Session T11 - Superconductivity: Critical Phenomena.
MIXED session, Thursday morning, March 23
103D, MCC

[T11.001] Vortices Freeze like Window Glass: the Vortex Molasses Scenario

We report the results of numerical simulations of the overdamped London Langevin model of driven vortices. Approaching the freezing transition from high temperatures, we locate the region of the linear I-V characteristics. The linear resistivity is well described by a Vogel-Fulcher law. The crossover current, separating the linear and non-linear regimes, does not collapse upon approaching the transition, as the Vortex Glass theory predicts. This suggests that at Tg the spatial correlations diverge much slower than the dynamics, if at all. We also perfomed careful finite size scaling to establish the robustness of the findings. These results can be comprehensively interpreted within a Vortex Molasses scenario, where the formation of the low temperature pinned phase occurs by the freezing of the vortex dynamics, accompaned by a much slower enhancement of the spatial correlations, in analogy to the window glass transition.

[T11.002] Investigation of Scaling Voltage-Current Measurements of YBCO Films

We report recent voltage versus current (IV) measurements near the superconducting phase transition of YBCO films. According to theory(D.S. Fisher \emphet al.), Phys. Rev. B \textbf43, 130 (1991), these IV curves are expected to collapse onto scaling functions in the critical region. As is typically done, by choosing an appropriate temperature dependent coherence length, \xi, a dynamic exponent, z, and a transition temperature, T_C, we find that it is possible to obtain a scaling collapse over a certain temperature range consistent with a critical region. Despite this agreement with theory, we also find that the data scales by defining lower T_Cs while increasing the value of z. We are even able to maintain the scaling collapse when T_C is defined outside of the critical region with the value of z changing by more than a factor of 2. This indicates that a successful scaling collapse alone does not conclusively determine these parameters. Furthermore, these results may explain reports of high dynamic exponents. We end by proposing an experimental criterion which would conclusively determine the critical exponents. *Supported in part by NSF Grant DMR-9732800.

[T11.003] Noise Measurements in a YBa_2Cu_3O_7-\delta Thin Film Near the Vortex-Solid Transition

Measurements of the transport voltage noise as a function of temperature and applied magnetic field are compared with measurements of the vortex-solid transition in the same YBa_2Cu_3O_7-\delta thin film sample. The noise spectra were measured on a 3000 Åx 140 \mum x 6mm YBa_2Cu_3O_7-\delta thin film sample under application of a dc bias current. At constant frequency, the measured noise voltage changes abruptly by up to two orders of magnitude at a magnetic-field-dependent onset temperature. Although the size of this transition depends on the frequency, the onset temperature shows no frequency-dependence. The vortex-solid transition temperature was extracted by several corroborating methods from I-V and R-T measurements, thereby allowing the direct comparison of the noise voltage onset temperature with the vortex-solid transition temperature of the sample.

[T11.004] Scaling Study of Simulated Current-Voltage Curves for Two-Dimensional Josephson Junction Arrays

There has been some controversy about dynamical scaling and the two-dimensional (2D) topological phase transition in superconductors. To look into this problem we produced simulated current-voltage (IV) curves for a 2D Josephson junction array using appropriate parameters and expressions above and below the Kosterlitz-Thouless-Berezinskii transition temperature (T_KTB). We also included a contribution arising from finite-size induced free vortices.^1 We then scaled the IV curves using the Fisher, Fisher, and Huse scaling ideas.^2 In doing so we chose different voltage cutoffs to simulate the minimum sensitivity of a voltmeter. We found that the value of the dynamical scaling exponent, z, for the best scaling fit and the optimal value of the transition temperature, depended upon the voltage cutoff level chosen; in effect the fit depended upon how much of the finite-sized linear portion of the IV curve we included. We will discuss the details of the simulation and of the scaling fits, as well as explore possible connections with recent suggestions on the dynamic scaling of 2D superconducting systems.^3

1. S. T. Herbert, et al., Phys. Rev. B, 57, 1154 (1998).

2. D. S. Fisher, M. P. A. Fisher, and D. A. Huse, Phys. Rev. B, 43, 130 (1991).

3. Stephen W. Pierson, et al., Phys. Rev. B, 60, 1309 (1999).

[T11.005] Phase Transitions in High Tc Superconductors and the Anisotropic 3-D XY Model

I will reveiw use of the three dimensional, anisotropic, uniformly frustrated XY model as a model for critical behavior in high temperature superconductors in an applied magnetic field parallel to the \hat c axis. Monte Carlo simulations will be used to compute the correlation length for phase coherence parallel to the applied magnetic field, as a measure of the extent of interplanar coupling at the vortex lattice melting transition. Preliminary results on the effects of uncorrelated point disorder will be presented.

[T11.006] Dynamic critical exponent of 2D and 3D XY models with RSJ and relaxational dynamics

We determine from simulations the dynamic critical exponent z for the 2D and 3D XY model with RSJ and relaxational dynamics (RD) using various scaling relations; both in equilibrium and by studying the relaxation towards equilibrium. The dependence on the boundary and its relation to experiments is discussed. An open boundary is consistent with z=2 and z = 1.5 in 2D and 3D, respectively, both for RSJ and RD. The standard periodic boundary condition is consistent with z=1.5 in case of RSJ both for 2D and 3D, whereas z=2 in case of RD both for 2D and 3D.

