Anomalous electron trapping by localized magnetic fields

We consider an electron with an anomalous magnetic moment g > 2 confined to a plane and interacting with a nonzero magnetic field B perpendicular to the plane. We show that if B has compact support and the magnetic flux in the natural units is F ≥ 0, the corresponding Pauli Hamiltonian has at least 1 + [F ] bound states, without making any assumptions about the field profile. Furthermore, in the zero-flux case there is a pair of bound states with opposite spin orientations. Using a Birman-Schwinger technique, we extend the last claim to a weak rotationally symmetric field with B(r) = O(r −2−δ) correcting thus a recent result. Finally, we show that under mild regularity assumptions the existence can be proved for non-symmetric fields with tails as well.