Multiband theory of Bloch-electron dynamics in a homogeneous electric field

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Abstract
A multiband theory of Bloch electron dynamics in a uniform electric field of arbitrary strength 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 insures conservation of 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 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 tunneling time is derived in terms of the applied uniform electric field and the relevant band parameters; specific results are derived from the general theory using a nearest-neighbor tight-binding, multiband model, and are shown to have identical parametric dependence on electric field, but different, more realistic dependence on the appropriate band-structure parameters than those of the well-known Kane and effective-mass two-band model. Further, 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.