# Research Interests

#### ACKNOWLEDGMENTS

I gratefully acknowledge support by the U. S. National Science Foundation, currently through grant NSF DMR04-13395 and before that, through DMR01-04987. The NSF has supported most of the work described in this web site, and most of my previous work. The NSF is, however, not responsible for any opinions or conclusions expressed on this web site. These are, of course, my own personal opinions and conclusions.

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.

#### JOSEPHSON JUNCTION ARRAYS

A Josephson junction is a weak link consisting of a layer of normal metal or insulator between two superconductors, They have very unusual IV (current-voltage) characteristics - for example, they conduct perfectly up to a critical value of the applied current, while above that current, an applied dc current produces an ac voltage.

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.

SELECTED RECENT PAPERS:

oQuantum Monte Carlo Study of a Disordered Two-Dimensional Josephson Junction Array,'' W. A. Al-Saidi and D. Stroud, Physica C402, 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. B65, 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. B65, 224512 (2002).

o Eigenstates of a Small Josephson Junction Coupled to a Resonant Cavity,'' W. A. Al-Saidi and D. Stroud, Physical Review B65, 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

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

#### GRANULAR MATERIALS AND NANOCOMPOSITES

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. B69, 014203 (2004).

oStructure Formation, Melting, and the Optical Properties of Gold/DNA Nanocomposites: Effects of Relaxation Time,'' Sung Yong Park and D. Stroud, Phys. Rev. B68, 224201 (2003).

o Theory of Melting and the Optical Properties of Gold/DNA Nanocomposites,'' Sung Yong Park and D. Stroud, Phys. Rev. B67, 212202 (2003).

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

oScaling Properties of Random Walks on Small World Networks,'' E. Almaas. R. V. Kulkarni, and D. Stroud, Phys. Rev. E68, 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. B64174419 (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. 79979 (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. B62, 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. Science34, 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 Physics84, 3451 (1998). ABSTRACT

oConductivity 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

oHarmonic 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

#### HIGH-TEMPERATURE SUPERCONDUCTORS

High-T$_c$ superconductors are materials, usually based on CuO$_2$ layers, which can carry current without losses up to temperatures as high as about 130 K. They are a major improvement on the older low-T$_c$ materials because they superconduct above liquid nitrogen temperatures. Our group is working on various problems relating to the behavior of these materials.

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:

oLangevin Vortex Dynamics for a Layered Superconductor in the Lowest Landau Level Approximation,'' W. A. Al-Saidi and D. Stroud, Phys. Rev. B68 144511 (2003).

o Possibility of c-axis Voltage Steps for a Cuprate Superconductor in a Resonant Cavity,'' Ivan Tornes and David Stroud, Phys. Rev. B68, 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

#### AB INITIO SIMULATION OF MATERIALS PROPERTIES

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. , 4458 (1999).

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).

oMolecular 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