Density-Functional Theory of Freezing of Vortex Liquid in Quasi-Two-Dimensional Superconductors

We present a theory of the vortex-liquid-to-solid transition in homogeneous quasi-2D superconductors. The free energy is written as a functional of the density of zeros of the fluctuating order parameter. The transition is weakly first order and well below the Hc2(T) line. Transition temperature, discontinuities of the average Abrikosov ratio and of the average Cooper pair density, the Debye-Waller factor, and the latent heat are in good agreement with Monte Carlo simulations. The density is only weakly modulated in the "vortex-solid" phase, consistent with the density-wave behavior.