Interplay between superconductivity and nonFermi liquid behavior at a quantum critical point in a metal. III. The γ model and its phase diagram across γ =1
Abstract
In this paper we continue our analysis of the interplay between the pairing and the nonFermi liquid behavior in a metal for a set of quantumcritical models with an effective dynamical electronelectron interaction V (Ω_{m}) ∝1 /Ω^{m γ} (the γ model). We analyze both the original model and its extension, in which we introduce an extra parameter N to account for nonequal interactions in the particlehole and particleparticle channel. In two previous papers [A. Abanov and A. V. Chubukov, Phys. Rev. B 102, 024524 (2020), 10.1103/PhysRevB.102.024524 and Y. Wu et al. Phys. Rev. B 102, 024525 (2020), 10.1103/PhysRevB.102.024525] we considered the case 0 <γ <1 and argued that (i) at T =0 , there exists an infinite discrete set of topologically different gap functions Δ_{n}(ω_{m}) , all with the same spatial symmetry, and (ii) each Δ_{n} evolves with temperature and terminates at a particular T_{p ,n}. In this paper we analyze how the system behavior changes between γ <1 and γ >1 , both at T =0 and a finite T . The limit γ →1 is singular due to infrared divergence of ∫d ω_{m}V (Ω_{m}) , and the system behavior is highly sensitive to how this limit is taken. We show that for N =1 , the divergencies in the gap equation cancel out, and Δ_{n}(ω_{m}) gradually evolve through γ =1 both at T =0 and a finite T . For N ≠1 , divergent terms do not cancel, and a qualitatively new behavior emerges for γ >1 . Namely, the form of Δ_{n}(ω_{m}) changes qualitatively, and the spectrum of condensation energies E_{c ,n} becomes continuous at T =0 . We introduce different extension of the model, which is free from singularities for γ >1 .
 Publication:

Physical Review B
 Pub Date:
 September 2020
 DOI:
 10.1103/PhysRevB.102.094516
 arXiv:
 arXiv:2007.14540
 Bibcode:
 2020PhRvB.102i4516W
 Keywords:

 Condensed Matter  Superconductivity;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 43 pages, 25 figures, Paper III in the series on the gammamodel. Papers I and II are arXiv:2004.13220 and arXiv:2006.02968 respectively