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We consider an electron with an anomalous magnetic moment, g>2, confined to aplane and interacting with a nonhomogeneous magnetic field B, and investigatethe corresponding Pauli Hamiltonian. We prove a lower bound on the number ofbound states for the case when B is of a compact support and the related fluxis $N+\epsilon, \epsilon\in(0,1]$. In particular, there are at least N+1 boundstates if B does not change sign. We also consider the situation where themagnetic field is due to a localized rotationally symmetric electric currentvortex in the plane. In this case the flux is zero; there is a pair of boundstates for a weak coupling, and higher orbital-momentum "spin-down" statesappearing as the current strength increases.

Anomalous electron trapping by magnetic flux tubes and electric current vortices