Nature of the vortex-glass order in strongly type-II superconductors

The stability and the critical properties of the three-dimensional vortex-glass order in random type-II superconductors with point disorder is investigated in the unscreened limit based on a lattice {\it XY} model with a uniform field. By performing equilibrium Monte Carlo simulations for the system with periodic boundary conditions, the existence of a stable vortex-glass order is established in the unscreened limit. Estimated critical exponents are compared with those of the gauge-glass model.Comment: Error in the reported value of the exponent eta is correcte

Vortex dynamics for two-dimensional XY models

Two-dimensional XY models with resistively shunted junction (RSJ) dynamics and time dependent Ginzburg-Landau (TDGL) dynamics are simulated and it is verified that the vortex response is well described by the Minnhagen phenomenology for both types of dynamics. Evidence is presented supporting that the dynamical critical exponent $z$ in the low-temperature phase is given by the scaling prediction (expressed in terms of the Coulomb gas temperature $T^{CG}$ and the vortex renormalization given by the dielectric constant $\tilde\epsilon$) $z=1/\tilde{\epsilon}T^{CG}-2\geq 2$ both for RSJ and TDGL and that the nonlinear IV exponent a is given by a=z+1 in the low-temperature phase. The results are discussed and compared with the results of other recent papers and the importance of the boundary conditions is emphasized.Comment: 21 pages including 15 figures, final versio

Defective Vortex Lattices in Layered Superconductors with Point Pins at the Extreme Type-II Limit

The mixed phase of layered superconductors with no magnetic screening is studied through a partial duality analysis of the corresponding frustrated XY model in the presence of weak random point pins. Isolated layers exhibit a defective vortex lattice at low temperature that is phase coherent. Sufficiently weak Josephson coupling between adjacent layers results in an entangled vortex solid that exhibits weak superconductivity across layers. The corresponding vortex liquid state shows an inverted specific heat anomaly that we propose accounts for that seen in YBCO. A three-dimensional vortex lattice with dislocations occurs at stronger coupling. This crossover sheds light on the apparent discrepancy concerning the observation of a vortex-glass phase in recent Monte Carlo simulations of the same XY model.Comment: 4 pages, 1 figure. To appear in PRB, rapid communicatio

Conductivity Due to Classical Phase Fluctuations in a Model For High-T_c Superconductors

We consider the real part of the conductivity, \sigma_1(\omega), arising from classical phase fluctuations in a model for high-T_c superconductors. We show that the frequency integral of that conductivity, \int_0^\infty \sigma_1 d\omega, is non-zero below the superconducting transition temperature $T_c$, provided there is some quenched disorder in the system. Furthermore, for a fixed amount of quenched disorder, this integral at low temperatures is proportional to the zero-temperature superfluid density, in agreement with experiment. We calculate \sigma_1(\omega) explicitly for a model of overdamped phase fluctuations.Comment: 4pages, 2figures, submitted to Phys.Rev.

Universality of Frequency and Field Scaling of the Conductivity Measured by Ac-Susceptibility of a Ybco-Film

Utilizing a novel and exact inversion scheme, we determine the complex linear conductivity $\sigma (\omega )$ from the linear magnetic ac-susceptibility which has been measured from 3\,mHz to 50\,MHz in fields between 0.4\,T and 4\,T applied parallel to the c-axis of a 250\,nm thin disk. The frequency derivative of the phase $\sigma ''/\sigma '$ and the dynamical scaling of $\sigma (\omega)$ above and below $T_g(B)$ provide clear evidence for a continuous phase transition at $T_g$ to a generic superconducting state. Based on the vortex-glass scaling model, the resulting critical exponents $\nu$ and $z$ are close to those frequently obtained on films by other means and associated with an 'isotropic' vortex glass. The field effect on $\sigma(\omega)$ can be related to the increase of the glass coherence length, $\xi_g\sim B$.Comment: 8 pages (5 figures upon request), revtex 3.0, APK.94.01.0

Superconducting Coherence and the Helicity Modulus in Vortex Line Models

We show how commonly used models for vortex lines in three dimensional superconductors can be modified to include k=0 excitations. We construct a formula for the k=0 helicity modulus in terms of fluctuations in the projected area of vortex loops. This gives a convenient criterion for the presence of superconducting coherence. We also present Monte Carlo simulations of a continuum vortex line model for the melting of the Abrikosov vortex lattice in pure YBCO.Comment: 4 pages RevTeX, 2 eps figures included using eps

Collapse of the vortex-lattice inductance and shear modulus at the melting transition in untwinned YBa2Cu3O7\rm YBa_2Cu_3O_7

