[ Acknowledgments|
Josephson Junction Arrays |
Granular Materials and
Nanocomposites]

[High-Temperature
Superconductors
| Ab Initio Simulation of Materials
Properties
]

I also gratefully acknowledge additional support from the U. S.-Israel Binational Science Foundation, and from the NASA Division of Microgravity Sciences (which has supported most of the ab initio studies of liquid metals and semiconductors). I also thank the Ohio Supercomputer Center for the use of their facilities for the calculations described below. These calculations would not have been possible without these facilities.

To download the listed papers, simply click on the open red dot.

** Conventional Josephson Arrays.** Our group is studying *arrays*
of Josephson junctions - usually
two-dimensional, but also one-dimensional and three-dimensional arrays.
We study the dynamical properties as a function of applied magnetic field,
temperature, and geometry. Our methods consist primarily of solving
coupled nonlinear dynamical equations. We use mostly numerical methods, but
also attempt to develop some analytical understanding. We have also
used these arrays as model systems for treating
transport in disordered high-temperature superconductors.

** Josephson Arrays in Resonant Cavities.** Recently, we have
extensively studied the response of Josephson arrays in resonant
cavities. Such cavities greatly enhance the ability of
*underdamped* arrays to synchronize. Our group has developed
a quite successful model which reproduces many of the properties
observed experimentally. These include (a) self-induced resonant
steps, analogous to Shapiro steps, which appear at a voltage related
to the resonant frequency of the cavity; (b) power radiated into
the cavity which is proportional to the square of the number of
junctions on the steps; and (c) a threshold number of
junctions for the cavity to phase lock and radiate coherently.
These results are discussed in several papers listed
below. We have also studied the analogous behavior in the
*quantum* regime, where the junctions as well as the cavity
mode are treated quantum-mechanically. In this case, the quantum
states of the cavity-array system are quantum-mechanically
entangled. At present, we are beginning to study these systems
as possible two-state ``qubits'' in quantum computation.

** Josephson Junctions as Qubits.** A qubit is simply a
two-level quantum system (like a spin-1/2 particle), which can be
controlled and manipulated with suitable external "knobs," such as a
magnetic field. Unlike a classical bit, which must be in either a
"yes" or a "no" state, a qubit can be a mixture of "yes" and "no". Thus,
it could conceivably form the basis for a much more powerful system of
computation than is presently available.

We are studying groups of small Josephson junctions, which could be realizations of such qubits. Under suitable conditions, these junctions may have only two quantum states available. We are focusing attention particularly on small junctions coupled to a suitable resonant cavity. Such a system can behave like a two-level system. Furthermore, when more than one junction is placed in a cavity, they may be coupled together, thereby allowing controllable interactions between the qubits.

For a brief presentation (in powerpoint) about the junction/cavity qubit, click here.

** SELECTED RECENT PAPERS: **

o``Quantum Monte Carlo Study
of a Disordered Two-Dimensional Josephson Junction Array,'' W. A. Al-Saidi
and D. Stroud, *Physica C***402**, 216-222 (2004).

o
``Theory of Two-Dimensional Josephson Arrays in a Resonant
Cavity,'' E. Almaas and D. Stroud, * Phys. Rev. B*
** 67 **, 064511 (2003).

o
``Phase Phonon Spectrum in a Quantum Rotor Model with Diagonal
Disorder,'' W. A. Al-Saidi and D. Stroud, * Phys. Rev. B *
** 67**, 024511 (2003).

o
"Dynamics of a Josephson Junction Array Coupled to a Resonant
Cavity," E. Almaas and D. Stroud, *Phys. Rev. B***65**,
134502 (2002).

o
"Several Small Josephson Junctions in a Resonant Cavity: Deviation
from the Dicke Model," W. A. Al-Saidi and D. Stroud, *Phys. Rev.
B***65**, 224512 (2002).

o
``Eigenstates of a Small Josephson Junction Coupled to a Resonant
Cavity,'' W. A. Al-Saidi and D. Stroud, *Physical Review
B***65**, 014512 (2002).

