Exact space symmetry of electron states in lattices under a magnetic field

Abstract

AbstractWe previously established the transformations (including the gauge transformations) induced within the electron Hamiltonian by the point‐ and space‐symmetry operations of three‐ and low‐periodic lattices under a uniform magnetic field [P. Tronc and V. P. Smirnov, Phys. Status Solidi B 244, 2010 (2007)]. We also determined the full symmetry group of electron eigenfunctions by taking into account the electron confinement in tubes whose axes are parallel to the magnetic field direction. The confinement is known from experiments with semiconductors. From the symmetry point of view, the confinement implies a lack of translational symmetry in the directions that are not parallel to the field. A theoretical proof is given here for the lack of translational symmetry in any lattice and the relation between the electron‐Hamiltonian symmetry group and the eigenfunction symmetry group is provided. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)