MULTIBAND THEORY OF BLOCH ELECTRON DYNAMICS IN ELECTRIC-FIELDS

A novel multiband theory of Bloch electron dynamics in homogeneous electric fields of arbitrary strength and time dependence is presented. In this formalism, the electric field is described through the use of the vector potential. Multiband coupling is treated through the use of the Wigner-Weisskopf approximation, thus allowing for a Bloch electron transition out of the initial band due to the power absorbed by the electric field; also, the approximation ensures conservation of the total transition probability over the complete set of excited bands. The choice of the vector potential gauge leads to a natural set of extended time-dependent basis functions for describing Bloch electron dynamics in a homogeneous electric field; an associated basis set of localized, electric-field-dependent Wannier and related envelope functions are developed and utilized in the analysis to demonstrate the inherent localization manifest in Bloch dynamics in the presence of relatively strong electric fields. From the theory, a generalized Zener tunnelling time is derived in terms of the applied uniform electric field and the relevant band parameters. The analysis shows an electric-field-enhanced broadening of the excited state probability amplitudes, thus resulting in spatial lattice delocalization and the onset of smearing of discrete, Stark ladder and band-to-band transitions due to the presence of the electric field. In addition, the velocities of a Bloch oscillation will be observed only for the electron that is initially in a Bloch state before Zener tunnelling. Further, the influence of electric fields on resonant tunnelling structure is examined.