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

Abstract

The melting of the Abrikosov vortex lattice in a 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 fimite 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 ∼ N σ , and 1/2 < σ < 1, where superconducting crystallites of correlated Bragg chains grow only along 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.

Supercooled vortex liquid and quantitative theory of melting of the flux-line lattice in type-II superconductors

“…The LLL GL model was also studied numerically in both Lawrence -Doniah model (a good approximation of the 3D GL for large number of layers) [26,27] and in 2D [28] and by a variety of nonperturbative analytical methods. Among them the density functional [29], 1/N [30][31][32], dislocation theory of melting [33] and others [34]. As we show in this paper, the BP liquid free energy combined with the correct two loop solid energy computed recently gives scaled melting temperature a m T = −9.5 and in addition predicts other characteristics of the model.…”

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

“…In 2D systems the energy scale of these fluctuations is much smaller than the SC condensation energy, implying a melting temperature T m well below the mean field T c . 6 Indeed, the magnetization irreversibility line, which follows the boundary between the vortex solid and the vortex liquid, appears in the quasi-2D organics at temperatures far below the mean field T c , 3,7 where magnetoquantum oscillations are detectable. 8,7 In accordance with the resistivity and specific heat data mentioned above, the SC-induced damping of the de Haas-van Alphen ͑dHvA͒ signal in the region around the mean field H c2 was found to be a very smooth function of the magnetic field.…”

“…9 This behavior is consistent with the broad crossover between the SC and normal states predicted theoretically for 2D superconductors. 6 The nature of the vortex lattice melting transition in 2D superconductors has been debated in the literature for many years. 9 Early proposals, 10,11 based on the similarity to the Kosterlitz-Thouless-Halperin-Nelson-Young ͑KTHNY͒ theory of melting in 2D solids, 12 have led to the conclusion that the melting transition is continuous.…”

Ginzburg-Landau theory of type II superconductors in magnetic field

“…One can further investigate the structure of these supersoft modes and identify them with "shear modes" (Moore, 1989(Moore, , 1992Maniv, 1999, 2002). To conclude, there are many broken continuous symmetries (translations in two directions, rotations and the U (1) phase transformations, forming a rather uncommon in physics Lie group) leading to a single Goldstone mode.…”