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A Study of the Energy Spectrum for a Periodic Array of Quantum Wells in a Parallel Magnetic Field
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| Master's thesis, Hunter College of the City University of New York |
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The energy eigenvalues are computed for a periodic array of quantum wells (QWs) when the magnetic field is parallel to the plane. The tunneling between the parallel two-dimensional electron gas (2DEG) layers poses a number of interesting features which we analyze numerically. This effect due to tunneling could of course be adjusted by varying the thickness of the barriers separating two adjacent QW's. Numerical results are presented for the energy eigenvalues as a function of the wave number ky parallel to the plane and as a function of the in-plane magnetic field. The role of tunneling can also be demonstrated in collective aspects such as the magnetoplasmon excitation spectrum. The energy eigenstates can be used to obtain the out-of-plane magnetoconductivity by using the Kubo formalism. In this case, the role played by impurity scattering can be included in both the self-energy and current vertex, in the self-consistent Born approximation. The aim of this project is to examine the nature of the energy eigenstates for a quantum well structure in an external magnetic field. We present results for: (i) a single QW in a parallel magnetic field (ii) a double-quantum well structure with a quantizing magnetic field parallel to the planes; (iii) a periodic array of QW's in a parallel magnetic field. However, as an introduction to the new results, we shall derive the energy spectrum for a two-dimensional electron gas (2DEG) when the background potential is uniform. The effective mass of the electron is constant.
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