Odd frequency pairing in a quantum critical metal

We analyze the possibility of odd-frequency pairing near a quantum critical point(QCP) in metal. consider model with dynamical interaction $V({\mathrm{\ensuremath{\Omega}}}_{n})\ensuremath{\sim}1/{|{\mathrm{\ensuremath{\Omega}}}_{n}|}^{\ensuremath{\gamma}}$ (the $\ensuremath{\gamma}$ model). This gives rise to non-Fermi liquid normal state and is attractive for pairing. The two trends compete each other. search solutions gap $\mathrm{\ensuremath{\Delta}}({\ensuremath{\omega}}_{m})=\ensuremath{-}\mathrm{\ensuremath{\Delta}}({\ensuremath{\omega}}_{m})$. show that $\ensuremath{\gamma}<1$, superconductivity loses competition does not develop. develop extended which channel larger than one particle-hole channel. For $\ensuremath{\gamma}>1$, we argue original at boundary towards detail how triggered by small external perturbation. In addition, $\ensuremath{\gamma}>2$, system gets frozen point finite range parameter space. highly unconventional phase diagrams flat regions.