Spin-1/2 Landau levels in the symmetric gauge from the zero energy modes

SOURROUILLE, LUCAS

Journal of Physics Communications

IOPscience

Lugar: Bristol; Año: 2018 vol. 2

Starting from the zero modes of the Dirac-Weyl equation for Landau levels in the symmetric gauge, wepropose a novel mechanism to construct the eigenvalues and its eigenfunctions. We show that theproblem may be addressed without numerical calculation and only solving the Dirac-Weyl equationfor the zero modes. Specifically, the eigenstates associated to the negative magnetic field configurationsmay be constructed from the zero mode with positive chirality. In addition, we obtain that theeigenstates associated to the positive magnetic field configurations may be constructed from the zeromode with negative chirality. Finally, we show that our mechanism may be used to obtain theeigenvalues and eigenfunctions of the Hamiltonian corresponding to bilayer graphene system.