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We quantitatively describe the competition between interactions, thermal fluctuations, and random quenched disorder using the dynamical Martin-Siggia-Rose approach ͓Phys. Rev. A 8, 423 ͑1973͔͒ to the Ginzburg-Landau model of the vortex matter. The approach first used by Dorsey et al. ͓Phys. Rev. B 45, 523 ͑1992͔͒ to describe the linear response far from H c1 is generalized to include both pinning and finite voltage. It allows one to calculate the non-Ohmic I-V curve, thereby extending the theory beyond the linear response. The static flux line lattice in type-II superconductors undergoes a transition into three disordered phases: the vortex liquid ͑not pinned͒, the homogeneous vortex glass ͑pinned, if one disregards an exponentially small creep at finite tem-peratures͒, and the crystalline Bragg glass ͑pinned͒ due to both thermal fluctuations and disorder. The location of the glass transition line in the homogeneous phase is determined and compared to experiments. The line is clearly different from both the melting line and the second peak line describing the translational and rotational symmetry breaking at high and low temperatures, respectively. Time correlation and response functions of the order parameter as functions of the time difference are calculated in both the liquid and the amorphous homogeneous phases. They determine the relaxation properties of the vortex matter due to the combined effect of pinning and thermal fluctuation. We calculate the critical current as a function of magnetic field and temperature in the homogeneous phase. The surface in the J-B-T space defined by this function separates between a dissipative moving vortex matter regime and vortex glass. A quantitative theory of the peak effect, qualitatively different from the conventional one due to Pippard ͓C.

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.

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It is shown that the transition to the low temperature superconducting state in a 3D metal at high magnetic field is smeared dramatically by thermal fluctuation of the superconducting order parameter. The resulting superconducting-to-normal crossover occurs in a vortex liquid state which is extended well below the mean-field Hc2. Application to MgB2 yields good quantitative agreement with recently reported data of dHvA oscillation in the superconducting state.It is well known that the transition from the normal to the superconducting (SC) state in type-II 3D superconductors in the absence of external magnetic field is a sharp, second-order phase transition, with a vanishing order parameter at the transition temperature T c continuously growing with the decreasing temperature below T c . Fluctuations effect can smear the transition significantly in high T c and low-dimensional superconductors [1], where the phase space accessible for the fluctuations is dramatically enhanced. The influence of an external magnetic field is similar to an effective reduction of dimensionality [2], resulting in a significant smearing of the transition even at very low temperatures. Such strong smearing effects have been observed in varies quasi 2D low T c superconductors at high magnetic fieldsIn the present paper we show theoretically, and confirm by comparison with very recent de-Haas van-Alphen (dHvA) oscillation data in the SC state [6], that the smearing of the SC transition by fluctuations in a conventional 3D type-II superconductor, such as MgB 2 , at high magnetic fields, is surprisingly strong, comparable in magnitude to that in 2D superconductors. This conclusion is reached by generalizing the Bragg-chain model of the 2D vortex liquid state at high perpendicular magnetic field [7] to an array of strongly coupled 2D SC layers. Within this model it is found that, similar to the situation in a single 2D SC layer, the vortex lattice melting point in a 3D superconductor at low temperature T is located well below the mean-field (MF) upper critical field H c2 (T ), so that in a broad field range above the melting point the corresponding system of fluctuations is equivalent to a 1D array of SC quantum dots at zero magnetic field [8].Our starting point is the microscopic BCS Hamiltonian for electrons in a layered 3D metal, interacting via an effective two-body attractive potential, under the influence of a strong static magnetic field. We assume, for simplicity, that the magnetic field direction (along z-axis) is perpendicular to the layers situated in (x, y)-plane. Writing down the functional integral expression for the partition function of this system, the electronic field can be eliminated by introducing bosonic complex field ∆ (r) ( by means of the Hubbard-Stratonovich transformations), which describes all possible realizations of Cooper-pairs condensates [9], [7]. Expansion of the resulting free energy functional, F G [∆ (r)], in the order parameter up to the quartic term is a good approximation for magnetic fields around mean...