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Norman J. Morgenstern HORING, Sina BAHRAMI; Landau Minibands in an Antidot Lattice; Advanced Nano-Bio-Materials and Devices; 2017:1(1):24-28
We derive the Schrödinger eigen-energy dispersion relation for electrons on a two dimensional sheet with a one dimensional periodic lattice of quantum antidot potential barriers, in the presence of a strong perpendicular magnetic field. This system is Landau quantized by the high magnetic field and we determine the associated Green's function for propagation along the axis of the antidot lattice, which we use to formulate the dispersion relation for the energy spectrum analytically in a closed form in terms of the Jacobi Theta Function (3rd kind). An approximate solution for the Landau quantized eigen-energies is obtained in terms of Laguerre polynomials, and the development of Landau minibands is explicitly exhibited.