Disorder Effects in Two-Dimensional d-wave Superconductors

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Influence of weak nonmagnetic impurities on the single-particle density of states $ho(\omega)$ of two-dimensional electron systems with a conical spectrum is studied. We use a nonperturbative approach, based on replica trick with subsequent mapping of the effective action onto a one-dimensional model of interacting fermions, the latter being treated by Abelian and non-Abelian bosonization methods. It is shown that, in a d-wave superconductor, the density of states, averaged over randomness, follows a nontrivial power-law behavior near the Fermi energy: $ho(\omega) \sim |\omega|^{\alpha}$. The exponent $\alpha>0$ is calculated for several types of disorder. We demonstrate that the property $ho(0) = 0$ is a direct consequence of a {\it continuous} symmetry of the effective fermionic model, whose breakdown is forbidden in two dimensions. As a counter example, we consider another model with a conical spectrum - a two-dimensional orbital antiferromagnet, where static disorder leads to a finite $ho(0)$ due to breakdown of a {\it discrete} (particle-hole) symmetry.

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TWO &#150 DIMENSIONAL SYSTEMS SUPERCONDUCTORS ORDER PARAMETERS D WAVES IMPURITIES ELECTRONIC STRUCTURE ENERGY &#150 LEVEL DENSITY SYMMETRY BREAKING