Weak-localization theory for quasiparticle dynamical conductivities of disordered d-wave superconductors

By the diagrammatic technique, we calculate the quantum interference (QI) contributions to the quasiparticle dynamical conductivities of two-dimensional d-wave superconductors with dilute nonmagnetic impurities either near the Born or near the unitary limit. For generic situations, only the 0-mode cooperon has QI contributions to the charge and spin conductivities. It is found that with decreasing frequency, the spin conductivity increases logarithmically while the charge one decreases logarithmically. Such a qualitative difference originates from a novel QI process related to the intrinsic particle-hole symmetry. In the combined limit of unitarity and nested Fermi surface, there exist additional diffusive π modes in addition to the usual diffusive 0 modes. The QI corrections in this limit are shown to vanish due to the cancellation of the contributions from 0-mode and π-mode cooperons, so that both the charge and spin conductivities approach their universal values.