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

Abstract

The melting of the Abrikosov vortex lattice in a two-dimensional (2D) type-II superconductor at high magnetic fields is studied analytically within the framework of the phenomenological Ginzburg-Landau theory. It is shown that local phase fluctuations in the superconducting order parameter, associated with low-energies sliding motions of Bragg chains along the principal crystallographic axes of the vortex lattice, lead to a weak first-order “melting” transition at a certain temperature Tm, well below the mean-field Tc, where the shear modulus drops abruptly to a nonzero value. The residual shear modulus above Tm decreases asymptotically to zero with increasing temperature. Despite the large phase fluctuations, the average positions of Bragg chains at finite temperature correspond to a regular vortex lattice, slightly distorted with respect to the triangular Abrikosov lattice. It is also shown that a genuine long-range phase coherence exists only at zero temperature; however, below the melting point the vortex state is very close to the triangular Abrikosov lattice. A study of the size dependence of the structure factor at finite temperature indicates the existence of quasi-long-range order with S(G→)∼Nσ, and 1/2<σ<1, where superconducting crystallites of correlated Bragg chains grow only around pinning chains. This finding may suggest a very efficient way of generating pinning defects in quasi-2D superconductors. Our results for the melting temperature and for the entropy jump agree with the state-of-the-art Monte Carlo simulations.

Source-reported materials — not catalogue approval

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