Abstract
The application of a method of conformal-like transformation of the two-dimensional momentum space is presented and discussed with regard to two-dimensional anisotropic superconductors. A new function, the kernel of the density of states, and some integral formulae are derived, interpreted and studied for a few specific cases. Evidences for the incompatibility between the Van Hove scenario and the conformal transformation method with respect to a couple of characteristic ratios, i.e. the transition temperature and the specific heat leap, are displayed in detail for d- and p-wave pairing. The established method allows us to obtain the gap equation in a standardized form common to the models of superconductivity with an arbitrary dispersion relation. Classification of superconductors with respect to the valuation of characteristic ratios is proposed and commented on.
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