Odd frequency pairing in a quantum critical metal

TL;DR

This paper investigates the emergence of odd-frequency superconductivity near a quantum critical point in a metal, revealing conditions under which it develops or is suppressed, and describing complex phase diagrams for different interaction regimes.

Contribution

It introduces a $ ext{γ}$-model to analyze odd-frequency pairing near a QCP, identifying critical values of $ ext{γ}$ that determine the stability and onset of unconventional superconductivity.

Findings

Odd-frequency pairing does not develop for γ<1.

Superconductivity emerges when the pairing interaction exceeds the particle-hole interaction.

For γ>2, the system exhibits a frozen critical point with flat phase diagram regions.

Abstract

We analyze a possibility for odd-frequency pairing near a quantum critical point(QCP) in a metal. We consider a model with dynamical pairing interaction $V(\Omega_n)\sim 1/|\Omega_n|^\gamma$ (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 looses 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 give rise to highly unconventional phase diagrams with flat regions.