Vortex lattice melting theories as example of science fiction.

Vortex lattice melting theories as example of science fiction. Abstract It is shown that the popular conception of the vortex lattice melting have appeared in consequence of a incorrect notion about the Abrikosov state and incorrect definition of the phase coherence. The famous Abrikosov solution gives qualitatively incorrect result. The transition into the Abrikosov state must be first order in ideal (without disorder) superconductor. Such sharp transition is observed in bulk superconductors with weak disorder below Hc2. No experimental evidence of the vortex lattice melting exists now. The absence of the sharp transition in thin films with weak disorder is interpreted as absence of long-rang phase coherence down to very low magnetic field. The observed smooth phase coherence appearance in superconductors with strong disorder is explained by increasing of the effective dimensionality. It is proposed to return to the Mendelssohn model for the explanation of the resistive properties of superconductors with strong disorder. It is conjectured that the Abrikosov state is not the vortex lattice with the crystalline long-rang order.