Topological phase fluctuations, amplitude fluctuations, and criticality in extreme type-II superconductors

We study the effect. of critical fluctuations on the (B,T) -phase diagram in extreme type-II superconductors in zero and finite magnetic field. In zero magnetic field the critical fluctuations are transverse phase fluctuations of the complex scalar Ginzburg-Landau order parameter, which when excited thermally will induce topological line defects in the form of closed vortex loops into the system. The distribution function D(p) of vortex loops of perimeter p changes from an exponential function D(p) similar to p(-alpha) exp[-epsilon(T)p/k(B)T] to a power law distribution D(p) similar to p(-alpha) at the zero-field critical temperature T = T-c. We find that-the long-wavelength vortex-line tension vanishes as epsilon(T) similar to \T - T-c\(gamma); gamma approximate to 1.45, as T --> T-c. At T = T-c, an extreme type-II superconductor suffers an unbinding of large vortex loops of order the system size. When this happens, the connectivity of the thermally excited vortex tangle of the system changes abruptly. The loss of phase stiffness in the Ginzburg-Landau order parameter, the anomaly in specific heat, the loss of vortex-line tension, and the change in the connectivity of the vortex tangle are all found at the same temperature, the critical temperature of the superconductor. At zero magnetic field, unbinding of vortex loops of order the system size can be phrased in terms of a global U(1)-symmetry breaking involving a local complex disorder held. which is dual to the order parameter of the usual Ginzburg-Landau theory. There is one parameter in the theory that controls the width of the critical region, and for the parameters we have used, we show that a vortex-loop unbinding gives a correct picture of the zero-field transition even in the presence of amplitude fluctuations. A key result is the extraction of the anomalous scaling dimension of the dual field directly from the statistics of the vortex-loop excitations of the Ginzburg-Landau theory in the phase-only approximation A scaling analysis of the vortex lattice melting line is carried out, yielding two different scaling regimes, namely, ia high-field scaling regime and a distinct low-field three-dimensional XY critical scaling regime. We also: find indications of an abrupt change in the connectivity of the vortex tangle in the vortex liquid along a line T-L(B), which at low enough fields appears to coincide with the vortex line lattice melting transition line within the resolution of our numerical calculations. We study the temperature at which this phenomenon takes place as a function of system size and shape. Our results show that this temperature decreases and appears to saturate with increasing system size, and is insensitive to aspect ratios of the systems on which the simulations are performed, for large enough systems. [S0163-1829(99)03145-8].