Ph.D. Thesis: "Phase transitions in extreme type-II superconductors:

From Despi's THESIS
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Name: Anh Kiet Nguyen
Title of Ph.D. Thesis: "Phase transitions in extreme type-II superconductors:
Topological defects, and dual description of the vortex system"
Supervisor: Professor Asle Sudbứ
Institution: Norwegian University of Science and Technology
Date: 1999



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Abstract:
The magnetic field versus temperature phase diagram for type-II superconductors is investigated using large-scale Monte Carlo simulations of the Ginzburg-Landau model in the London, frozen gauge, and both London and frozen gauge approximations.

We show that the uniformly frustrated 3D XY model provides an excellent description of the magnetic field versus temperature phase diagram for extreme type-II superconductors at intermediate and low fields.

In zero magnetic field, we find that the superconducting - normal phase transition of type-II superconductors is exclusively driven by a vortex loop blowout. This blowout is a 3D counterpart of the 2D Kosterlitz-Thouless vortex - anti vortex unbinding transition. Amplitude fluctuations are irrelevant and do not modify this blowout picture. The size of the critical regime is set by the mean-field crossover temperature TMF, where Cooper-pairs would start to form at the mean-field level. When kBTMF/J0, the transition is well described by the mean-field approximation. Here, J0 is the energy scale for the Bose-Einstein condensation temperature.

In finite field, we find that the vortex-line lattice melts via a first-order melting transition into an incoherent vortex liquid, where global phase coherence is lost in all directions. The vortex lines in the liquid undergo frequent cuttings and recombinations, and are therefore not entangled. Furthermore, we find two distinct scaling regimes for the vortex-line lattice melting line:

1) a lines-only scaling regime where interactions between the field induced vortex lines dominate and drive the melting transition, and

2) a critical scaling regime where thermally excited vortex loops dominate and 3DXY critical scaling dictates the melting line.


In ad***ion to the vortex-line lattice melting transition and the Bc2 crossover, we find strong numerical support for a novel U(1) phase transition within the incoherent vortex liquid phase. It represents the finite field counterpart of the zero field vortex loop blowout. The U(1) phase transition is characterized by a subtle change in the connectivity of the vortex tangle, driven by a proliferation of topological defects in the form of vortex-loops. In the low temperature phase, the connectivity of the vortex system across the superconductor is determined by field induced vortices only. Above the transition temperature, there exist vortex pathspenetrating the superconductor in all directions. The effective vortex-line tension, or equivalently the free energy per unit length, has been driven to zero across the vortex-loop blowout transitions. The vortex-line tension may therefore serve as a``generalized stiffness" characterizing the low temperature vortex-liquid phase, and which is destroyed in the high temperature vortex-liquid phase. The vortex-line lattice melting line and the U(1) line seem to merge at low fields and terminate at Tc, the zero field critical temperature. In this regime, descriptions of the vortex system only in terms of field induced vortex lines are inadequate at and above the melting temperature.

We show that in 3D and zero magnetic field, the coupled-gauge symmetric (charged) Ginzburg-Landau model has a U(1) symmetric dual counterpart, and the U(1) symmetric (neutral) Ginzburg-Landau model has a coupled-gauge symmetric dual counterpart. Thus, the Ginzburg-Landau model is not self dual.

Furthermore, we show that the Ginzburg-Landau model and its dual counterpart belong to different universality classes, i.e. the 3DXY and the inverted 3DXY universality classes have different sets of critical exponents. The critical exponents for the 3DXY and the inverted 3DXY universality classes are given by (
upsi ~ 2/3, etapsi ~ 0.04) and (
uphi ~ 2/3, etaphi ~ -0.18), respectively. Here,
u is the critical exponent for the coherence length and eta is the anomalous dimension of the order field. The subscripts psi and phi denote the order field for a U(1)-symmetric model and a coupled-gauge symmetric model, respectively.

Using the Ginzburg-Landau order field psi and its dual counterpart phi, the magnetic field versus temperature phase-diagram of clean extreme type-II superconductors consists of three regimes at low to intermediate magnetic fields. We denote these regimes as I, II, and III. The regimes have the following characteristics:
I) A vortex-line lattice phase with <psi> > 0 and <phi> =0. Here, there is long-range superconducting phase coherence along the direction of the magnetic field, but the dual field phi has not yet condensed. The physical meaning of the latter statement is that thermally excited vortex loops are confined.
II) A low temperature incoherent vortex-liquid phase where <psi> = 0 and <phi> = 0. Here, phase coherence is lost in any direction and vortex-loops are still confined to small sizes. We may view this phase as a liquid phase of {it field induced vortex-lines}.
III) A high temperature vortex-liquid phase where <psi>=0 and <phi> > 0. Here, phase coherence is still lost in all directions, but the dual field now has condensed. The latter statement corresponds to a vortex-loop blowout. We view this phase as a vortex-liquid phase where the picture in terms of a liquid of field induced vortex lines has broken down.