Superconducting instability in non-Fermi liquids

Abstract

We use renormalization group (RG) analysis and dimensional regularization techniques to study potential superconductivity-inducing four-fermion interactions in systems with critical Fermi surfaces of general dimensions (m) and codimensions (d−m), arising as a result of quasiparticle interaction with a gapless Ising-nematic order parameter. These are examples of non-Fermi liquid states in d spatial dimensions. Our formalism allows us to treat the corresponding zero-temperature low-energy effective theory in a controlled approximation close to the upper critical dimension d=dc(m). The fixed points are identified from the RG flow equations, as functions of d and m. We find that the flow toward the non-Fermi liquid fixed point is preempted by Cooper pair formation for both the physical cases of (d=3,m=2) and (d=2,m=1). In fact, there is a strong enhancement of superconductivity by the order parameter fluctuations at the quantum critical point.

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