorrect result. The transition into the Abrikosov state should be first order in ideal (without disorder) superconductor. Such a transition is observed only in bulk superconductors with weak disorders. The absence of a sharp transition in thin films with weak disorder is interpreted as the absence of long-range phase coherence down to a very low magnetic field. The observed smooth phase coherence appearance in superconductors with strong disorder is explained by the increase of the effective dimensionality. It is claimed that no experimental evidence of the vortex lattice melting exists now. It is shown that this popular concept has appeared on a consequence of incorrect conception about the Abrikosov state and incorrect definition of the phase coherence.