Vortices and 2D Bosons: A Path-Integral Monte Carlo Study

The Landau-Ginzburg-Wilson hamiltonian is studied for different values of the parameter λ which multiplies the quartic term (it turns out that this is equivalent to consider different values of the coherence length ξ in units of the lattice spacing a). It is observed that amplitude fluctuations can change dramatically the nature of the phase transition: for small values of λ (ξ/a > 0.7) , instead of the smooth Kosterlitz-Thouless transition there is a first order transition with a discontinuous jump in the vortex density v and a larger non-universal drop in the helicity modulus. In particular, for λ sufficiently small (ξ/a ∼ = 1) , the density of bound pairs of vortex-antivortex below Tc is so low that, v drops to zero almost for all temperature T < T c.

Physical Review B, 1999

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.

Physical Review B

The Landau-Ginzburg-Wilson hamiltonian is studied for different values of the parameter λ which multiplies the quartic term (it turns out that this is equivalent to consider different values of the coherence length ξ in units of the lattice spacing a). It is observed that amplitude fluctuations can change dramatically the nature of the phase transition: for small values of λ (ξ/a > 0.7) , instead of the smooth Kosterlitz-Thouless transition there is a first order transition with a discontinuous jump in the vortex density v and a larger non-universal drop in the helicity modulus. In particular, for λ sufficiently small (ξ/a ∼ = 1) , the density of bound pairs of vortex-antivortex below Tc is so low that, v drops to zero almost for all temperature T < T c.

Physical review letters, 2001

The rhombic-to-square transition field H(square)(T) for cubic and tetragonal materials in fields along [001] is evaluated using the nonlocal London theory with the account of thermal vortex fluctuations. Unlike extended Ginzburg-Landau models, our approach shows that the line H(square)(T) and the upper critical field H(c2)(T) do not cross due to strong fluctuations near H(c2)(T) which suppress the square anisotropy induced by the nonlocality. In increasing fields, fluctuations cause a reentrance of the rhombic vortex lattice, in agreement with recent neutron scattering data on borocarbides.

Physical Review B, 1998

The statistical mechanics of the flux-line lattice in extreme type-II superconductors is studied within the framework of the uniformly frustrated anisotropic three-dimensional XY -model. It is assumed that the externally applied magnetic field is low enough to invalidate the lowest Landaulevel approach to the problem. A finite-field counterpart of an Onsager vortex-loop transition in extreme type-II superconductors renders the vortex liquid phase-incoherent when the Abrikosov vortex lattice undergoes a first order melting transition. For the magnetic fields considered in this paper, corresponding to filling fractions f given by 1/f = 12, 14, 16, 20, 25, 32, 48, 64, 72, 84, 96, 112, and 128, the vortex liquid phase is not describable as a liquid of well-defined field-induced vortex lines. This is due to the proliferation of thermally induced closed vortex-loops with diameters of order the magnetic length in the problem, resulting in a "percolation transition" driven by non-field induced vortices also transverse to the direction of the applied magnetic field. This immediately triggers flux-line lattice melting and loss of phase-coherence along the direction of the magnetic field. Due to this mechanism, the field induced flux lines loose their line tension in the liquid phase, and cannot be considered to be directed or well defined. In a non-relativistic 2D boson-analogy picture, this latter feature would correspond to a vanishing mass of the bosons. Scaling functions for the specific heat are calculated in zero and finite magnetic field. From this we conclude that the critical region is of order 10% of Tc for a mass-anisotropy Mz/M = 3, and increases with increasing mass-anisotropy. The entropy jump at the melting transition is calculated in two ways as a function of magnetic field for a mass-ansitropy slightly lower than that in Y BCO, namely with and without a T -dependent prefactor in the Hamiltonian originating at the microscopic level and surfacing in coarse grained theories such as the one considered in this paper. In the first case, it is found to be ∆S = 0.1kB per pancake-vortex, roughly independent of the magnetic field for the filling fractions considered here. In the second case, we find an enhancement of ∆S by a factor which is less than 2, increasing slightly with decreasing magnetic field. This is still lower than experimental values of ∆S ≈ 0.4kB found experimentally for Y BCO using calorimetric methods. We attribute this to the slightly lower mass-anisotropy used in our simulations. 74.25.Dw, 74.25.Ha,74.60.Ec

