23 research outputs found
Critical Dynamics of a Vortex Loop Model for the Superconducting Transition
We calculate analytically the dynamic critical exponent measured in
Monte Carlo simulations for a vortex loop model of the superconducting
transition, and account for the simulation results. In the weak screening
limit, where magnetic fluctuations are neglected, the dynamic exponent is found
to be . In the perfect screening limit, . We relate
to the actual value of observable in experiments and find that , consistent with some experimental results
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.
Experimental observation of high field diamagnetic fluctuations in Niobium
We have performed a magnetic study of a bulk metallic sample of Nb with
critical temperature K. Magnetization versus temperature (M {\it
vs} T) data obtained for fixed magnetic fields above 1 kOe show a
superconducting transition which becomes broader as the field is increased. The
data are interpreted in terms of the diamagnetic lowest Landau level (LLL)
fluctuation theory. The scaling analysis gives values of the superconducting
transition temperature consistent with % . We search for
universal 3D LLL behavior by comparing scaling results for Nb and YBaCuO, but
obtain no evidence for universality.Comment: 5 pages, 6 figures, Accepted for publication in Phys.Rev.
A comparative study of high-field diamagnetic fluctuations in deoxygenated YBa2Cu3O(7-x) and polycrystalline (Bi-Pb)2Sr2Ca3O(10)
We studied three single crystals of YBa2Cu3O{7-x} with Tc= 62.5, 52, and 41
K, and a textured specimen of (Bi-Pb)2Sr2Ca2Cu3O10 with Tc=108 K, for H//c
axis. The reversible data were interpreted in terms of 2D lowest-Landau-level
fluctuation theory. The data were fit well by the 2D LLL expression for
magnetization obtained by Tesanovic etal., producing reasonable values of kappa
but larger values of dHc2/dT. Universality was studied by obtaining a
simultaneous scaling of Y123 data and Bi2223. An expression for the 2D x-axis
LLL scaling factor used to obtain the simultaneous scaling was extracted from
theory, and compared with the experimental values. The comparison between the
values of the x-axis produced a deviation of 40% which suggests that the
hypothesis of universality of the 2D-LLL fluctuations is not supported by the
studied samples. We finaly observe that Y123 magnetization data for
temperatures above obbey a universal scaling obtained for the diamagnetic
fluctuation magnetization from a theory considering non-local field effects.
The same scaling was not obbeyed by the corresponding magnetization calculated
from the two-dimensional lowest-Landau-level theory.Comment: 7 pages 5 figures, accept in Journ. Low Temp. Phy
Critical-point scaling function for the specific heat of a Ginzburg-Landau superconductor
If the zero-field transition in high temperature superconductors such as
YBa_2Cu_3O_7-\delta is a critical point in the universality class of the
3-dimensional XY model, then the general theory of critical phenomena predicts
the existence of a critical region in which thermodynamic functions have a
characteristic scaling form. We report the first attempt to calculate the
universal scaling function associated with the specific heat, for which
experimental data have become available in recent years. Scaling behaviour is
extracted from a renormalization-group analysis, and the 1/N expansion is
adopted as a means of approximation. The estimated scaling function is
qualitatively similar to that observed experimentally, and also to the
lowest-Landau-level scaling function used by some authors to provide an
alternative interpretation of the same data. Unfortunately, the 1/N expansion
is not sufficiently reliable at small values of N for a quantitative fit to be
feasible.Comment: 20 pages; 4 figure
3D Lowest Landau Level Theory Applied to YBCO Magnetization and Specific Heat Data: Implications for the Critical Behavior in the H-T Plane
We study the applicability of magnetization and specific heat equations
derived from a lowest-Landau-level (LLL) calculation, to the high-temperature
superconducting (HTSC) materials of the YBaCuO (YBCO)
family. We find that significant information about these materials can be
obtained from this analysis, even though the three-dimensional LLL functions
are not quite as successful in describing them as the corresponding
two-dimensional functions are in describing data for the more anisotropic HTSC
Bi- and Tl-based materials. The results discussed include scaling fits, an
alternative explanation for data claimed as evidence for a second order flux
lattice melting transition, and reasons why 3DXY scaling may have less
significance than previously believed. We also demonstrate how 3DXY scaling
does not describe the specific heat data of YBCO samples in the critical
region. Throughout the paper, the importance of checking the actual scaling
functions, not merely scaling behavior, is stressed.Comment: RevTeX; 10 double-columned pages with 7 figures embedded. (A total of
10 postscript files for the figures.) Submitted to Physical Review
Dynamic scaling for 2D superconductors, Josephson junction arrays and superfluids
The value of the dynamic critical exponent is studied for two-dimensional
superconducting, superfluid, and Josephson Junction array systems in zero
magnetic field via the Fisher-Fisher-Huse dynamic scaling. We find
, a relatively large value indicative of non-diffusive
dynamics. Universality of the scaling function is tested and confirmed for the
thinnest samples. We discuss the validity of the dynamic scaling analysis as
well as the previous studies of the Kosterlitz-Thouless-Berezinskii transition
in these systems, the results of which seem to be consistent with simple
diffusion (). Further studies are discussed and encouraged.Comment: 19 pages in two-column RevTex, 8 embedded EPS figure
Nature of the Low Field Transition in the Mixed State of High Temperature Superconductors
We have numerically studied the statics and dynamics of a model
three-dimensional vortex lattice at low magnetic fields. For the statics we use
a frustrated 3D XY model on a stacked triangular lattice. We model the dynamics
as a coupled network of overdamped resistively-shunted Josephson junctions with
Langevin noise. At low fields, there is a weakly first-order phase transition,
at which the vortex lattice melts into a line liquid. Phase coherence parallel
to the field persists until a sharp crossover, conceivably a phase transition,
near which develops at the same temperature as an infinite
vortex tangle. The calculated flux flow resistivity in various geometries near
closely resembles experiment. The local density of field induced
vortices increases sharply near , corresponding to the experimentally
observed magnetization jump. We discuss the nature of a possible transition or
crossover at (B) which is distinct from flux lattice melting.Comment: Updated references. 46 pages including low quality 25 eps figures.
Contact [email protected] or visit
http://www.physics.ohio-state.edu:80/~ryu/ for better figures and additional
movie files from simulations. To be published in Physical Review B1 01Jun9
Extreme Type-II Superconductors in a Magnetic Field: A Theory of Critical Fluctuations
A theory of critical fluctuations in extreme type-II superconductors
subjected to a finite but weak external magnetic field is presented. It is
shown that the standard Ginzburg-Landau representation of this problem can be
recast, with help of a novel mapping, as a theory of a new "superconductor", in
an effective magnetic field whose overall value is zero, consisting of the
original uniform field and a set of neutralizing unit fluxes attached to
fluctuating vortex lines. The long distance behavior is related to
the anisotropic gauge theory in which the original magnetic field plays the
role of "charge". The consequences of this "gauge theory" scenario for the
critical behavior in high temperature superconductors are explored in detail,
with particular emphasis on questions of 3D XY vs. Landau level scaling,
physical nature of the vortex "line liquid" and the true normal state, and
fluctuation thermodynamics and transport. A "minimal" set of requirements for
the theory of vortex-lattice melting in the critical region is also proposed
and discussed.Comment: 28 RevTeX pages, 4 .ps figures; appendix A added, additional
references, streamlined Secs. IV and V in response to referees' comment