Ginzburg-Landau theory and the superconducting transition in thin, amorphous bismuth films

The Aslamasov-Larkin (AL) theory can be derived from a classical treatment of the conductivity due to short-lived statistical fluctuations into the superconducting state if one truncates the Ginzburg-Landau free energy density expression to read F[psi] = α0 vertical barpsi vertical bar2 + c0 vertical bar del psi vertical bar2, where psi is the superconducting order parameter. The next largest term in the GL free energy is (b/2) (vertical bar psi vertical bar2)2 and is conventionally interpreted as representing the energy associated with interactions between the fluctuations. My dissertation consists of the calculation of the effect of this term on the fluctuation conductivity in three different approximations and the comparison of my predictions to the data of R.E. Glover III and M.K. Chien on thin amorphous bismuth films. The first approximation calculates the contribution to the fluctuations' self energy of the ''tadpole'' diagrams. This approximation yields a 4 parameter equation. Its fits were particularly outstanding for the films deposited on quartz or roughened glass substrates and only for two smooth glass substrates were there non-isolated data points that were not fit at the lowest temperatures measured. (The equation runs into trouble for these films at approximately R(T)/R/sub o/ =.08.) The values of the theoretical equation's fitting parameters were determined by a least squares method and turns out to depend on film thickness in the manner predicted by the theory. The next calculation improves the self energy approximation by including all the ''ring'' diagrams