Simple analytical model of vortex-lattice melting in two-dimensional superconductors

The melting of the Abrikosov vortex lattice in a two-dimensional (2D) type- II superconductor at high magnetic fields is studied analytically within th e framework of the phenomenological Ginzburg-Landau theory. It is shown tha t local phase fluctuations in the superconducting order parameter, associat ed with low-energies sliding motions of Bragg chains along the principal cr ystallographic axes of the vortex lattice, lead to a weak first-order "melt ing" transition at a certain temperature T-m, well below the mean-field T-c , where the shear modulus drops abruptly to a nonzero value. The residual s hear modulus above T-m decreases asymptotically to zero with increasing tem perature. Despite the large phase fluctuations, the average positions of Br agg chains at finite temperature correspond to a regular vortex lattice, sl ightly distorted with respect to the triangular Abrikosov lattice. It is al so shown that a genuine long-range phase coherence exists only at zero temp erature; however, below the melting point the vortex state is very close to the triangular Abrikosov lattice. A study of the size dependence of the st ructure factor at finite temperature indicates the existence of quasi-long- range order with S((G) over right arrow) similar to N-sigma, and 1/2 < sigm a < 1, where superconducting crystallites of correlated Bragg chains grow o nly around pinning chains. This finding may suggest a very efficient way of generating pinning defects in quasi-2D superconductors. Our results for th e melting temperature and for the entropy jump agree with the state-of-the- art Monte Carlo simulations. [S0163-1829(99)08129-1].