Artem G. Abanov | Searcharxiv

arXiv2026

Non-BCS Pairing by a Singular Dynamical Interaction

This review examines the theory of superconductivity in systems with {\em singular dynamical} electron-electron interaction and contrasts it with a conventional BCS superconductivity. Examples include metals near a Quantum Critical Point, quantum dots and system near a localization (Mott) transition. We show, that the singular interaction destroys the traditional separation of energy scales, invalidating the significance of Cooper logarithm, and, as the consequence, the whole BCS framework. We explore the universal model with dynamical interaction $Γ(Ω) \propto 1/|Ω|^γ$ (the $γ$-model) and analyze the competition/interplay between the tendency towards pairing and towards non-Fermi liquid behavior. We show that superconductivity still develops once the pairing interaction exceeds a certain threshold, but the origin of the pairing is qualitatively different from that in BCS theory. We show that the gap equation at $T=0$ has an infinite set of topologically distinct solutions. These solution disappear one by one once the pairing interaction becomes non-singular (massive). We review the physics underlying these phenomena and outline future directions.

cond-mat.supr-con↗

arXiv2016

Superconductivity near a quantum-critical point: The special role of the first Matsubara frequency

Near a quantum-critical point in a metal strong fermion-fermion interaction mediated by a soft collective boson gives rise to incoherent, non-Fermi liquid behavior. It also often gives rise to superconductivity which masks the non-Fermi liquid behavior. We analyze the interplay between superconductivity and fermionic incoherence for a set of quantum-critical models with effective dynamical interaction between low-energy fermions. We argue that superconductivity always develops above a quantum-critical point, no matter how strong the fermionic self-energy is. We argue that superconductivity should not be viewed as a pairing of incoherent fermions, as previously thought. Rather, $T_c$ is non-zero due to the fact that the self-energy is suppressed at the two lowest fermionic Matsubara frequencies $ω_m = \pm πT$. We obtain the analytic formula for $T_c$ which reproduces well numerical results for the electron-phonon model at vanishing Debye frequency.

cond-mat.supr-con↗