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

Abstract

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 magneticfield configurationsmay be constructed from the zero mode with positive chirality. In addition, we obtain that theeigenstates associated to the positive magneticfield 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.