Density of states for dirty d-wave superconductors: A unified and dual approach for different types of disorder

A two-parameter field theoretical representation is given of a 2-dimensional dirty d-wave superconductor that interpolates between the Gaussian limit of uncorrelated weak disorder and the unitary limit of a dilute concentration of resonant scatterers. It is argued that a duality holds between these two regimes from which follows that a linearly vanishing density of states in the Gaussian limit transforms into a diverging one in the unitary limit arbitrarily close to the Fermi energy.