F Bentosela et al 1999 J. Phys. A: Math. Gen. 32 3029 doi:10.1088/0305-4470/32/16/011
Anomalous electron trapping by localized magnetic fields
F Bentosela
, R M Cavalcanti
, P Exner§ and V A Zagrebnov
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 natural units is 
, the corresponding Pauli Hamiltonian has at least 
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 
, thus correcting a recent result. Finally, we show that under mild regularity assumptions existence of the bound states can also be proved for non-symmetric fields with tails.
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Issue 16 (23 April 1999)
Received 22 December 1998
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Anomalous electron trapping by localized magnetic fields
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