Pseudogaps, impurity states, and pairing polarons in superconductors

The origin of the pseudo gap in low carrier density superconductors is discussed. The role of phase fluctuations of the order parameter lead to destruction of long range order, preserving the short range order observed in tunneling and photoemission spectra. The electronic structure of magnetic impurities in s-wave superconductors is presented. One finds a first order quantum phase transition as a function of the exchange coupling in which a spin one half is trapped at the impurity. In addition, the possibility of polarons involving the amplitude of the gap parameter is explored. One finds rings of quasi particles form with gap states occurring on the ring wall.