Higher angular momentum pairing from transverse gauge interactions

TL;DR

This paper investigates how nonrelativistic fermions coupled to a transverse gauge field can develop unconventional superconductivity with higher angular momentum, depending on the strength of the gauge coupling, revealing a quantum critical point.

Contribution

It demonstrates that non-Fermi liquids can be stable against superconductivity below a critical coupling and become unconventional superconductors with angular momentum ge 2 above it.

Findings

Non-Fermi liquid stability below critical coupling.

Unconventional ge 2 angular momentum superconductivity above critical coupling.

Existence of a quantum critical point between non-Fermi liquid and superconducting states.

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, {\i.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.