o
"Model for a Josephson Junction Array Coupled to a Resonant
Cavity," J. Kent Harbaugh and D. Stroud, *Phys. Rev. B***
61**, 14765 (2000).

o
"Dynamical Phase Transition in a Fully Frustrated Josephson Array
on a Square Lattice," K. D. Fisher, D. Stroud, and L. Janin,
*Phys. Rev.***B60**, 15371-78 (1999).

o
"Two-Dimensional Arrays
of Josephson Junctions in a Magnetic Field: A Stability Analysis
of Synchronized States," B. R. Trees and D. Stroud,
*Phys. Rev.***B59**, 7108 (1999).

o"Critical
Currents of Josephson-Coupled Wire Arrays," J. Kent Harbaugh
and D. Stroud, *Phys. Rev. ***B58**, R14759 (1998).

o
``Vortex Noise and Fluctuation Conductivity in Josephson Junction
Arrays,'' I.-J. Hwang and D. Stroud, *Phys. Rev.* ** B57**, 6036
(1998). ABSTRACT

o
``Josephson Junction Arrays with Long Range Interactions,'' J. Kent
Harbaugh and D. Stroud, *Phys. Rev. B* **56**, 8335 (1997).
ABSTRACT

o
``Screening in Josephson-junction Ladders,'' Ing-Jye Hwang,
Seungoh
Ryu, and D. Stroud, *Phys. Rev. B* **53**, 506 (1996)
(Rapid Communications).
ABSTRACT

o``Supersolid Phases in Underdamped Josephson Junction Arrays:
Quantum Monte Carlo Simulations,'' Eric Roddick and David Stroud,
*Phys. Rev. B* **51**, 8672 (1995) (Rapid Communications).
ABSTRACT

** What is a composite material?** Many of the most useful
materials in nature and the laboratory are
made up, not of pure elements or compounds, but of mixtures of two or
more such compounds. These mixtures, or composites, can be prepared
on almost any length scale, ranging from nanometers (0.000000001 m) to meters.
If they are studied at wavelengths long compared to their
characteristic scale, they appear like single pure materials, but with
properties different from any of their constituents.

For example, suspensions of nanometer-size gold in a glass matrix can appear a beautiful red under transmission. This is due to a special absorption line, called a surface plasmon resonance, which is generated on the small particles. It is thought that these suspensions are responsible for the colors of some medieval stained glass windows, as well as more modern materials.

To see an illustration of a stained glass window in which the color is due to gold nanoparticles, and also to see a brief explanation of the surface plasmon resonance, take a look at this presentation (which is in powerpoint format).

Our group is developing models for the electrical, optical, magnetic, and superconducting properties of these materials. The models include an effective medium approximation, which is reviewed here. On the numerical side, one can calculate these properties by using various types of finite-element simulations (e. g., modeling the material as an impedance network).

** Nonlinear optical response and magnetic properties of granular
media.** Recently, we have been especially
interested in two broad classes of problems: response of composite
media in a magnetic field, and nonlinear response. A magnetic field
produces a range of unusual, highly anisotropic response in
composite media. It is possible to obtain an enormously enhanced
optical nonlinear susceptibilities in a composite, compared to
the same material in bulk, because of huge local field enhancements.

** Composites of small gold particles and DNA.** When small gold
particles are placed in a solution which also contains strands of
DNA, the DNA molecules attach themselves to the gold nanoparticles
via thiol groups. At high temperatures, the gold particles float
freely in solution. At lower temperatures, however, the DNA strands
on neighboring gold nanoparticles link together, and the particles
form a large agglomerate. This process can be viewed as a "freezing"
of the gold/DNA system. It can be detected optically, because the
surface plasmon resonance of the individual gold nanoparticles is
sharp at high T, but is broadened and red-shifted at lower T.

We have succeeded in modeling both the melting and the optical properties of these gold/DNA nanoparticle systems as a function of T, in good agreement with experiment. For a few highlights of this work (in powerpoint), click here.

