Nonzero Fermi Level Density of States for a Disordered d -Wave Superconductor in Two Dimensions

In 3D, arbitrarily weak disorder in superconductors with line nodes gives rise to a nonzero Fermi level density of states $N(0)$, leading to characteristic low-temperature thermodynamics similar to that observed in cuprate and heavy-fermion systems. In a strictly 2D model, possibly appropriate for the cuprates, it has been argued that $N(0)$ vanishes. We perform an exact calculation for a 2D d-wave superconductor with Lorentzian disorder and find a nonzero $N(0)$. For other continuous distributions we obtain a nonzero lower bound for $N(0)$. We discuss the reasons for this discrepancy.