Thermal fluctuations and phase transitions in the vortex state of a layered superconductor

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Abstract
We study thermal fluctuations in a layered superconductor in the presence of a magnetic field applied orthogonal to the layers. A phase diagram for this case is proposed. In the weak-field region, fluctuations of a vortex lattice are of three-dimensional (3D) nature. This leads to a two-stage melting: When the temperature is raised, a phase transition to the vortex-line liquid occurs, then independent liquid systems of 2D vortices in different layers are formed. For fields larger than the crossover value, both fluctuations and melting of the vortex lattice become of 2D type. We study the effect of vortex-lattice fluctuations on the long-range superconducting order. We demonstrate the existence of a phase transition within the vortex-lattice state: The superconducting coherence between distant layers vanishes at a temperature which is substantially lower than the melting temperature.