Confined Dirac particles in a constant and tilted magnetic field

We study the confinement of charged Dirac particles in a plane embedded in 3 + 1 space-time due to the presence of a constant magnetic field that is tilted on the given plane. 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 wave functions, 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.