Symmetry of electron states in semiconductor structures under a magnetic field

Abstract

AbstractWe present a group‐theory analysis of the electron states in bulk and low‐dimensional semiconductor structures under a uniform magnetic field. The analysis takes into account the gauge transformations under the symmetry operations. It is shown that the symmetry operations commute in dots, rods and tubes whatever is the orientation of the magnetic field whereas they commute in layers only when the field is in the plane. The commutations properties allow using conventional symmetry groups. In bulk materials, the confinement of electrons within rods whose axes are parallel to the field makes it possible to derive approximate wavefunction symmetries from the rod group involving the geometrical symmetry operations common to the field and the crystal but excluding the translations that are not parallel to the field. An approximation of the same kind can also be made for low‐dimensional structures. Applications to bulk materials with the wurtzite or zinc blende structure as well as related nanostructures are presented. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)