** Surface plasmons in chains of metallic nanoparticles.** Recently,
several groups have succeeded in showing that energy can be propagated
along ordered chains of metallic nanoparticles via delocalized surface plasmon
modes. These surface plasmon modes are analogous to the tight-binding
bands in conventional periodic solids.

We have developed a "generalized tight-binding" approach to calculate this novel band structure, including ALL the surface plasmon states from an individual nanoparticle (dipolar, quadrupolar,and higher). The results show startling effects when the particles get very close to each other, which are due to percolation. We are presently extending this work to two dimensions, where researchers have also succeeded in making ordered arrays of metallic nanoparticles.

** Control of surface plasmons in gold nanoparticles, using
nematic liquid crystals.** Recent experimental work by Muller et al
has shown that the frequency of a surface plasmon in a gold nanoparticle
can be controlled by a nematic liquid crystalline surface layer. We have
recently developed a simple theory to calculate the scattering from
this type of liquid-crystal-covered metal nanooparticle. Such liquid
crystal coatings may be useful as means of controlling the optical
properties of metal nanoparticles, using electric fields.

**Small-World Networks.** Small world networks were invented
several years ago by Watts and Strogatz, and have since been found
to have astonishingly broad applications in physics, biology, and
even economics and social sciences. A small world network is
a network which may be ordered locally but is disordered on
a macro-scale. It achieves this character by having a few nodes
which have connections to very distant nodes. Our group has
carried out several recent investigations (listed below) in which
we have worked out the scaling properties of these networks
both analytically and numerically.

** SELECTED RECENT PAPERS:**

o
``Surface Plasmon Dispersion Relations in Chains of Metallic Nanoparticles:
Exact Quasistatic Calculation," Sung Yong Park and David Stroud,
*Phys. Rev. B*, in press (Feb. 2004).

o
``Second Harmonic Generation for a Dilute Suspension of Coated Particles,''
P. M. Hui, C. Xu, and D. Stroud, * Phys. Rev. B***69**,
014203 (2004).

o``Structure Formation, Melting,
and the Optical Properties of Gold/DNA Nanocomposites: Effects of Relaxation
Time,'' Sung Yong Park and D. Stroud, *Phys. Rev. B***68**,
224201 (2003).

o
``Theory of Melting and the Optical Properties of Gold/DNA
Nanocomposites,'' Sung Yong Park and D. Stroud, *Phys. Rev.
B***67**, 212202 (2003).

o ``Models for Enhanced Absorption in Inhomogeneous
Superconductors,'' Sergey V. Barabash and D. Stroud,
* Phys. Rev. B* ** 67 **, 144506 (2003).

o``Scaling
Properties of Random
Walks on Small World Networks,'' E. Almaas. R. V. Kulkarni, and D. Stroud,
*Phys. Rev. E***68**, 056105 (2003).

o
"Characterizing the Structure of Small-World Networks,"
E. Almaas, R. V. Kulkarni, and D. Stroud, *Phy. Rev. Lett.
***88** 098101 (2002).

o
"Magnetoresistance of a Three-Component composite: Percolation Near
a Critical Line," Sergey V. Barabash, David J. Bergman, and
D. Stroud, * Phys. Rev. ***B64**174419 (2001).

o "Response of Composite Media Made of Weakly Nonlinear Constituents," David J. Bergman and David G. Stroud, in {\em Optical Properties of Nanostructured Random Media}, edited by V. M. Shalaev (springer, Berlin, 2002), pp. 19-41.

o
"Negative Magnetoresistance Produced by Hall Fluctuations in a
Ferromagnetic Domain Structure," Sergey V. Barabash and D. stroud,
*Appl. Phys. Lett. ***79**979 (2001).

o
"Exact
Results and Scaling Properties of Small-World Networks,"
R. V. Kulkarni, E. Almaas, and D. Stroud, *Phys. Rev. E *
**61**, 4268-71 (2000).

o"High Field
Magnetotransport in Composite Conductors: the Effective Medium
Approximation Revisited," David J. Bergman and David G. Stroud,
*Phys. Rev. B***62**, 6603-13 (2000).

