Higher angular momentum pairing from transverse gauge interactions

Abstract

In this paper, we study superconductivity of nonrelativistic fermions at finite-density coupled to a transverse $U(1)$ gauge field, with the effective interaction including the Landau-damping. This model, first studied by Holstein, Norton, and Pincus [Phys. Rev B, {\bf 8}, 2649 (1973)] has been known as an example of a non-Fermi liquid, {ı.e.} a metallic state in which the decay rate of a quasiparticle is large compared to the characteristic quasiparticle energy; other examples of the non-Fermi liquid includes the 2d electron gas in a magnetic field at $\nu =1/2$ and the normal state of optimally doped cuprate superconductors. Our study thus addresses the question of whether or not non-Fermi liquids, like Fermi liquids, are unstable towards the formation of superconductivity.The results are (i) the non-Fermi liquid is stable against superconductivity below a critical gauge coupling, (ii) above this critical coupling, the ground state is an unconventional superconductor with angular momentum $\ell \ge 2$. Our results are obtained from a solution of the Dyson-Nambu equation. Note that in this problem there is a quantum critical point between a non-Fermi liquid state and the superconducting state, as the critical coupling is nonzero. This is in contrast to a weakly coupled metal, which exhibits superconductivity for infinitesimally weak interaction regardless of its sign.

8 pages and 10 figures

References in corpus (5)

• Color superconductivity in dense quark matter
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• A controlled expansion for certain non-Fermi liquid metals
• Spin-triplet pairing instability of the spinon Fermi surface in a U(1) spin liquid
• The Kohn-Luttinger Effect in Gauge Theories

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• Pairing in half-filled Landau level
• UV/IR Mixing In Non-Fermi Liquids: Higher-Loop Corrections In Different Energy Ranges
• Thermoelectric and thermal properties of the weakly disordered non-Fermi liquid phase of Luttinger semimetals
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• Strange Metals from Quantum Geometric Fluctuations of Interfaces