Abstract
We have calculated the shift and change in width, due to superconductivity, for a q=0 Raman-active phonon in a two-dimensional, tight-binding band structure with a d-wave pairing interaction. We find that additional structure appears in the phonon self-energy due to the van Hove singularity, which occurs in two dimensions. A more general model of a superconductor with nodes in the gap function is also examined and related to both the d-wave model and another model for layered superconductors. In contrast to the usual isotropic s-wave case where a phonon with frequency less than twice the gap value is softened and narrowed, we find softening with broadening in these models. Comparison of the anisotropic models is made with experiment.
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