o
"Thermal Conductivity of Graded Composites:
Numerical Simulations and an Effective Medium Approximation,"
P. M. Hui, X. Zhang, A. J. Markworth, and D. Stroud,*J. Mater.
Science***34**, 5497-5503 (1999).

o
``The Effective Medium Approximations: Some Recent Developments,''
David
Stroud, *Superlattices and Microstructures* **23**, 567 (1998)
ABSTRACT

o
``Theory of Third Harmonic Generation in Random Composites of Nonlinear
Dielectrics,'' P. M. Hui, P. Cheung, and D. Stroud, *Journal
of Applied Physics***84**, 3451 (1998).
ABSTRACT

o``Conductivity and Magnetoresistance of Periodic Composites by
Network Discretization,''K. D. Fisher and D. Stroud,
* Phys. Rev.*
** B56 **, 14366 (1997).
ABSTRACT

o
``Theory of Second Harmonic Generation in Composites of Nonlinear
Dielectrics,'' P. M. Hui and D. Stroud, *J. Appl. Phys.* **82**,
4740 (1997).
ABSTRACT

o
``Giant Enhancement of Cubic Nonlinearity in a Polycrystalline
Material,'' David Stroud, *Phys. Rev. B* **54**, 3295 (1996).
ABSTRACT

o
``Optical Sum Rules and Effective Medium Theories for a
Polycrystalline Material: Application to a Model for Polypyrrole,''
D.
Stroud and A. Kazaryan, *Phys. Rev. B* **53**, 7076 (1996).
ABSTRACT

o``Harmonic Generation, Induced Nonlinearity, and Optical
Bistability in Nonlinear Composites,'' Ohad Levy, David J. Bergman, and
David G. Stroud, *Phys. Rev. E* **52**, 3184 (1995).
ABSTRACT

**Flux lattice melting.** One problem of great interest is
the behavior of high-Tc superconductors in a magnetic field.
A field penetrates high-T$_c$ materials in the form of individual
quantized vortex lines called Abrikosov vortices. Each vortex
carries about
2$\times 10^{-7}$ gauss-cm$^2$ of flux. At low temperatures, these
lines form a triangular lattice parallel to the field. At higher
temperatures, the lattice melts. When the lattice melts, the lines
move around freely, causing
energy to be dissipated - i. e., the superconductor no longer
superconducts.
We have worked extensively on understanding this melting transition,
using both numerical simulations various analytical
techniques. The goal is to find ways of pushing the
melting temperature up higher, so that the materials will be even
more useful. Melting can occur either because of thermal
fluctuations, or (at zero temperatures), because of
quantum-mechanical zero-point motion of the vortices. We have
investigated both (see papers listed below).

** Inhomogeneities in High-Tc Superconductors. ** A surprising
recent experimental finding is that the cuprate superconductors
are often intrinsically inhomogeneous. This may be due to
the presence of stripes (quasi-one-dimensional regions of
superconductor immersed in a non-superconducting background) or
to random fluctuations in hole doping, which give rise to
random variations in the superconducting gap. It has recently
been experimentally shown (using scanning tunneling microscopy)
that the gap does, indeed, vary spatially in underdoped BSCCO.

We have been studying the possible effects of inhomogeneity on
the * electromagnetic * response of the cuprates. We have
found that inhomogeneity gives rise to extra absorption below
the gap, at temperatures below the phase ordering transition
at Tc. This extra absorption is similar to what has been
seen in some experiments. We also find a critical absorption
*near * Tc, arising from phase fluctuations, also seen in
experiments. Most recently, we have been extending this work
to the (abnormal) normal state of the cuprates, where the presence of
stripes may give rise to unusual signatures in the sub-THz
absorption spectrum.

