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It has been known for some time that, in three dimensions, arbitrarily weakdisorder in unconventional superconductors with line nodes gives rise to anonzero residual density of zero-energy quasiparticle states N(0), leading tocharacteristic low-temperature thermodynamic properties similar to thoseobserved in cuprate and heavy-fermion systems. In a strictly two-dimensionalmodel possibly appropriate for the cuprates, it has been argued that N(0)vanishes, however. We perform exact calculations for d- and extended s-wavesuperconductors with Lorentzian disorder and similar models with continuousdisorder distribution, and show that in these cases the residual density ofstates is nonzero even in two dimensions. We discuss the reasons for thisdiscrepancy, and the implications of our result for the cuprates.

physical review letters

Nonzero Fermi Level Density of States for a Disordered<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">d</mml:mi></mml:math>-Wave Superconductor in Two Dimensions

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