Journal of Experimental and Theoretical Physics Letters, 1998

Microscopic theory of the type of Efetov's supermatrix sigma-model is constructed for the lowlying electron states in a mixed superconductive-normal system with disorder. The developed technique is used for the study of the localized states in the core of a vortex in a moderately clean superconductor (1/∆ ≪ τ ≪ ω −1 0 = EF /∆ 2 ). At sufficiently low energies ǫ ≪ ω T h , the energy level statistics is described by the "zero-dimensional" limit of this supermatrix theory, with the effective "Thouless energy" ω T h ∼ (ω0/τ ) 1/2 . Within this energy range the result for the density of states is equivalent to that obtained within Altland-Zirnbauer random matrix model of class C. Nonzero modes of the sigma-model increase the mean interlevel distance ω0 by the relative amount of the order of [2 ln(1/ω0τ )] −1 .

Physical Review B, 1997

We present a theoretical study of the melting of the Abrikosov vortex lattice in the mixed state of high-T c superconductors. We start from the Ginzburg-Landau theory which provides, in a wide region of the mixed state, the surface density of the vortex lattice in terms of the external magnetic field and the temperature. The interaction between vortex lines is modeled by means of a pairwise potential built up as a sum of a hard-core contribution plus a repulsive long-range tail. The free energy of the vortex system is evaluated by means of a density-functional theory which carries out a nonlocal treatment of the repulsive cores of the vortices. We present results for a Ginzburg-Landau susceptibility ϭ72 as appropriate for YBa 2 Cu 3 O 7Ϫy ͑YBCO͒. The competition between the entropic term due to excluded volume effects and the repulsive vortex-vortex interactions determines, in our model, the coexistence of both a solid and a fluid phase. The corresponding melting transition exhibits a reentrant behavior, in agreement with previous theoretical works and has a very weak first-order character. ͓S0163-1829͑97͒01738-4͔

Physica C: Superconductivity, 2001

The self-consistent theory of Singwi, Tosi, Land, and Sj olander is used to describe the liquid±solid phase in a layered superconductor in the limit of weak interplane correlation eects as would be applicable to BSCCO materials. We calculate the local-®eld corrections, static structure factor, and pair correlation function and compare our results with other methods. The Hansen±Verlet criterion is used to estimate the freezing temperature of the vortex system.

Physical Review B, 2004

Stable vortex states are studied in large superconducting thin disks (for numerical purposes we considered disks with radius R =50). Configurations containing more than 700 vortices were obtained using two different approaches: the nonlinear Ginzburg-Landau (GL) theory and the London approximation. To obtain better agreement with results from the GL theory we generalized the London theory by including the spatial variation of the order parameter following Clem's ansatz. We find that configurations calculated in the London limit are also stable within the Ginzburg-Landau theory for up to ϳ230 vortices. For large values of the vorticity (typically, L տ 100), the vortices are arranged in an Abrikosov lattice in the center of the disk, which is surrounded by at least two circular shells of vortices. A Voronoi construction is used to identify the defects present in the ground state vortex configurations. Such defects cluster near the edge of the disk, but for large L also grain boundaries are found which extend up to the center of the disk.

We consider the vortex matter in a three-dimensional two-component superconductor with individually conserved condensates with different bare phase stiffnesses in a finite magnetic field, such as the projected superconducting state of liquid metallic hydrogen. The ground state is a lattice of composite, i.e. co-centered, vortices in both order parameters. We investigate quantitatively two novel phase transitions when temperature is increased at fixed magnetic field. i) A "vortex sub-lattice melting" phase transition where vortices in the field with lowest phase stiffness ("light vortices") loose co-centricity with the vortices with large phase stiffness ("heavy vortices"), thus entering a liquid state. Remarkably, the structure factor of the light vortex sub-lattice vanishes continuously. This novel transition, which has no counterpart in one-component superconductors, is shown to be in the 3Dxy universality class. Across this transition, the lattice of heavy vortices remains intact. ii) A first order melting transition of the lattice of heavy vortices, with the novel feature that these are interacting with a background liquid of light vortices. These findings are borne out in large-scale Monte Carlo simulations.