MULTIBAND THEORY OF BLOCH ELECTRON DYNAMICS IN ELECTRIC-FIELDS

A novel multiband theory of Bloch electron dynamics in homogeneous ele ctric fields of arbitrary strength and time dependence is presented. I n this formalism, the electric field is described through the use of t he 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 e lectric field; also, the approximation ensures conservation of the tot al transition probability over the complete set of excited bands. The choice of the vector potential gauge leads to a natural set of extende d time-dependent basis functions for describing Bloch electron dynamic s in a homogeneous electric field; an associated basis set of localize d, electric-field-dependent Wannier and related envelope functions are developed and utilized in the analysis to demonstrate the inherent lo calization manifest in Bloch dynamics in the presence of relatively st rong 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-enhanc ed broadening of the excited state probability amplitudes, thus result ing in spatial lattice delocalization and the onset of smearing of dis crete, Stark ladder and band-to-band transitions due to the presence o f the electric field. In addition, the velocities of a Bloch oscillati on will be observed only for the electron that is initially in a Bloch state before Zener tunnelling. Further, the influence of electric fie lds on resonant tunnelling structure is examined.