Magnetic subband structure of electrons in hexagonal lattices

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Abstract
The energy spectrum of an electron in the presence of a uniform magnetic field and a potential of hexagonal symmetry is analyzed. Two alternative approaches are used, one that takes as a basis set free-electron Landau functions, and a second one that treats an effective single-band Hamiltonian with the Peierls substitution. Both methods lead to consistent results. The energy spectrum is found to have recursive properties similar to those discussed by Hofstadter for the case of a square lattice. The density of states over each subband of the spectrum has the same structure as that for the original field-free band. The plot of integrated density of states versus field is also discussed.