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

Critical magnetic field for 2d magnetic Dirac-Coulomb operators and Hardy inequalities