The complex resistivity $\hat{\rho}(\omega)$ of the vortex lattice in an untwinned crystal of 93-K $\rm YBa_2Cu_3O_7$ has been measured at frequencies $\omega/2\pi$ from 100 kHz to 20 MHz in a 2-Tesla field $\bf H\parallel c$, using a 4-probe RF transmission technique that enables continuous measurements versus $\omega$ and temperature $T$. As $T$ is increased, the inductance ${\cal L}_s(\omega) ={\rm Im} \hat{\rho}(\omega)/ \omega$ increases steeply to a cusp at the melting temperature $T_m$, and then undergoes a steep collapse consistent with vanishing of the shear modulus $c_{66}$. We discuss in detail the separation of the vortex-lattice inductance from the `volume' inductance, and other skin-depth effects. To analyze the spectra, we consider a weakly disordered lattice with a low pin density. Close fits are obtained to $\rho_1(\omega)$ over 2 decades in $\omega$. Values of the pinning parameter $\kappa$ and shear modulus $c_{66}$ obtained show that $c_{66}$ collapses by over 4 decades at $T_m$, whereas $\kappa$ remains finite.Comment: 11 pages, 8 figures, Phys. Rev. B, in pres

Numerical study of duality and universality in a frozen superconductor

The three-dimensional integer-valued lattice gauge theory, which is also known as a "frozen superconductor," can be obtained as a certain limit of the Ginzburg-Landau theory of superconductivity, and is believed to be in the same universality class. It is also exactly dual to the three-dimensional XY model. We use this duality to demonstrate the practicality of recently developed methods for studying topological defects, and investigate the critical behavior of the phase transition using numerical Monte Carlo simulations of both theories. On the gauge theory side, we concentrate on the vortex tension and the penetration depth, which map onto the correlation lengths of the order parameter and the Noether current in the XY model, respectively. We show how these quantities behave near the critical point, and that the penetration depth exhibits critical scaling only very close to the transition point. This may explain the failure of superconductor experiments to see the inverted XY model scaling.Comment: 17 pages, 18 figures. Updated to match the version published in PRB (http://link.aps.org/abstract/PRB/v67/e014525) on 27 Jan 200

Critical scaling of the a.c. conductivity for a superconductor above Tc

We consider the effects of critical superconducting fluctuations on the scaling of the linear a.c. conductivity, \sigma(\omega), of a bulk superconductor slightly above Tc in zero applied magnetic field. The dynamic renormalization- group method is applied to the relaxational time-dependent Ginzburg-Landau model of superconductivity, with \sigma(\omega) calculated via the Kubo formula to O(\epsilon^{2}) in the \epsilon = 4 - d expansion. The critical dynamics are governed by the relaxational XY-model renormalization-group fixed point. The scaling hypothesis \sigma(\omega) \sim \xi^{2-d+z} S(\omega \xi^{z}) proposed by Fisher, Fisher and Huse is explicitly verified, with the dynamic exponent z \approx 2.015, the value expected for the d=3 relaxational XY-model. The universal scaling function S(y) is computed and shown to deviate only slightly from its Gaussian form, calculated earlier. The present theory is compared with experimental measurements of the a.c. conductivity of YBCO near Tc, and the implications of this theory for such experiments is discussed.Comment: 16 pages, submitted to Phys. Rev.

Scaling critical behavior of superconductors at zero magnetic field

We consider the scaling behavior in the critical domain of superconductors at zero external magnetic field. The first part of the paper is concerned with the Ginzburg-Landau model in the zero magnetic field Meissner phase. We discuss the scaling behavior of the superfluid density and we give an alternative proof of Josephson's relation for a charged superfluid. This proof is obtained as a consequence of an exact renormalization group equation for the photon mass. We obtain Josephson's relation directly in the form $\rho_{s}\sim t^{\nu}$, that is, we do not need to assume that the hyperscaling relation holds. Next, we give an interpretation of a recent experiment performed in thin films of $YBa_{2}Cu_{3}O_{7-\delta}$. We argue that the measured mean field like behavior of the penetration depth exponent $\nu'$ is possibly associated with a non-trivial critical behavior and we predict the exponents $\nu=1$ and $\alpha=-1$ for the correlation lenght and specific heat, respectively. In the second part of the paper we discuss the scaling behavior in the continuum dual Ginzburg-Landau model. After reviewing lattice duality in the Ginzburg-Landau model, we discuss the continuum dual version by considering a family of scalings characterized by a parameter $\zeta$ introduced such that $m_{h,0}^2\sim t^{\zeta}$, where $m_{h,0}$ is the bare mass of the magnetic induction field. We discuss the difficulties in identifying the renormalized magnetic induction mass with the photon mass. We show that the only way to have a critical regime with $\nu'=\nu\approx 2/3$ is having $\zeta\approx 4/3$, that is, with $m_{h,0}$ having the scaling behavior of the renormalized photon mass.Comment: RevTex, 15 pages, no figures; the subsection III-C has been removed due to a mistak