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Here the vector notation q has been explicitly used for clarity.
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Superconductivity is only detectable as an instability of the Fermi liquid, the superconducting phase itself being characterized by an order parameter of higher order in 1/N. This makes it difficult to put superconducting and charge instabilities on equal footing in order to investigate their interplay.
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A specific example of this effect can be given by a mean-field treatment of a Kondo-lattice model [21], which showed, indeed, the large stabilizing effect that superconductivity may have in providing a better alternative than phase separation to use the attraction present in the system.
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These fluctuation effects are not present in our treatment: Our leading order large-N approach, having a diagrammatic structure very similar to RPA, shares many features of a mean-field approach.
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