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 Tc 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 ωm=±πT. We obtain the analytic formula for Tc, which reproduces well earlier numerical results for the electron-phonon model at vanishing Debye frequency.
Bibliographical noteFunding Information:
This work was supported in part by the NSF DMR-1523036 (A.???C.), the Gordon and Betty Moore Foundation???s EPiQS Initiative through Grant No.? GBMF4305 at the University of Illinois (Y.???W.), and by the David and Lucille Packard Foundation (E.???Y.). Ar. A. and A.???C. are thankful to the Aspen Center for Physics where part of this work has been done. B.???A., E. Y, and A.???C. acknowledge partial support from KITP at UCSB. The research at KITP was supported in part by the National Science Foundation under Grant No.? PHY11-25915.
© 2016 American Physical Society.