Spectrum structure for a three-dimensional periodic array of quantum dots in a uniform magnetic field

J. Bruening; V. V. Demidov; V. A. Geyler; A. V. Popov

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Spectrum structure for a three-dimensional periodic array of quantum dots in a uniform magnetic field

J. Bruening·V. V. Demidov·V. A. Geyler·A. V. Popov

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Abstract

By means of the operator extension theory, we construct an explicitly solvable model of a simple-cubic three-dimensional regimented array of quantum dots in the presence of a uniform magnetic field. The spectral properties of the model are studied. It is proved that for each magnetic flux the band is the image of the spectrum of the tight-binding operator under an analytical transformation. In the case of rational magnetic flux the spectrum is described analytically. The flux-energy and angle-energy diagrams are obtained numerically.

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J. Bruening, V. V. Demidov, V. A. Geyler, A. V. Popov. 2006-05-25. Spectrum structure for a three-dimensional periodic array of quantum dots in a uniform magnetic field. https://arxiv.org/abs/cond-mat/0605629

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