Topics in the theory of inhomogeneous media: Composite superconductors and dielectrics.

摘要

For composite superconductors, three topics are studied. First, a fully frustrated three-dimensional XY model is studied using Monte Carlo calculations, finite-size scaling, and renormalization group methods. We find that the system has a continuous phase transition with critical temperature Tc = 0:681J/kB and critical exponents alpha/nu = 0.87 +/- 0.01, v/nu = 0.82 +/- 0.01, and nu = 0.72 +/- 0.07. Second, the superconductor-insulator transition of a disordered 2D superconducting film as a function of the applied magnetic field is studied using quantum Monte Carlo calculations of the (2+1)D XY model. The magnetic phase factor Aij is assumed to have a mean of zero and a standard deviation of Delta Aij. The critical coupling constant Kc and the universal conductivity sigma* at Kc are found for several values of DeltaAij. Three different phases, superconductor, Mott insulator, and Bose glass, are identified in the phase diagram of 1 = Kc vs. Delta Aij. Third, the intermodulation coefficient of inhomogeneous high-Tc cuprate superconductors with spatially varying gaps is calculated using an analogy to the description for an inhomogeneous dielectric with a nonzero cubic nonlinearity. Depending on the topology of the system, the intermodulation critical supercurrent density J IMD is enhanced, leading to a desirable material property.;For composite dielectrics, two topics are studied. First, a method to calculate the electric force acting on a sphere in two dielectric spheres immersed in a host with a different dielectric constant is described. The method uses a spectral representation, so the force is presented in a closed analytic form. The force between spheres approaches the dipole-dipole limit when the separation between spheres is very large. Then, the photonic band structures of metallic inverse opals above and below a plasma frequency o p is calculated. A plane wave expansion for the electric field E and the magnetic field B is used for the calculations. We obtain the same results using either field for o > op . We find that the plane wave method converges well for o > o p, but not for o op.