Classification of non-Fermi liquids and their universal superconducting fluctuations: Part I

When a Fermi surface becomes coupled to quantum critical fluctuations, its Fermi liquid description may break down in qualitatively different ways, depending on the nature of the critical mode(s). Generically, fermions become incoherent and subject to a universal pairing interaction generated by the critical fluctuations. Due to the Fermi momentum, which sets a scale in the system, the universal pairing interaction is bound to depend explicitly on the energy scale. Therefore, the stability of a non-Fermi liquid is determined by a scale-dependent competition between the incoherence of fermions, which tends to deter pairing, and the universal pairing interaction. In this talk, we present a systematic classification of non-Fermi liquids and their superconducting instabilities through projective fixed points that generalize the notion of fixed points for metals. More details on physical predictions will follow in the subsequent talk (Part II).