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Anomalous electron trapping by localized magnetic fields

F. Bentosela·R. M. Cavalcanti·P. Exner·V. A. Zagrebnov
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Abstract

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\ge 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.

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F. Bentosela, R. M. Cavalcanti, P. Exner, V. A. Zagrebnov. 1999-03-13. Anomalous electron trapping by localized magnetic fields. https://doi.org/10.1088/0305-4470%2F32%2F16%2F011

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