Interplay between superconductivity and non-Fermi liquid behavior at a quantum critical point in a metal. III. The γ model and its phase diagram across γ=1

Yi-Ming Wu, Artem Abanov, and Andrey V. Chubukov
Phys. Rev. B 102, 094516 – Published 23 September 2020

Abstract

In this paper we continue our analysis of the interplay between the pairing and the non-Fermi liquid behavior in a metal for a set of quantum-critical models with an effective dynamical electron-electron interaction V(Ωm)1/|Ωm|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 particle-hole and particle-particle channel. In two previous papers [A. Abanov and A. V. Chubukov, Phys. Rev. B 102, 024524 (2020) and Y. Wu et al. Phys. Rev. B 102, 024525 (2020)] 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 Δn(ωm), all with the same spatial symmetry, and (ii) each Δn evolves with temperature and terminates at a particular Tp,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 γ1 is singular due to infrared divergence of dωmV(Ωm), 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 Δn(ωm) gradually evolve through γ=1 both at T=0 and a finite T. For N1, divergent terms do not cancel, and a qualitatively new behavior emerges for γ>1. Namely, the form of Δn(ωm) changes qualitatively, and the spectrum of condensation energies Ec,n becomes continuous at T=0. We introduce different extension of the model, which is free from singularities for γ>1.

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  • Received 28 July 2020
  • Accepted 3 September 2020

DOI:https://doi.org/10.1103/PhysRevB.102.094516

©2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yi-Ming Wu1, Artem Abanov2, and Andrey V. Chubukov1

  • 1School of Physics and Astronomy and William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA
  • 2Department of Physics, Texas A&M University, College Station, Texas, USA

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Vol. 102, Iss. 9 — 1 September 2020

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