  This paper is devoted to the study of the two-dimensional Dirac-Coulomb
operator in presence of an Aharonov-Bohm external magnetic potential. We
characterize the highest intensity of the magnetic field for which a
two-dimensional magnetic Hardy inequality holds. Up to this critical magnetic
field, the operator admits a distinguished self-adjoint extension and there is
a notion of ground state energy, defined as the lowest eigenvalue in the gap of
the continuous spectrum.
