Confined Dirac Particles in Constant and Tilted Magnetic Field

TL;DR

This paper investigates how charged Dirac particles are confined in 3+1 dimensions under a constant, tilted magnetic field, analyzing solutions of the Dirac equation and their implications for the relativistic quantum Hall effect.

Contribution

It introduces a specific gauge choice for the magnetic field, deriving localized spinor wavefunctions in terms of Hermite polynomials, and compares these results with 2+1 dimensional cases.

Findings

Wavefunctions are localized in the plane perpendicular to the vector potential.

Solutions depend on the gauge choice of the magnetic field.

Results have implications for the relativistic quantum Hall effect.

Abstract

We study the confinement of charged Dirac particles in 3+1 space-time due to the presence of a constant and tilted magnetic field. We focus on the nature of the solutions of the Dirac equation and on how they depend on the choice of vector potential that gives rise to the magnetic field. In particular, we select a "Landau gauge" such that the momentum is conserved along the direction of the vector potential yielding spinor wavefunctions, which are localized in the plane containing the magnetic field and normal to the vector potential. These wave functions are expressed in terms of the Hermite polynomials. We point out the relevance of these findings to the relativistic quantum Hall effect and compare with the results obtained for a constant magnetic field normal to the plane in 2+1 dimensions.