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 non-zero magnetic field B perpendicular to the plane. We show that if B has compact support and the magnetic flux in n atural units is F greater than or equal to 0, the corresponding Pauli Hamil tonian has at least 1 + [F] bound states, without making any assumptions ab out the field profile. Furthermore, in the zero-flux case there is a pair o f bound states with opposite spin orientations. Using a Birman-Schwinger te chnique, we extend the last claim to a weak rotationally symmetric field wi th B(r) = O(r(-2-delta)), thus correcting a recent result. Finally, we show that under mild regularity assumptions existence of the bound states can a lso be proved for non-symmetric fields with tails.