title: Superconductivity near a Quantum-Critical Point: The Special Role of the First Matsubara Frequency.
abstract: 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 the tendency to pairing and fermionic incoherence for a set of quantum-critical models with effective dynamical interaction between low-energy fermions. We argue that superconducting T_{c} is nonzero even for strong incoherence and/or weak interaction due to the fact that the self-energy from dynamic critical fluctuations vanishes for the two lowest fermionic Matsubara frequencies ω_{m}=±πT. We obtain the analytic formula for T_{c}, which reproduces well earlier numerical results for the electron-phonon model at vanishing Debye frequency.
authors: Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
authors: Yuxuan
authors: Y
authors: Wang
authors: Department of Physics, Texas A&M University, College Station, Texas 77843, USA.
authors: Artem
authors: A
authors: Abanov
authors: Department of Physics, Columbia University, New York, New York 10027, USA.
authors: Boris L
authors: BL
authors: Altshuler
authors: Center for Materials Theory, Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA.
authors: Emil A
authors: EA
authors: Yuzbashyan
authors: School of Physics and Astronomy and William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA.
authors: Andrey V
authors: AV
authors: Chubukov