** Superconductivity and Structure in MgB2. ** An exciting
recent experimental development is the discovery of
superconductivity at 39K in MgB2. This is the highest known
Tc in a material with phonon-mediated superconductivity, and in contrast
to the cuprates, this material is ductile, like a metal, rather than
being brittle, like the ceramic cuprate superconductors. Our
investigations in this field have so far resulted in two papers
(see below). The first presents a structural model for
phase separation and structural transitions in Al-doped MgB2,
and the relation of these to superconductivity in this alloy.
The second is a very simple model for far-infrared absorption
in MgB2, based on a multigap description of the superconducting
state.

**SELECTED RECENT PAPERS:**

o``Langevin Vortex Dynamics for
a Layered Superconductor in the Lowest Landau Level Approximation,''
W. A. Al-Saidi and D. Stroud, *Phys. Rev. B***68** 144511 (2003).

o
``Possibility of c-axis Voltage Steps for a Cuprate Superconductor
in a Resonant Cavity,'' Ivan Tornes and David Stroud,
*Phys. Rev. B***68**, 052512 (2003).

o
``Transition Spectra for a BCS Superconductor with Multiple Gaps:
Model Calculations for MgB_2,'' Sergey V. Barabash and David
Stroud, *Phys. Rev.
* **B66**, 172501 (2002).

o
``Structural and Superconducting Transitions in Mg_(1-x)Al_xB_2.''
Sergey V. Barabash and David Stroud, * Phys. Rev.
* ** B66**, 012509 (2002).

o
"Simple Model for the Variation of Superfluid Density with Zn
Concentration in YBa_2Cu_3O_{7-\delta},'' J. D. Chai, S. V.
Barabash, and D. Stroud, * Physica C366*, pp. 13-22 (2001).
ABSTRACT

o
"Conductivity Due to Classical Phase Fluctuations in a Model for
High-Tc Superconductors,'' S. Barabash, D. Stroud, and I.-J.
Hwang, * Phys. Rev. B* **61**, R14924 (2000).

o
"Flux Noise Resulting from Vortex Avalanches in a Simple Kinetic
Model,'' G. Mohler and D. Stroud, * Phys. Rev. * **B60**,
9738-9743 (1999).

o
``Nature of the Low Field Transition in the Mixed State of
High-Temperature Superconductors,''
Seungoh Ryu and D. Stroud,
*Phys. Rev.* **B57**, 14476 (1998).

o
``Magnetization Jump in a Model for Flux Lattice Melting at Low Magnetic
Fields,''
Seungoh Ryu and D. Stroud, *Phys. Rev. Lett.* **78**,
4629 (1997).

o ``Dynamical Phase Transition in a Driven Disordered
Vortex Lattice,''
Seungoh Ryu, M. Hellerqvist, S. Doniach, A. Kapitulnik, D. Stroud,
*Phys. Rev. Lett.* **77**, 5114 (1996).

o
``Quantum Melting of a Two-Dimensional Vortex Lattice at Zero
Temperature,''
A. Rozhkov and D. Stroud, *Phys. Rev. B* **54**, R12697
(1996).

o
``First Order Melting and Dynamics of Flux Lines in a Model for
YBa$_2$Cu$_3$O$_{7-\delta}$,''
Seungoh Ryu and D. Stroud,
*Phys. Rev. B* **54**, 1320 (1996).

o ``First-Order Vortex Lattice Melting and Magnetization of
YBa$_2$Cu$_3$O$_{7-\delta}$,''
R. Sasik and D. Stroud,
*Phys. Rev. Lett.* **75** 2582 (1995).

o
``Effect of Phase Fluctuations on the Low-Temperature Penetration
Depth of High-T$_c$ Superconductors,'' Eric Roddick and David Stroud,
*Phys. Rev. Lett.* **74**, 1430 (1995).
ABSTRACT

Our group has a continued interest in determining various
materials properties from ``first principles.'' In practice,
this means the following. First, we calculate the total
energy of a material (solid or liquid) with the atoms in a
given configuration, using some version of density functional
formalism (either in the local-density approximation or
in a more elaborate approach which includes gradients in the
energies). We also calculate the *force* on each atom
using the same approach, combined with the Hellmann-Feynman
theorem (which expresses the force as a quantum-mechanical
expectation value of the gradient of the Hamiltonian). Next,
move the ions using classical molecular dynamics (i. e., simply
by solving Newton's second law numerically). We have used
this approach for a variety of projects, some of which are
briefly described below.

