arXiv subjects

M. A. Moore

Publications and source records attributed to M. A. Moore.

108 records · Page 6Linked to original sources

arXiv1997

Simple Ginzburg-Landau Theory for Vortices in a Crystal Lattice

We study the Ginzburg-Landau model with a nonlocal quartic term as a simple phenomenological model for superconductors in the presence of coupling between the vortex lattice and the underlying crystal lattice. In mean-field theory, our model is consistent with a general oblique vortex lattice ranging from a triangular lattice to a square lattice. This simple formulation enables us to study the effect of thermal fluctuations in the vortex liquid regime. We calculate the structure factor of the vortex liquid nonperturbatively and find Bragg-like peaks with four-fold symmetry appearing in the structure factor even though there is only a short-range crystalline order.

cond-mat.supr-con↗

arXiv1997

Perturbative studies of the conductivity in the vortex-liquid regime

We calculate the Aslamazov-Larkin term of the conductivity in the presence of a magnetic field applied along the c-axis from the time-dependent Ginzburg-Landau equation perturbatively using two approaches. In the first a uniform electric field is explicitly applied; in the second the Kubo formula is used to extract the linear response. The former yields a version of the flux-flow formula for the uniform ab-plane conductivity, sigma_{xx}(k=0), that holds to all orders of perturbation theory. Obtaining the same result from the Kubo formula requires considerable cancellation of terms. We also use the Kubo calculation to examine the nonlocal ab-plane conductivity, sigma_{xx}( k \neq 0) (where the cancellations no longer occur), as well as the nonlocal c-axis conductivity sigma_{zz}( k \neq 0), and look for the perturbative precursors of the growing viscous length scales. In addition, we consider the effects of weak disorder -- both uncorrelated (point defects) and correlated (columnar and planar defects).

cond-mat.supr-con↗

arXiv1997

Influence of Dislocations in Thomson's Problem

We investigate Thomson's problem of charges on a sphere as an example of a system with complex interactions. Assuming certain symmetries we can work with a larger number of charges than before. We found that, when the number of charges is large enough, the lowest energy states are not those with the highest symmetry. As predicted previously by Dodgson and Moore, the complex patterns in these states involve dislocation defects which screen the strains of the twelve disclinations required to satisfy Euler's theorem.

cond-mat↗

arXiv1996

Instabilities in the Flux Line Lattice of Anisotropic Superconductors

The stability of the flux line lattice has been investigated within anisotropic London theory. This is the first full-scale investigation of instabilities in the `chain' state. It has been found that the lattice is stable at large fields, but that instabilities occur as the field is reduced. The field at which these instabilities first arise, $b^*(ε,θ)$, depends on the anisotropy $ε$ and the angle $θ$ at which the lattice is tilted away from the $c$-axis. These instabilities initially occur at wavevector $k^*(ε,θ)$, and the component of $k^*$ along the average direction of the flux lines, $k_z$, is always finite. As the instability occurs at finite $k_z$ the dependence of the cutoff on $k_z$ is important, and we have used a cutoff suggested by Sudb\ospace and Brandt. The instabilities only occur for values of the anisotropy $ε$ appropriate to a material like BSCCO, and not for anisotropies more appropriate to YBCO. The lower critical field $H_{c_1}(ϕ)$ is calculated as a function of the angle $ϕ$ at which the applied field is tilted away from the crystal axis. The presence of kinks in $H_{c_1}(ϕ)$ is seen to be related to instabilities in the equilibrium flux line structure.

cond-mat↗

arXiv1996

Is there a Phase Transition to the Flux Lattice State?

The sharp drops in the resistance and magnetization which are usually attributed to a phase transition from the vortex liquid state to a crystal state are explained instead as a crossover between three and two dimensional behavior, which occurs when the phase coherence length in the liquid becomes comparable to the sample thickness. Estimates of the width of the crossover region and the phase coherence length scales are in agreement with experiment.

cond-mat↗

arXiv1996

Vortices in a Thin Film Superconductor with a Spherical Geometry

We report results from Monte Carlo simulations of a thin film superconductor in a spherical geometry within the lowest Landau level approximation. We observe the absence of a phase transition to a low temperature vortex solid phase with these boundary conditions; the system remains in the vortex liquid phase for all accessible temperatures. The correlation lengths are measured for phase coherence and density modulation. Both lengths display identical temperature dependences, with an asymptotic scaling form consistent with a continuous zero temperature transition. This contrasts with the first order freezing transition which is seen in the alternative quasi-periodic boundary conditions. The high temperature perturbation theory and the ground states of the spherical system suggest that the thermodynamic limit of the spherical geometry is the same as that on the flat plane. We discuss the advantages and drawbacks of simulations with different geometries, and compare with current experimental conclusions. The effect of having a large scale inhomogeneity in the applied field is also considered.

