The Superconductor to Insulator Transition

Most people are familiar with the onset of superconductivity from a metallic phase or with the well known metal-insulator transition. Recently it has been proposed that at zero temperature in disordered two-dimensional films it should be possible to study a direct superconductor-insulator transition. Experimentally such a transition can be tuned through by varying the thickness and thereby the disorder in for example Bi films. The transition is in this case between a novel insulating 'Bose glass' phase and a superconducting state. Surprisingly, no metallic phase is believed to exist in two dimensions at zero temperature but a superconducting phase is allowed. However, right at the critical point, between the insulating and superconducting phase, these amorphous films should behave as metals and have a finite universal conductivity, sigma^*. Experiments indicate that this universal conductivity should be approximately 1/(6.45 kOmega). In this thesis the 2-D zero-temperature superconductor -insulator transition is studied by Monte Carlo simulations of interacting bosons (Cooper pairs) moving in a quenched random potential. We calculate the universal conductivity sigma^* and the critical exponents at the superconductor-insulator transition. For short -range repulsive interactions we find sigma ^*=(0.14+/- 0.03)sigma_{Q }, where sigma_sp{Q }{-1}equiv R_{Q}equiv h/(2e)^2~eq 6.45 kOmega , and for long-range Coulomb interactions we find sigma^*=(0.55+/- 0.1)sigma _{Q}.