2020/04/30 by Artem Abanov, Andrey V. Chubukov · 6 citations
Physics and Astronomy · #cond-mat.str-el #cond-mat.supr-con
paper · pdf · doi:10.1103/physrevb.102.024524
published as Phys. Rev. B 102, 024524 (2020) · Replaced with the published version
arxiv created 2020/08/03 · arxiv updated 2020/08/05
We analyze a class of quantum-critical models, in which momentum integration and the selection of a particular pairing symmetry can be done explicitly, and the competition between non-Fermi liquid and pairing can be analyzed within an effective model with dynamical electron-electron interaction V(Ωm)∼ 1/|Ωm|γ (the γ-model). In this paper, the first in the series, we consider the case T=0 and 0<γ<1. We argue that tendency to pairing is stronger, and the ground state is a superconductor. We argue, however, that superconducting state is highly non-trivial as there exists a discrete set of topologically distinct solutions for the pairing gap Δn (ωm) (n = 0, 1, 2..., ∞). All solutions have the same spatial pairing symmetry, but differ in the time domain: Δn (ωm) changes sign n times as a function of Matsubara frequency ωm. The n =0 solution Δ0 (ωm) is sign-preserving and tends to a finite value at ωm =0, like in BCS theory. The n = ∞ solution corresponds to an infinitesimally small Δ(ωm). As a proof, we obtain the exact solution of the linearized gap equation at T=0 on the entire frequency axis for all 0<γ<1, and an approximate solution of the non-linear gap equation.We argue that the presence of an infinite set of solutions opens up a new channel of gap fluctuations. We extend the analysis to the case where the pairing component of the interaction has additional factor 1/N and show that there exists a critical Ncr >1, above which superconductivity disappears, and the ground state becomes a non-Fermi liquid.We show that all solutions develop simultaneously once N gets smaller than Ncr.