  Different superconducting pairing mechanisms are markedly distinct in the
underlying Cooper pair kinematics. Pairing interactions mediated by
quantum-critical soft modes are dominated by highly collinear processes,
falling into two classes: forward scattering and backscattering. In contrast,
phonon mechanisms have a generic non-collinear character. We show that the type
of kinematics can be identified by examining the evolution of superconductivity
when tuning the Fermi surface geometry. We illustrate our approach using
recently measured phase diagrams of various graphene systems. Our analysis
unambiguously connects the emergence of superconductivity at ``ghost
crossings'' of Fermi surfaces in distinct valleys to the pair kinematics of a
backscattering type. Together with the observed non-monotonic behavior of
superconductivity near its onset (sharp rise followed by a drop), it provides
strong support for a particular quantum-critical superconductivity scenario.
These findings conclusively settle the long-standing debate on the origin of
superconductivity in this system and demonstrate the essential role of
quantum-critical modes in superconducting pairing. Moreover, our work
highlights the potential of tuning bands via ghost crossings as a promising
means of boosting superconductivity.
