Tight-Binding Approach to Electrons in a Crystal Potential and an External Magnetic Field

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Abstract
A general transformation of the tight-binding determinant for a finite orthorhombic crystal in an external magnetic field is introduced. It yields interacting finite Peierls determinants, where the interaction terms arise from distinct surfaces. This result is applied to the energy structure of wires and foils. The formation of Landau levels is demonstrated. The gap widths obtained in films are applicable also to infinite crystals. It is shown that the level broadening near the edges of the unperturbed band and the gap widths near the center decrease exponentially with the magnetic field.