Weak-Localization Correction To The Density Of States In Disordered D-Wave Superconductors

A number of experimental studies revealed that the order parameter in high-Tc cuprates is of d-wave symmetry, and thus the properties of d-wave superconductors have been investigated theoretically for many years. The issue that the disorder effect due to impurity scattering on features of d-wave superconductors has been received much attention. Many numerical and analytical works suggested that the weak-localization effect has important influence on quasi-particle density of states and transport properties in d-wave superconductors. In this paper, we study the weak-localization effect due to nonmagnetic impurity scattering on the density of states in d-wave superconductors. Although there have been existed some theoretical works on this problem, the weak-localization theory is not well established, and the results are in disagreement.The tight-binding model for two-dimensional square lattice is used to study the low-energy density of states around nodal points in d-wave superconductors. With the diagrammatic techniques and self-consistent T-matrix approximation, we obtain the one-particle Green's functions of d-wave superconductors, and derive the expressions of the diffusive modes. The quantum interference correction to the density of states due to these modes are calculated, and the main results are as follows.(1) For generic Fermi surface, only the 0-mode cooperon contributes to the weak-localization correction to density of states, which is of logarithmic suppression.(2) In the case of nesting Fermi surface and unitary limit (UN limit), those self-energy diagrams with two π -mode diffusons have additional contributions to the density of states. Therefore, the density of states is subject to a negative correction. This result is qualitatively different from previous one.The present work is expected to be helpful in understanding the density of states in disordered d-wave superconductors. Our main new results are as follows: (1) The detailed derivations of the diffusive modes in d-wave superconductors are presented, which were not provided in the previous works; (2) We find some new self-energy diagrams with two π -mode diffusions, which were neglected by previous workers. These new diagrams are shown to have important influence on the density of states in the UN limit, and thus leads to a result qualitatively different from the previous one.