Matrix field theory for disordered local pairing superconductors with two glass order parameters and spin-flip pairbreaking processes

Abstract

We derive the exact matrix field theory for a replicated grassmannian representation of a local pairing superconducting disorder ensemble including three superconducting order parameters and the spin-flip pairbreaking mechanism. Disorder is assumed to be gaussian distributed. We find by exactly solving the saddle-point equation the criterion for a vanishing gap 〈Δ〉≦τ ⁻¹_σ +τ ⁻¹_Δ , where 〈Δ〉 denotes the averaged superconducting order parameter, τ ⁻¹_σ the spin-flip scattering rate, and τ ⁻¹_Δ the scattering rate corresponding to correlations of Re(Δ−〈Δ〉). Taken at Δ=0, our field theory, which is exact in all orders of τ ⁻¹_σ , contains new terms in addition to those of theO(τ ⁻¹_σ ) model derived by Efetov et al. Our formulation transfers correctly to all orders the invariances of the action into symmetries of the matrix field theory. The saddle point approximation is outlined and it is shown how singular corrections to the saddle point density of states arise atE _F in a gapless superconductor. Finally singular corrections in the two particle propagator, the density correlation function and the conductivity are calculated for 〈Δ〉=0 in one loop order. It turns out that these corrections can be entirely expressed by those of the single particle density of states.