Disorder effect in low dimensional superconductors

The quasiparticle density of states (DOS), the energy gap, the superfluid density $\rho_s$, and the localization effect in the s- and d-wave superconductors with non-magnetic impurity in two dimensions (2D) are studied numerically. For strong (unitary) scatters, we find that it is the range of the scattering potential rather than the symmetry of the superconducting pairing which is more important in explaining the impurity dependences of the specific heat and the superconducting transition temperature in Zn doped YBCO. The localization length is longer in the d-wave superconducting state than in the normal state, even in the vicinity of the Fermi energy.