Distributed curvature and spinorial holonomy in Yukawa-regularized disclinations: a finite-core model for graphene-like Dirac systems

Conical geometries provide the standard description of disclinations, but they concentrate the curvature at a singular apex. We introduce a Yukawa-type regularization that replaces the apex singularity by a finite core with an integrable, logarithmically peaked curvature distribution, while preserving the asymptotic conical geometry and its deficit angle. The metric is continuous and locally Euclidean at the origin, although the Ricci scalar diverges logarithmically there. Exact expressions are obtained for the conformal factor, the curvature, and the curvature enclosed by a circle of radius ρ ρ , which is scale dependent and reaches the topological value only asymptotically. The corresponding vector and spinorial holonomies are derived from the spin connection. For massless Dirac quasiparticles in a single valley, we show that the spin-connection term can be removed from the radial equations by a rescaling, so that the core acts only through the conformal factor, and that the far-field problem reproduces the standard Dirac equation on a cone. The model describes the geometric part of the disclination problem in graphene-like systems and does not include the valley-mixing gauge holonomy.