The role of the impurity-potential range in disordered d-wave superconductors

We analyse how the range of disorder affects the localization properties of quasiparticles in a two-dimensional d-wave superconductor within the standard non-linear sigma-model approach to disordered systems. We show that for purely long range disorder, which only induces intra-node scattering processes, the approach is free from the ambiguities which often beset the disordered Dirac-fermion theories, and gives rise to a Wess-Zumino-Novikov-Witten action leading to vanishing density of states and finite conductivities. We also study the crossover induced by inter-node scattering due to a short range component of the disorder, thus providing a coherent non-linear sigma-model description in agreement with all the various findings of different approaches.