Resonating valence bond pairing energy in graphene by quantum Monte Carlo

Whether short-range electron pairing can be stabilized in graphene remains a central question because pristine graphene is a semimetal with vanishing density of states at the Dirac point. We show that geometry alone can enhance short-range pairing correlations in confined graphene. Using real-space quantum Monte Carlo with correlated trial wavefunctions, we control a simple geometric knob, the commensurability of the simulation cell with the Dirac points, which creates or removes a small, single-particle gap in finite graphene samples. Diffusion quantum Monte Carlo reveals a clear dichotomy, when this geometry-induced gap is present, a resonance-valence-bond(RVB)-like state is energetically favored. Whereas when the spectrum is gapless and cell includes the Dirac points, no RVB energy gain is found. The effect persists in large cells at fixed geometry, establishing that confinement and commensurability can tip the energetic balance toward singlet pairing, while pristine bulk graphene shows no intrinsic RVB instability. These results identify a practical, geometry-controlled route to amplify pairing tendencies in nanoscale graphene devices and provide many-body benchmarks for interpreting finite-cell calculations. Our results also suggest design principles, via shape, aspect ratio, or mild superlattice modulations, to engineer stronger electronic correlations in carbon-based nanoelectronics.