Magnetic layers with periodic point perturbations
Abstract
We study spectral properties of a spinless quantum particle confined to an infinite planar layer with hard walls, which interacts with a periodic lattice of point perturbations and a homogeneous magnetic field perpendicular to the layer. It is supposed that the lattice cell contains a finite number of impurities and the flux through the cell is rational. Using the LandauZak transformation, we convert the problem into investigation of the corresponding fiber operators which is performed by means of Krein's formula. This yields an explicit description of the spectral bands, which may be absolutely continuous or degenerate, depending on the parameters of the model.
 Publication:

Reports on Mathematical Physics
 Pub Date:
 October 2003
 DOI:
 10.1016/S00344877(03)900164
 arXiv:
 arXiv:mathph/0212053
 Bibcode:
 2003RpMP...52..255E
 Keywords:

 Mathematical Physics;
 Condensed Matter;
 Quantum Physics
 EPrint:
 LaTeX 2e, 30 pages