Topological phase fluctuations, amplitude fluctuations, and criticality inextreme type-II superconductors

We study the effect. of critical fluctuations on the (B,T) -phase diagram i n extreme type-II superconductors in zero and finite magnetic field. In zer o magnetic field the critical fluctuations are transverse phase fluctuation s of the complex scalar Ginzburg-Landau order parameter, which when excited thermally will induce topological line defects in the form of closed vorte x 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(-alph a) at the zero-field critical temperature T = T-c. We find that-the long-wa velength vortex-line tension vanishes as epsilon(T) similar to \T - T-c\(ga mma); 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 s ystem size. When this happens, the connectivity of the thermally excited vo rtex 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 t angle are all found at the same temperature, the critical temperature of th e superconductor. At zero magnetic field, unbinding of vortex loops of orde r the system size can be phrased in terms of a global U(1)-symmetry breakin g involving a local complex disorder held. which is dual to the order param eter of the usual Ginzburg-Landau theory. There is one parameter in the the ory 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 t he Ginzburg-Landau theory in the phase-only approximation A scaling analysi s of the vortex lattice melting line is carried out, yielding two different scaling regimes, namely, ia high-field scaling regime and a distinct low-f ield three-dimensional XY critical scaling regime. We also: find indication s of an abrupt change in the connectivity of the vortex tangle in the vorte x liquid along a line T-L(B), which at low enough fields appears to coincid e with the vortex line lattice melting transition line within the resolutio n of our numerical calculations. We study the temperature at which this phe nomenon takes place as a function of system size and shape. Our results sho w that this temperature decreases and appears to saturate with increasing s ystem 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].