Quantum transport for Bloch electrons in a spatially homogeneous electric field
1987; American Physical Society; Volume: 35; Issue: 18 Linguagem: Inglês
10.1103/physrevb.35.9644
ISSN1095-3795
Autores Tópico(s)Terahertz technology and applications
ResumoQuantum transport for Bloch electrons in a spatially homogeneous arbitrarily time-dependent electric field is presented. Using a vector potential to describe the electric field, a natural basis (the accelerated Bloch states) for describing Bloch dynamics is employed to revisit the Kohn and Luttinger theory of electron transport in the presence of randomly distributed impurities. This basis, which treats the intraband effects of the field exactly, is also used to extend a recent treatment of quantum transport of Bloch electrons obeying nondegenerate statistics, interacting with phonons, to the multiband case. In particular, for the above-mentioned problems the quantum transport equations are derived from the Liouville equation for the single-particle density matrix with use of the accelerated Bloch states as a basis; results explicitly manifest all possible quantum effects to lowest nonzero order in the scattering strength, such as intraband and interband scattering, interband Zener tunneling, and nonlinear transient transport in a homogeneous electric field of arbitrary time dependence and strength. We find, for either impurity or phonon scattering, that, in addition to the usual intercollisional field effect, the collision integral involves products of field- and time-dependent matrix elements of the scattering interaction at different times instead of the usual ``golden-rule'' result, the latter being obtained only in the limit in which the field dependence of the matrix elements is neglected. Furthermore, we find that, in addition to the incoherent scattering by impurities, our transport equation includes the effect of direct coherent impurity interband scattering when the impurities are randomly positioned on the lattice sites of the crystal.
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