Pseudogap in the electronic density of states of superconducting glasses

Two loop order results for the electronic density of states (DOS) of both Ising- and XY-type superconducting glass phases are presented. Maximal depression of the DOS by critical fluctuation corrections to its finite mean field value is found to occur at the Fermi energyE _F . The theory is renormalizable and exponentiation of the loop expansion yields (E _F)=0 for the DOS in two dimensions and for arbitrarily small disorder. It is also concluded that the DOS assumes nonzero values, when either |E–E _F|, or magnetic field H, or temperature T become nonzero. A pseudogap (atT=0,H=0) or a smeared gap (forH0 orT0) is thus obtained with a DOS-minimum at the Fermi level. A rough estimate of the effective width is given. In three dimensions, the DOS atE _F vanishes like (n _c ^I –n)^1/2 for the Ising-type glass and like (n _c ^XY –n)¹ for the XY-type glass as the impurity concentrationn exceeds characteristic values. At second loop order, the calculation contains a nontrivial indication of a lower critical dimension two.