Using the massless Dirac-Weyl model of monolayer graphene, we study the effect of a negatively charged Coulomb impurity on the low-lying spectra of single-electron magnetic dot and ring systems. The numerical results show that the electron-hole symmetry in the spectra is broken by the Coulomb potential, and the original degenerate energy level lying at zero energy becomes nondegenerate and splits into infinite discrete angular momentum states, which have positive energies and thus are electron-like. For higher LLs, each has a reverse ordering of the energy levels when r_(02)~2/a~2 is larger than its critical value in the positive energy states for magnetic dot systems owing to the competition between the Coulomb potential and the magnetic confinement.
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