Superconductivity of Incoherent Electrons near the Relativistic Mott Transition in Twisted Dirac Materials

We demonstrate that superconductivity driven by strong quantum-critical fluctuations can emerge near relativistic Mott transitions in twisted two-dimensional materials. In twisted double-bilayer WSe$_2$, all time-reversal-even, gap-opening collective modes promote pairing, whereas time-reversal-odd modes do not. In twisted bilayer graphene, all transitions into intervalley-coherent insulators give rise to superconductivity. Hence, the two separate superconducting domes of insulating or semimetallic undoped systems are expected to merge near the Gross-Neveu transition angle. A crucial ingredient of the theory is that critical fluctuations render the electronic states strongly incoherent, allowing attractive pairing channels to overcome the bare Dirac semimetal behavior. The richer the Dirac structure, the more readily pairs can form. Finally, we demonstrate a direct relation between boson-mediated pairing and the formation of charge-carrying skyrmions in the proximate insulating state.