Landau problem and electron vortex in pure gauge fields

Abstract

Recently, electron vortices have attracted attention both experimentally and theoretically. A study on the Landau–Dirac problem is made to understand the nature of electron vortices. This line of investigation is motivated by the recent literature on the Landau problem that throws new insights on the nature of orbital angular momentum, i.e. canonical versus kinetic in the context of QCD. The significance of pure gauge vector potential, nontrivial topology and exchange of modular orbital angular momentum to understand the physical origin of electron vortices in the Landau–Dirac problem are new contributions of this paper.