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 (the model). We analyze both the original model and its extension, in which we introduce an extra parameter 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 and argued that (i) at , there exists an infinite discrete set of topologically different gap functions , all with the same spatial symmetry, and (ii) each evolves with temperature and terminates at a particular . In this paper we analyze how the system behavior changes between and , both at and a finite . The limit is singular due to infrared divergence of , and the system behavior is highly sensitive to how this limit is taken. We show that for , the divergencies in the gap equation cancel out, and gradually evolve through both at and a finite . For , divergent terms do not cancel, and a qualitatively new behavior emerges for . Namely, the form of changes qualitatively, and the spectrum of condensation energies becomes continuous at . We introduce different extension of the model, which is free from singularities for .
18 More- Received 28 July 2020
- Accepted 3 September 2020
DOI:https://doi.org/10.1103/PhysRevB.102.094516
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