Abstract

We investigate superconductivity in two-dimensional massless Dirac fermions at charge neutrality, coupled to bosonic collective modes via a Yukawa interaction. Despite the absence of carriers at zero temperature, we uncover the surprising possibility that such systems can become superconducting near a Gross–Neveu quantum critical point. Remarkably, superconductivity emerges precisely when the fermionic excitations lose coherence—once their anomalous dimension in the normal state becomes sufficiently large. In other words, well-defined quasiparticles fail to superconduct, whereas strongly incoherent ones can.

To capture this behavior, we develop a general framework for four-component Dirac systems and derive explicit algebraic criteria for the onset of pairing. Within this description, different bosonic modes—classified by their transformation under time-reversal and internal symmetries—select distinct superconducting channels. We then apply this approach to Dirac models of spin–orbit–coupled systems with orbitals of opposite parity and extend it to analyze superconductivity in moiré Dirac materials such as double-bilayer WSe₂ and twisted bilayer graphene