Superconductivity in systems with diluted interactions

Full text: Superconductivity arises from the formation and condensation of Cooper pairs. For pairs to form, an attractive interaction which somehow avoids the instantaneous Coulomb repulsion must be present. In conventional superconductors, this attraction is provided by a temporally retarded interaction mediated by phonons. In high temperature superconductors, it is believed that spin fluctuations might play the same role. Many of the detailed properties of superconductors depend on the precise microscopic mechanism. On the other hand, many interesting qualitative features of superconductivity can be studied without worrying about the precise origin of the attraction and the attractive Hubbard Hamiltonian has proven to be a very useful model to study qualitative features of superconducting phase transitions, for example the coexistence of a sharp Fermi surface with a Bose-like spin gap, and the competition of superconductivity and ordering into insulating charge density wave states. We use Quantum Monte Carlo to study pairing correlations in the two-dimensional attractive Hubbard model when the on-site interaction is turned off randomly on a fraction of lattice sites. We determine the critical dilution as a function of lattice occupation, and show results for the behavior of the density of states through the superconducting phase transition. (author)