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.