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

TL;DR

This paper develops an explicit solvable model for a 3D array of quantum dots under a uniform magnetic field, analyzing its spectral properties and providing analytical and numerical results for various magnetic flux conditions.

Contribution

It introduces a new solvable model for quantum dot arrays in magnetic fields using operator extension theory, with detailed spectral analysis and analytical descriptions for rational flux.

Findings

Spectral properties depend on magnetic flux

Spectrum is the image of a tight-binding operator spectrum

Analytical descriptions are provided for rational flux

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.