Superconducting instability near a quantum critical point – fate of the fermions

At the Ising nematic quantum critical point, soft order parameter bosons induce a superconducting instability. We study the impact of this instability on the fermionic quasiparticles, by tracking the evolution of the fermionic self-energy at T = 0 from the normal to the superconducting state. This is achieved by resumming a class of "planar diagrams", which contain hidden 1d physics. We find that around the characteristic superconducting energy scale the self-energy develops a prominent feature, whose precise form is determined by the momentum dependence of the nematic fluctuations, and is in marked difference to the BSC case. Implications for real and numerical experiments are discussed.