2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167401We study the distribution of vacuum polarization charge induced by a Coulomb impurity in massive graphene. By analytically computing the polarization function, we show that the charge density is distributed in space in a non-trivial fashion, and on a characteristic length-scale set by the effective Compton wavelength. The density crosses over from a logarithmic behavior below this scale, to a power law variation above it. Our results in the continuum limit are confirmed by explicit diagonalization of the corresponding tight-binding model on a finite-size lattice. Electron-electron interaction effects are also discussed.6 pages, 4 figures; expanded versionMesoscale and Nanoscale PhysicsStrongly Correlated Electronstext