Odd frequency pairing in a quantum critical metal

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