Magnetoconductivity of planar crystalline systems and its semiclassical quantization

Abstract

The tensor of magnetoconductivity is examined for the tightly-bound s-electrons in the planar crystallographic lattices originating from three cubic lattice kinds (simple, body-centered and face-centered). The magnetic field is assumed to be directed perpendicularly to the crystallographic plane and the relaxation time entering the conductivity tensor is derived from the crystal band structure. The presence of the lattice potential is found to be essential for calculating a finite value of the Hall conductivity, which, in general, exhibits a rather feeble dependence on position of the Landau level within the energy band. A quasi-constant behavior in the band of states is obtained also for a quantal increment of the Hall conductivity between two neighboring Landau levels. For different cubic lattices this increment is an approximately constant number being close to e2/h. On the other hand, the quanta of the diagonal components of the tensor of magnetoconductivity per one Landau level are much larger than e2/h for an almost empty band, but they tend to decrease very rapidly to zero with an increase of the band filling. For a strong magnetic field – and not too low temperatures – the components of the tensor of magnetoresistance are found to increase linearly with the strength of the field. A remarkable quantitative agreement between the theory and experiment is demonstrated for the Hall resistance of the planar crystalline structures. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)