Breakdown of Charge-Conjugation Symmetry of Disclinations in 2D Crystals

Abstract

Disclinations are elementary topological defects in two-dimensional (2D) crystalline membranes, yet their elastic properties remain largely unexplored. Using atomistic simulations, we address the energetics, morphology, and interactions of disclinations in free-standing graphene, a prototypical 2D crystal. We find that while disclinations with positive topological charges follow an expected behavior, negative disclinations exhibit sublinear energy scaling with charge as well as equilibrium shape that deviates sharply from the conventional saddle ansatz. This breakdown of charge-conjugation symmetry leads to qualitatively distinct interactions: positive disclinations repel, whereas negative disclinations display a robust long-range attraction. These trends are shown to be further amplified by self-adhesion in folded membranes. Our results uncover a fundamentally different energetic landscape for negative curvature defects and provide a basis for understanding the stability, self-folding behavior, and defect-driven morphology of graphene and other 2D membranes.