What is the Vortex Lattice Melting, Reality or Fiction?

Abstract

This work fights against the widespread delusion cond-mat/0111052 on the vortex lattice melting. In spite of the outward appearances the Abrikosov state is not the vortex lattice with crystalline long-range order because pinning disorders destroy this order in real superconductors (A.I.Larkin, 1970) and the Abrikosov's solution 1957 year is not valid in the ideal case (K.Maki and H.Takayama, 1972). Only long-range order - long-range phase coherence exists in the Abrikosov state. Therefore the vortex lattice melting theories are science fiction cond-mat/9811051. The phase transition interpreted erroneously as the vortex lattice melting is in reality a disappearance of long-range phase coherence. In spite of the widespread opinion these two transitions are different transitions when a suitable definition of phase coherence is used. The superconducting state without phase coherence differs in essence from the mythical vortex liquid. The vortex, as a singularity in superconducting state with phase coherence, can not exist without phase coherence.