Non-Fermi liquid Superconductivity: Eliashberg versus the Renormalization Group

Abstract

We address the problem of superconductivity for non-Fermi liquids using two commonly adopted, yet apparently distinct methods: 1) the renormalization group (RG) and 2) Eliashberg theory. The extent to which both methods yield consistent solutions for the low energy behavior of quantum metals has remained unclear. We show that the perturbative RG beta function for the 4-Fermi coupling can be explicitly derived from the linearized Eliashberg equations, under the assumption that quantum corrections are approximately local across energy scales. We apply our analysis to the test case of phonon mediated superconductivity and show the consistency of both the Eliashberg and RG treatments. We next study superconductivity near a class of quantum critical points and find a transition between superconductivity and a "naked" metallic quantum critical point with finite, critical BCS couplings. We speculate on the applications of our theory to the phenomenology of unconventional metals.

34 pages, 6 figures

References in corpus (15)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Quantum Criticality in Heavy Fermion Metals
• Quantum criticality
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Are non-Fermi-liquids stable to Cooper pairing?
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Stability of the U(1) spin liquid with spinon Fermi surface in 2+1 dimensions
• A controlled expansion for certain non-Fermi liquid metals
• Quantum critical metals in $4-\epsilon$ dimensions
• Renormalization Group Approach to Strong-Coupled Superconductors
• Fermi surfaces in general co-dimension and a new controlled non-trivial fixed point
• Pairing in half-filled Landau level
• Aspects of Renormalization in Finite Density Field Theory
• Pairing gaps near ferromagnetic quantum critical points

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