Spin-1/2 Landau levels in the symmetric gauge from the zero energy modes
arXiv:1705.09821 · doi:10.1088/2399-6528/aabdf3
Abstract
Starting from the zero modes of the Dirac-Weyl equation for Landau levels in the symmetric gauge, we propose a novel mechanism to construct the eigenvalues and its eigenfunctions. We show that the problem may be addressed without numerical calculation and only solving the Dirac-Weyl equation for the zero modes. Specifically, the eigenstates associated to the negative magnetic field configurations may be constructed from the zero mode with positive chirality. In addition, we obtain that the eigenstates associated to the positive magnetic field configurations may be constructed from the zero mode with negative chirality. Finally, we show that our mechanism may be used to obtain the eigenvalues and eigenfunctions of the Hamiltonian corresponding to bilayer graphene system.
21 pages, 0 figures, version to be published in Journal of Physics Communications
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