Bielectron Vortices in Monolayer Dirac Semimetals

Abstract The exploration of emergent phases in low‐dimensional quantum systems continues to be a focal point of condensed matter physics. Among these, monolayer Dirac materials stand out due to their relativistic‐like charge carriers, and potential for technological innovation. In this work, a rigorous analysis of interacting electron‐electron systems is presented within the framework of the fully covariant two‐body Dirac equation derived from quantum electrodynamics. This approach enables the exact determination of binding conditions for massless electron pairs at zero total energy, interacting via attractive potentials that decay more rapidly than the Coulomb potential. The critical coupling constants governing the onset of bound states are analytically derived, revealing their dependence on the Dirac semimetal fine‐structure constant and their sensitivity to localized defects. By resolving state‐specific critical thresholds associated with defect configurations, the emergence of stable, doubly charged electron pairs beyond these couplings is demonstrated. Notably, these bound states manifest exclusively as rotating, ring‐like configurations, characterized by zero net energy and topologically nontrivial behavior. The results unveil a new class of stable, zero‐energy electron–electron bound states in monolayer Dirac semimetals, pointing to the formation of quantized rotational vortices in these systems.