NONRELATIVISTIC ZITTERBEWEGUNG IN 2-BAND SYSTEMS

The notion of zitterbewegung and the resulting formalism, originally proposed for relativistic quantum dynamics, is applied to describe the acceleration of a nonrelativistic electron moving in a crystal, due to the periodic force experienced. A general linear-combination-of-atomic-orbitals (LCAO) approach is developed for multiband systems, and the special case of two-band systems is studied in detail. It is shown that the zitterbewegung determines the minimum spatial extension of localized wave packets formed by a combination of Bloch functions belonging to a single band, in a manner that depends strongly on the relative parity of the orbitals entering the LCAO bands. In the case of two orbitals with opposite parity, one is able to extend the notion of effective mass to deep defect levels, and to estimate the width of the tails of localized states in glassy semiconductors, as a function of the separation between the mobility edges. © 1990 The American Physical Society.