[T11.007] Dynamical fluctuations and scaling of the microwave conductivity of YBa_2Cu_3O_7-\delta thin films near T_C

Employing a broadband (45~MHz--45~GHz) microwave reflection configuration we have investigated dynamical fluctuation effects in the complex frequency- and temperature-dependent conductivity of YBa_2Cu_3O_7-\delta thin films near the superconducting phase transition at T_C\approx 89~K. >From these data we directly obtain a value for the dynamical critical exponent z. There has been much discussion about the value of this and other scaling exponents in these cuprate materials, with different experimental techniques giving widely varying results. In order to address this issue, we have also performed voltage versus current measurements near T_C on the same films, and will compare the results of the two techniques. In addition we show that the fluctuation conductivity \hat\sigma^ fl(ømega,T) data exhibit scaling behavior in the vicinity of T_C and can be collapsed onto universal curves. We will compare our experimentally determined scaling function to the recent prediction of Wickham and Dorsey.(cond-mat/9906124)

[T11.008] Finite-size scaling of the two-dimensional irrationally frustrated XY model

This study investigates in detail the finite-size scaling of the two-dimensional irrationally frustrated XY model. By means of Monte Carlo simulations with entropic sampling, we examine the size dependence of the specific heat, and find remarkable deviation from the finite-size scaling theory of a conventional first-order or second-order transition, indicating the presence of novel finite-size effects. The relaxation dynamics of the system is also studied, and the finite-size scaling of the relaxation time is constructed, which indeed confirms the novel finite-size effects.

[T11.009] Scaling Laws to Vortices: Conceptual Changes for a Fourth Order Phase Transition

Phase transitions of order higher than two are conceptually different from the transitions we are familiar with, namely the first (``discontinuous") and the second order (``continuous"). For example, in going beyond a mean-field theory of a second order phase transition, scaling exponents have been introduced which are expected to satisfy scaling laws and which can be calculated using creative techniques in statistical mechanics. Taking as an example, a fourth order transition, recently suggested for the superconducting transition in BKBO, we introduce scaling exponents and derive scaling laws. We also calculate properties of macroscopic defects in the purported ground state. While the topological symmetries remain the same, the metrics (energetics: domain wall energies and interaction energies) are changed. In case of a 1-dimensional defect, we have calculated the energies of domain walls and of interaction between them. We have also calculated vortex energies and interaction energy between two vortices.

[T11.010] Multicritical Phenomena of Superconductivity and Antiferromagnetism in Organic Conductor \kappa-(BEDT-TTF)_2X

We study theoretically the multicritical phenomena of the superconductivity (SC) and antiferromagnetism (AF) in organic conductors \kappa-BEDT salts. This system is in the strong coupling regime both for the SC and the AF, and the critical fluctuation is observed within the temperature region T-T_c \leq 10K. The phase diagram and the experimental data on NMR relaxation rate 1/T_1 is analysed in terms of the renormalization group (RG) method, and the following results are obtained; (i) the bicritical phenomenon observed experimentally indicates the rotational symmetry, i.e., SO(5) symmetry, within the 5-dimensional order paramter space of the SC and the AF. (ii) the critical exponent x for the divergence of 1/T_1 is well explained by the formula x = \nu ( z - 1 - \eta) with the dynamical exponent z = 3/2 for the AF region while z = \phi/\nu \sim 1.84 at the bicritical point. These results strongly suggest that the origin of the SC is common with the AF and its symmetry is d-wave.

[T11.011] Ehrenfest Order of the Superconducting Transition in Ba_0.6K_0.4BiO_3

We suggest that the transition to superconductivity in a single crystal of Ba_0.6K_0.4BiO_3 with T_c = 32K, and having critical fields with anomalous temperature dependences and vanishing discontinuities in specific heat and magnetic susceptibility, may well be an example of a fourth order phase transition. We describe the anomalies which cannot be understood within the framework of a second order phase transition. We have studied a model free energy functional and derived the critical fields, the lower, thermodynamic and the upper, for a fourth order transition. These temperature dependences are found to be in agreement with experiments. The superconducting ground state can be a familiar x-y model. However the free energy (energy metric) must be different for the transition order to be larger than two. We also briefly discuss the fluctuations influenced by the new free energy.

[T11.012] Critical scaling behavior of I-V curves of YBCO thin films at low magnetic fields

The current-voltage curves were measured for YBCO thin films in low magnetic fields (0-5kG). At all fields, including the zero field, the I-V isotherms can be separated into two regions: one where the isotherms exhibit positive curvature at low current densities and other where they exhibit negative(downward) curvature at all current densities. For all fields, it was possible to scale the I-V isotherms in a manner consistent with a three-dimensional vortex-liquid to vortex-glass phase transition. The temperature (T_g) that separates the two regions is field-dependent. The dynamic critical exponent z, extracted from scaling, is field dependent for fields below 3kG, increasing from 4.2 at zero field to 9 at 3kG. Above 3kG z becomes field independent. On the other hand the static critical exponent \nu was found to be field independent for all fields studied.

Part T of program listing