Anomalous electron trapping by localized magnetic fields

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.

A LaTeX file, 12 pages; to appear in J. Phys. A: Math. Gen

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Cited by in corpus (7)

• Hamiltonian self-adjoint extensions for (2+1)-dimensional Dirac particles
• Bound States in Mildly Curved Layers
• Weakly coupled bound states of Pauli operators
• Weak perturbations of the p-Laplacian
• Anomalous Pauli electron states for magnetic fields with tails
• On quantum waveguide with shrinking potential
• Weak coupling asymptotics for the Pauli operator in two dimensions