The Intermodulation Coefficient of an Inhomogeneous Superconductor

The high-T_c cuprate superconductors are now believed to be intrinsically inhomogeneous. We develop a theory to describe how this inhomogeneity affects the intermodulation coefficient of such a material. We show that the continuum equations describing intermodulation in a superconducting layer with spatially varying properties are formally equivalent to those describing an inhomogeneous dielectric with a nonzero cubic nonlinearity. Using this formal analogy, we calculate the effect of inhomogeneity on the intermodulation coefficient in a high-T_c material, using several assumptions about the topology of the layer, and some simple analytical approximations to treat the nonlinearity. For some topologies, we find that the intermodulation critical supercurrent density J_{IMD} is actually enhanced compared to a homogeneous medium, thereby possibly leading to more desirable material properties. We discuss this result in light of recent spatial mappings of the superconducting energy gap in BSCCO-2212.Comment: 26 pages, 9 figures, accepted for publication in the Journal of Applied Physic

High field magnetotransport in composite conductors: the effective medium approximation revisited

The self consistent effective medium approximation (SEMA) is used to study three-dimensional random conducting composites under the influence of a strong magnetic field {\bf B}, in the case where all constituents exhibit isotropic response. Asymptotic analysis is used to obtain almost closed form results for the strong field magnetoresistance and Hall resistance in various types of two- and three-constituent isotropic mixtures for the entire range of compositions. Numerical solutions of the SEMA equations are also obtained, in some cases, and compared with those results. In two-constituent free-electron-metal/perfect-insulator mixtures, the magnetoresistance is asymptotically proportional to $|{\bf B}|$ at {\em all concentrations above the percolation threshold}. In three-constituent metal/insulator/superconductor mixtures a line of critical points is found, where the strong field magnetoresistance switches abruptly from saturating to non-saturating dependence on $|{\bf B}|$, at a certain value of the insulator-to-superconductor concentration ratio. This transition appears to be related to the phenomenon of anisotropic percolation.Comment: 16 pages, 3 figure

Model for Vortex Pinning in a Two-Dimensional Inhomogeneous d-wave Superconductor

We study a model for the pinning of vortices in a two-dimensional, inhomogeneous, Type-II superconductor in its mixed state. The model is based on a Ginzburg-Landau (GL) free energy functional whose coefficients are determined by the mean-field transition temperature T_{c0} and the zero-temperature penetration depth \lambda(0). We find that if (i) T_{c0} and \lambda(0) are functions of position, and (ii) \lambda^2(0) is proportional to T_{c0}^y, with y greater than 0, then the vortices tend to be pinned where T_{c0}, and hence the magnitude of the superconducting order parameter \Delta, are large. This behavior is in contrast to the usual picture of pinning in Type-II superconductors, where pinning occurs in the small-gap regions. We also compute the local density of states of a model BCS Hamiltonian with d-wave symmetry, in which the pairing field is obtained from Monte Carlo simulations of a GL free energy. Several features observed in scanning tunneling spectroscopy measurements on YBa_2Cu_3O_{6+x} and Bi_2Sr_2CaCu_2O_{8+x} are well reproduced by our model: far from the cores, the local density of states spectrum has a small gap and sharp coherence peaks, while near the cores it has a larger gap with low, broad peaks. Additionally, also in agreement with experiment, the spectrum near the core does not exhibit a zero-energy peak which is, however, observed in other theoretical studies.Comment: 25 pages, 11 figures. Accepted for publication in Phys. Rev.

Thermophysical properties of simple liquid metals: A brief review of theory

In this paper, we review the current theory of the thermophysical properties of simple liquid metals. The emphasis is on thermodynamic properties, but we also briefly discuss the nonequilibrium properties of liquid metals. We begin by defining a 'simple liquid metal' as one in which the valence electrons interact only weakly with the ionic cores, so that the interaction can be treated by perturbation theory. We then write down the equilibrium Hamiltonian of a liquid metal as a sum of five terms: the bare ion-ion interaction, the electron-electron interaction, the bare electron-ion interaction, and the kinetic energies of electrons and ions. Since the electron-ion interaction can be treated by perturbation, the electronic part contributes in two ways to the Helmholtz free energy: it gives a density-dependent term which is independent of the arrangement of ions, and it acts to screen the ion-ion interaction, giving rise to effective ion-ion pair potentials which are density-dependent, in general. After sketching the form of a typical pair potential, we briefly enumerate some methods for calculating the ionic distribution function and hence the Helmholtz free energy of the liquid: monte Carlo simulations, molecular dynamics simulations, and thermodynamic perturbation theory. The final result is a general expression for the Helmholtz free energy of the liquid metal. It can be used to calculate a wide range of thermodynamic properties of simple metal liquids, which we enumerate. They include not only a range of thermodynamic coefficients of both metals and alloys, but also many aspects of the phase diagram, including freezing curves of pure elements and phase diagrams of liquid alloys (including liquidus and solidus curves). We briefly mention some key discoveries resulting from previous applications of this method, and point out that the same methods work for other materials not normally considered to be liquid metals (such as colloidal suspensions, in which the suspended microspheres behave like ions screened by the salt solution in which they are suspended). We conclude with a brief discussion of some non-equilibrium (i.e., transport) properties which can be treated by an extension of these methods. These include electrical resistivity, thermal conductivity, viscosity, atomic self-diffusion coefficients, concentration diffusion coefficients in alloys, surface tension and thermal emissivity. Finally, we briefly mention two methods by which the theory might be extended to non-simple liquid metals: these are empirical techniques (i.e., empirical two- and three-body potentials), and numerical many-body approaches. Both may be potentially applicable to extremely complex systems, such as nonstoichiometric liquid semiconductor alloys

Superfluid Inhomogeneity and Microwave Absorption in Model High-T_c Superconductors

We investigate the microwave absorption arising from inhomogeneity in the superfluid density of a model high-T_c superconductor. Such inhomogeneities may arise from a wide variety of sources, including quenched random disorder and static charge density waves such as stripes. We show that both mechanisms will inevitably produce additional absorption at finite frequencies. We present simple model calculations for this extra absorption, and discuss applications to other transport properties in high-T_c materials. Finally, we discuss the connection of these predictions to recent measurements by Corson et al. of absorption by the high-temperature superconductor BSCCO in the THz frequency regime.Comment: Presented at ETOPIM-6; latex file requires espcrc2.st

Robotic Astronomy with the Faulkes Telescopes and Las Cumbres Observatory Global Telescope

We present results from ongoing science projects conducted by members of the Faulkes Telescope (FT) team and Las Cumbres Observatory Global Telescope (LCOGT). Many of these projects incorporate observations carried out and analysed by FT users, comprising amateur astronomers and schools. We also discuss plans for the further development of the LCOGT network.Comment: 8 pages, 2 figures, conference proceedings from "Workshop on Robotic Autonomous Observatories", held at Malaga, Spain from 18-21 May 2009, acccepted for publication in Advances in Astronom