The effect of spontaneous generation of the self-consistent axial-symmetric vacuum current and dipole-type magnetic field for graphene-type planar electron-positron system and graphene-type heterostructures with external supercritical extended Coulomb source with charge $Z$ is considered. It is shown that the main contribution to this effect comes from discrete levels diving into the lower continuum. The form of induced vacuum magnetic field is explored in detail. It is also shown that the magnetic component of vacuum polarization arising in such a way decreases the Casimir (vacuum) energy of the system significantly and therefore can arise spontaneously.
31.30.J- Relativistic and quantum electrodynamic
31.30.jf QED calculations of level energies, transition frequencies, fine structure intervals
81.05.ue Graphene
$^1$Department of Quantum Theory and High Energy Physics, Faculty of Physics, M.V.Lomonosov Moscow State University
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