** Diffusion in Liquid Semiconductors.**
As part of a NASA project, we have calculate atomic diffusion
coefficients and electronic properties of liquid elemental
semiconductors such as Si and Ge, and alloys such
as GaAs (both stoichiometric and nonstoichiometric).
These properties are important in modeling growth
processes in semiconductors, which are often grown from the melt.
This project involves large-scale numerical simulations, carried out
primarily on the facilities of the Ohio Supercomputer Center.
We are presently extending this work to other properties of
these materials, including the dynamic structure factor in the
liquid state, and to properties of quenched liquid semiconductors
(which tend to form a metastable, glassy state). One result is
that liquid semiconductors, unlike their solid counterparts, are
often metallic, with a rather close-packed arrangement of atoms.

** Surface Properties of Solid Semiconductors.** We have used
similar approaches to calculate the lowest-energy configurations
of impurities such as Si adsorbed onto various surfaces of solid
Ge.

** Energetics of MgB2-based Superconductors.** Both Mg and B,
and typical alloying elements such as Al and Li, are ideally suited
for total energy calculations carried out using the pseudopotential
density-functional approach just described. We have thus far
used this approach to treat Al-doped MgB2, with results described
in the preprint below. The same approach gives information about
the electronic density of states, and hence is useful in
understanding the superconducting properties.

** Empirical Molecular Dynamics Studies of Materials.** For
some materials, it is computationally too expensive to calculate
forces from first principles. Under these conditions, many
``second principles'' techniques are useful. We have used several
such approaches, in which the interatomic forces are obtained
just by fitting to appropriate measured quantities in the solid
liquid state. Most of our recent applications have involved
large-scale studies of the bulk and surface properties of
liquid semiconductors, such as Si and Ge. With ingenious
numerical techniques, we can get results for samples approaching
10^6 atoms. Some of our recent work is described in a paper
listed below.

** SELECTED RECENT PAPERS:**

o ``Ab Initio Molecular Dynamics Study of Liquid and
Amorphous Ge: Focus on the Dynamic Structure Factor,''
Jeng-Da Chai, D. Stroud, J. Hafner, and G. Kresse,
*Phys. Rev. ***B67**, 104205 (2003).

o
"Structural and Superconducting Transitions in Mg_(1-x)Al_xB_2,''
Sergey V. Barabash and David Stroud,
*Phys. Rev.***B66**, 012509 (2002).

o
"Ab Initio Molecular Dynamics Simulations of Liquid Ga_xAs_(1-x)
Alloys," R. V. Kulkarni and D. Stroud, *Phys. Rev.*
**B62**, 4991-98 (2000).

o"Energetics and Bias-Dependent
STM Images of Si ad-dimers on Ge(001)," S. V. Khare, R. V.
Kulkarni, D. Stroud, and J. W. Wilkins, *Phys. Rev.*

o ``Ab Initio Molecular Dynamics Simulation of Liquid GaxGe(1-x)
Alloys,'' R. V. Kulkarni and D. Stroud, *Phys. Rev.* **B57**,
10476( 1998).
ABSTRACT

``Microscopic Simulations of Interfacial Phenomena in Solids
and Liquids'', edited by Paul D. Bristowe, Simon Phillpot, John R. Smith,
David Stroud, published as vol. 492 of
the *Proceedings of the Materials Research Society*
(Materials Research Society, Warrendale, PA, 1998).

o``Molecular Dynamics Study of Surface Segregation in Liquid Semiconductor
Alloys,'' Wenbin Yu and D. Stroud, *Phys. Rev. B* **56 **, 12243
(1997).
ABSTRACT

o
``*Ab Initio* Molecular Dynamics Study of Structural and
Transport
Properties of Liquid Germanium,'' R. V. Kulkarni, W. G. Aulbur, and D. Stroud,
*Phys. Rev. B* **55**, 6896 (1997).
ABSTRACT