Landau orbital description of the vortex state in a two-dimensional extremely type-II superconductor

We extend the application of the recently developed Landau orbital approach to the fluctuating vortex lattice in two-dimensional (2D) extremely type-II superconductors at high magnetic fields to the region above the melting point. We find that the abrupt incomplete melting of the quasicrystalline vortex phase at T=T_m≪T_c is followed by a broad crossover into an intermediate state with a nematic liquid-crystalline-like order without 2D positional order. A special type of amplitude fluctuations, which can be described as classical transverse vibrations of vortex chains (while vortices are accumulated and depleted alternately in individual chains), controls this crossover. Due to the 1D nature of these vibrations, the structure factor suffers thermal broadening of the diffraction peaks, which remains effective at temperatures well below the mean field T_c. The complete melting into an isotropic vortex fluid is shown to occur only far above T_m, since the energy cost of the fluctuations which break the chain structure is of the order of the superconducting condensation energy.