cond-mat↗

arXiv1996

Parquet Graph Resummation Method for Vortex Liquids

We present in detail a nonperturbative method for vortex liquid systems. This method is based on the resummation of an infinite subset of Feynman diagrams, the so-called parquet graphs, contributing to the four-point vertex function of the Ginzburg-Landau model for a superconductor in a magnetic field. We derive a set of coupled integral equations, the parquet equations, governing the structure factor of the two-dimensional vortex liquid system with and without random impurities and the three-dimensional system in the absence of disorder. For the pure two-dimensional system, we simplify the parquet equations considerably and obtain one simple equation for the structure factor. In two dimensions, we solve the parquet equations numerically and find growing translational order characterized by a length scale $R_c$ as the temperature is lowered. The temperature dependence of $R_c$ is obtained in both pure and weakly disordered cases. The effect of disorder appears as a smooth decrease of $R_c$ as the strength of disorder increases.

cond-mat↗

arXiv1995

Nonlocal conductivity in the vortex-liquid regime

We investigate the nonlocal conductivity calculated from the time-dependent Ginzburg-Landau equation. When the fluctuations of the vector potential are negligible, the high-temperature (Gaussian) and low-temperature (flux-flow) forms of the uniform conductivity withan an ab plane (sigma_yy) are essentially identical. We find to what extent the nonlocal conductivity shares this feature. The results suggest that for pure samples in theses regimes the length scales of the nonlocal resistivity, rho_yy(y-y',z-z'), remain short-ranged in the y and z directions in contrast to the assumptions made by the hydrodynamic modelling of the multiterminal transport measurements. On the other hand, the resistivity is seen to have a long length scale in the x direction rho_yy(x-x'). The implications for the interpretation of recent experiments are discussed.

cond-mat↗

arXiv1995

Non-perturbative approach to correlations in two-dimensional vortex liquids

We calculate the renormalized quartic vertex function of the Ginzburg-Landau model for a superconducting film in a magnetic field by summing an infinite subset of diagrams, the so-called parquet graphs. Using this non-perturbative solution, we obtain the structure factor of the two-dimensional vortex liquid. We find growing crystalline order in the system as the temperature is lowered. Our results suggest that the length scale characterizing the crystalline orderdiverges only in the zero-temperature limit, which indicates the absence of a finite temperature phase transition to the vortex lattice phase.

cond-mat↗

arXiv1995

Critical Fluctuations and Disorder at the Vortex Liquid to Crystal Transition in Type-II Superconductors

We present a functional renormalization group (FRG) analysis of a Landau-Ginzburg model of type-II superconductors (generalized to $n/2$ complex fields) in a magnetic field, both for a pure system, and in the presence of quenched random impurities. Our analysis is based on a previous FRG treatment of the pure case [E.Brézin et. al., Phys. Rev. B, {\bf 31}, 7124 (1985)] which is an expansion in $ε= 6-d$. If the coupling functions are restricted to the space of functions with non-zero support only at reciprocal lattice vectors corresponding to the Abrikosov lattice, we find a stable FRG fixed point in the presence of disorder for $1 4$ and so the physical case ($n = 2$) is likely to have a first order transition. We speculate that the recent experimental findings that disorder removes the apparent first order transition are consistent with these calculations.

cond-mat↗

arXiv1995

Plastic energies in layered superconductors

We estimate the energy cost associated with two pancake vortices colliding in a layered superconductor. It is argued that this energy sets the plastics energy scale and is the analogue of the crossing energy for vortices in the continuum case. The starting point of the calculation is the Lawrence-Doniach version of the Ginzburg-Landau free energy for type-II superconductors. The magnetic fields considered are along the c-direction and assumed to be sufficiently high that the lowest Landau level approximation is valid. For Bi-2212, where it is know that layering is very important, the results are radically different from what would have been obtained using a three-dimensional anisotropic continuum model. We then use the plastic energy for Bi-2212 to successfully explain recent results from Hellerqvist {\em et al.}\ on its longitudinal resistance.

