Anomalous electron trapping by magnetic flux tubes and electric current vortices

TL;DR

This paper investigates how magnetic flux tubes and electric current vortices can trap electrons with anomalous magnetic moments, establishing bounds on bound states and analyzing effects of magnetic field configurations.

Contribution

It provides new theoretical bounds on the number of bound states for electrons in nonhomogeneous magnetic fields and explores electron trapping by current vortices.

Findings

At least N+1 bound states when magnetic flux does not change sign.

Existence of bound states in current vortices with zero flux.

Bound states emerge with increasing vortex strength.

Abstract

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