Non-BCS behavior of the pairing susceptibility near the onset of superconductivity in a quantum-critical metal

In a quantum critical metal, superconductivity out of non-Fermi liquid normal state develops only when the pairing interaction exceeds a certain threshold. The authors show here that the dynamic pairing susceptibility exhibits an unexpected behavior: it diverges at the onset of pairing only for a certain subclass of bare/test pairing amplitudes and remains nonsingular for other amplitudes, and below the instability becomes a nonunique function. The authors argue that this behavior reflects a highly non-BCS nature of the pairing at quantum criticality.