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

2020/07/29 by Yi-Ming Wu, Yi‐Ming Wu, Ar. Abanov +2 · 19 citations
Materials Science · Physics and Astronomy · #Fermi liquid theory #Iron-based superconductors research #Mathematical physics #Omega #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Rare-earth and actinide compounds #Superconductivity #cond-mat.str-el #cond-mat.supr-con

paper · pdf · doi:10.1103/physrevb.102.094516

published in Physical review. B./Physical review. B 102(9) (American Physical Society) · 43 pages, 25 figures, Paper III in the series on the gamma-model. Papers I and II are arXiv:2004.13220 and arXiv:2006.02968 respectively

arxiv created 2020/07/29 · openalex created_date 2020/08/03 · openalex publication_date 2020/09/23 · arxiv updated 2020/09/30 · openalex updated_date 2026/08/06

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(\mathrm\ensuremathΩ_m)\ensuremath∝1/|\mathrm\ensuremathΩ_m|^\ensuremathγ (the \ensuremathγ 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<\ensuremathγ<1 and argued that (i) at T=0, there exists an infinite discrete set of topologically different gap functions \mathrm\ensuremathΔ_n(\ensuremathω_m), all with the same spatial symmetry, and (ii) each \mathrm\ensuremathΔ_n evolves with temperature and terminates at a particular T_p,n. In this paper we analyze how the system behavior changes between \ensuremathγ<1 and \ensuremathγ>1, both at T=0 and a finite T. The limit \ensuremathγ\ensuremath→1 is singular due to infrared divergence of \ensuremath∫d\ensuremathω_mV(\mathrm\ensuremathΩ_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 \mathrm\ensuremathΔ_n(\ensuremathω_m) gradually evolve through \ensuremathγ=1 both at T=0 and a finite T. For N\ensuremath≠1, divergent terms do not cancel, and a qualitatively new behavior emerges for \ensuremathγ>1. Namely, the form of \mathrm\ensuremathΔ_n(\ensuremathω_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 \ensuremathγ>1.

Citations

• Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. I: The γ-model and its phase diagram at T=0. The case 0 < γ<1
• Interplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal. II. The γ-model at a finite T for 0<γ<1
• Phase fluctuations, dissipation, and superfluid stiffness ind-wave superconductors
• Classical Spins in Superconductors
• Quantum-critical pairing with varying exponents
• Fermi-edge singularities in x-ray spectra of strongly correlated fermions
• BOUND STATE IN SUPERCONDUCTORS WITH PARAMAGNETIC IMPURITIES
• Two-Dimensional Non-Fermi-Liquid Metals: A Solvable Large-N Limit

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• Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. IV: The γ model and its phase diagram at 1<γ<2
• Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal: V. The γ model and its phase diagram. The case γ=2
• Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. VI. The γ model and its phase diagram at 2 < γ<3