TY - JOUR

T1 - 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

AU - Wu, Yi Ming

AU - Abanov, Artem

AU - Chubukov, Andrey V.

N1 - Publisher Copyright:
© 2020 American Physical Society.

PY - 2020/9/1

Y1 - 2020/9/1

N2 - 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)10.1103/PhysRevB.102.024524 and Y. Wu 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 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 γ→1 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 N≠1, 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.

AB - 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)10.1103/PhysRevB.102.024524 and Y. Wu 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 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 γ→1 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 N≠1, 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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U2 - 10.1103/PhysRevB.102.094516

DO - 10.1103/PhysRevB.102.094516

M3 - Article

AN - SCOPUS:85093100900

SN - 2469-9950

VL - 102

JO - Physical Review B

JF - Physical Review B

IS - 9

M1 - 094516

ER -