cond-mat↗

arXiv1995

Glassy Solutions of the Kardar-Pasrisi-Zhang Equation

It is shown that the mode-coupling equations for the strong-coupling limit of the KPZ equation have a solution for d>4 such that the dynamic exponent z is 2 (with possible logarithmic corrections) and that there is a delta function term in the height correlation function = (A/k^{d+4-z}) δ(w/k^z) where the amplitude A vanishes as d -> 4. The delta function term implies that some features of the growing surface h(x,t) will persist to all times, as in a glassy state.

cond-mat↗

arXiv1994

Failure of hydrodynamics within the vortex liquid phase

The recent discovery that some of the coefficients of the viscosity tensor are negative is shown to invalidate the hydrodynamic approach to the vortex liquid phase of a type-II superconductor. A satisfactory theory requires retention of all the spatial gradients of the velocities or electric fields and not just the first derivatives, as assumed in a hydrodynamic theory. We illustrate such a procedure by using time-dependent Ginzburg-Landau theory to determine the electric field distribution near a single ``twin-plane boundary" due to a current passing through the boundary.

cond-mat↗

arXiv1994

Topological Defects in the Abrikosov Lattice of Vortices in Type-II Superconductors

The free energy costs for various defects within an Abrikosov lattice of vortices are calculated using the lowest Landau level approximation (LLL). Defect solutions with boundary conditions for lines to meet at a point (crossing defect) and for lines to twist around each other (braid defect) are sought for 2, 3, 6, and 12 lines. Many results have been unexpected, including the nonexistence of a stable two- or three-line braid. This, and the high energy cost found for a six-line braid lead us to propose that the equilibrium vortex state is not entangled below the irreversibility line of the high-$T_c$ superconductors or in a large part of the vortex-liquid phase above this line. Also, the solution for an infinite straight screw dislocation is found, and used to give a limiting form for the free energy cost of very large braids. This depends on the area enclosed by the braid as well as its perimeter length.

cond-mat↗

arXiv1994

Energy cost associated with vortex crossing in superconductors

Starting from the Ginzburg-Landau free energy of a type II superconductor in a magnetic field we estimate the energy associated with two vortices crossing. The calculations are performed by assuming that we are in a part of the phase diagram where the lowest Landau level approximation is valid. We consider only two vortices but with two markedly different sets of boundary conditions: on a sphere and on a plane with quasi-periodic boundary conditions. We find that the answers are very similar suggesting that the energy is localised to the crossing point. The crossing energy is found to be field and temperature dependent -- with a value at the experimentally measured melting line of $U_\times \simeq 7.5 k T_m \simeq 1.16/c_L^2$, where $c_L$ is the Lindemann melting criterion parameter. The crossing energy is then used with an extension of the Marchetti, Nelson and Cates hydrodynamic theory to suggest an explanation of the recent transport experiments of Safar {{\em et al.}\ }.

cond-mat↗

arXiv1993

Monte Carlo Studies of the Two-Dimensional Vortex Liquid: Absence of Transition and Dynamical Properties

Monte Carlo simulations are performed to study the properties of type-II superconducting films in a magnetic field in which the vortices move in the two-dimensional geometry represented by the surface of a sphere. No numerical evidence is found for any melting transition, although the correlation length over which vortex crystalline order exists grows as the temperature is reduced. At low temperatures, the relaxation timescales are of an Arrhenius form which can be associated with the creation of dislocations of a size comparable to the correlation length.

cond-mat↗

arXiv1993

A Calculation of the Exponent $μ$ for the Gauge Glass model

Removed according to the author's request : Dear Administrator, Please,please could you remove the paper,tentatively assigned the number 9312070, with title "A calculation of the exponent mu for the gauge glass model" and just submitted to the cond-mat board as it contains an important error. Mike Moore

cond-mat↗

arXiv1993

Generalizations of the KPZ equation (minor changes to enable easy latexing)

We generalize the KPZ equation to an O(3) $N=2j+1$ component model. In the limit $N \to \infty$ we show that the mode coupling equations become exact. Solving these approximately we find that the dynamic exponent $z$ increases from $3/2$ for $d=1$ to $2$ at the dimension $d\approx3.6$. For $d=1$ it can be shown analytically that $z=3/2$ for all $j$. The case $j=2$ for $d=2$ is investigated by numerical integration of the KPZ equation.

cond-mat↗