Anomalous electron trapping by localized magnetic fields

TL;DR

This paper proves the existence of bound states for an electron with an anomalous magnetic moment in a plane under various magnetic field configurations, expanding understanding of magnetic trapping phenomena.

Contribution

It establishes new bounds on the number of bound states for electrons in localized magnetic fields, including non-symmetric and weakly decaying fields, using advanced spectral techniques.

Findings

At least 1+[F] bound states for compact support fields with flux F≥0

Existence of a pair of bound states in zero-flux case with opposite spins

Extension of results to weak, rotationally symmetric, and non-symmetric 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-\delta}) 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.