12 research outputs found
Magnetic-field dependence of dynamical vortex response in two-dimensional Josephson junction arrays and superconducting films
The dynamical vortex response of a two-dimensional array of the resistively
shunted Josephson junctions in a perpendicular magnetic field is inferred from
simulations. It is found that, as the magnetic field is increased at a fixed
temperature, the response crosses over from normal to anomalous, and that this
crossover can be characterized by a single dimensionless parameter. It is
described how this crossover should be reflected in measurements of the complex
impedance for Josephson junction arrays and superconducting films.Comment: 4 pages including 5 figures in two columns, final versio
Theory of Two-Dimensional Josephson Arrays in a Resonant Cavity
We consider the dynamics of a two-dimensional array of underdamped Josephson
junctions placed in a single-mode resonant cavity. Starting from a well-defined
model Hamiltonian, which includes the effects of driving current and
dissipative coupling to a heat bath, we write down the Heisenberg equations of
motion for the variables of the Josephson junction and the cavity mode,
extending our previous one-dimensional model. In the limit of large numbers of
photons, these equations can be expressed as coupled differential equations and
can be solved numerically. The numerical results show many features similar to
experiment. These include (i) self-induced resonant steps (SIRS's) at voltages
V = (n hbar Omega)/(2e), where Omega is the cavity frequency, and n is
generally an integer; (ii) a threshold number N_c of active rows of junctions
above which the array is coherent; and (iii) a time-averaged cavity energy
which is quadratic in the number of active junctions, when the array is above
threshold. Some differences between the observed and calculated threshold
behavior are also observed in the simulations and discussed. In two dimensions,
we find a conspicuous polarization effect: if the cavity mode is polarized
perpendicular to the direction of current injection in a square array, it does
not couple to the array and there is no power radiated into the cavity. We
speculate that the perpendicular polarization would couple to the array, in the
presence of magnetic-field-induced frustration. Finally, when the array is
biased on a SIRS, then, for given junction parameters, the power radiated into
the array is found to vary as the square of the number of active junctions,
consistent with expectations for a coherent radiation.Comment: 11 pages, 8 eps figures, submitted to Phys. Rev
Dynamic Scaling and Two-Dimensional High-Tc Superconductors
There has been ongoing debate over the critical behavior of two-dimensional
superconductors; in particular for high Tc superconductors. The conventional
view is that a Kosterlitz-Thouless-Berezinskii transition occurs as long as
finite size effects do not obscure the transition. However, there have been
recent suggestions that a different transition actually occurs which
incorporates aspects of both the dynamic scaling theory of Fisher, Fisher, and
Huse and the Kosterlitz-Thouless-Berezinskii transition. Of general interest is
that this modified transition apparently has a universal dynamic critical
exponent. Some have countered that this apparent universal behavior is rooted
in a newly proposed finite-size scaling theory; one that also incorporates
scaling and conventional two-dimensional theory. To investigate these issues we
study DC voltage versus current data of a 12 angstrom thick YBCO film. We find
that the newly proposed scaling theories have intrinsic flexibility that is
relevant to the analysis of the experiments. In particular, the data scale
according to the modified transition for arbitrarily defined critical
temperatures between 0 K and 19.5 K, and the temperature range of a successful
scaling collapse is related directly to the sensitivity of the measurement.
This implies that the apparent universal exponent is due to the intrinsic
flexibility rather than some real physical property. To address this intrinsic
flexibility, we propose a criterion which would give conclusive evidence for
phase transitions in two-dimensional superconductors. We conclude by reviewing
results to see if our criterion is satisfied.Comment: 14 page
Quantum Interference in Superconducting Wire Networks and Josephson Junction Arrays: Analytical Approach based on Multiple-Loop Aharonov-Bohm Feynman Path-Integrals
We investigate analytically and numerically the mean-field
superconducting-normal phase boundaries of two-dimensional superconducting wire
networks and Josephson junction arrays immersed in a transverse magnetic field.
The geometries we consider include square, honeycomb, triangular, and kagome'
lattices. Our approach is based on an analytical study of multiple-loop
Aharonov-Bohm effects: the quantum interference between different electron
closed paths where each one of them encloses a net magnetic flux. Specifically,
we compute exactly the sums of magnetic phase factors, i.e., the lattice path
integrals, on all closed lattice paths of different lengths. A very large
number, e.g., up to for the square lattice, exact lattice path
integrals are obtained. Analytic results of these lattice path integrals then
enable us to obtain the resistive transition temperature as a continuous
function of the field. In particular, we can analyze measurable effects on the
superconducting transition temperature, , as a function of the magnetic
filed , originating from electron trajectories over loops of various
lengths. In addition to systematically deriving previously observed features,
and understanding the physical origin of the dips in as a result of
multiple-loop quantum interference effects, we also find novel results. In
particular, we explicitly derive the self-similarity in the phase diagram of
square networks. Our approach allows us to analyze the complex structure
present in the phase boundaries from the viewpoint of quantum interference
effects due to the electron motion on the underlying lattices.Comment: 18 PRB-type pages, plus 8 large figure
Concentric circular arrays of Josephson junctions as dressed models of granular superconductors
74.50.+r Tunneling phenomena, point contacts, weak links, Josephson effects, 74.81.Fa Josephson junction arrays and wire networks, 74.81.Bd Granular, melt-textured, amorphous, and composite superconductors,