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 co-dimensions ($d-m$), 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 $d=d_c(m)$. The fixed points are identified from the RG flow equations, as functions of $d$ and $m$. We find that the flow towards 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.

There were a few typographical and other errors in the published version. These errors affect the RG flow equations in the main text, thus changing the fixed points. However, they do not affect our main results and conclusions. This arxiv version includes the corrected results. The erratum has been published as Phys. Rev. B 109, 079902 (2024)

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