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HIGH-ELECTRIC-FIELD QUANTUM TRANSPORT BEYOND THE KADANOFF-BAYM ANSATZ
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\underline{P. Kleinert}  and V.V. Bryksin

Paul-Drude-Institute f\"ur Festk\"orperelektronik, Hausvogteiplatz 5-7,
10117 Berlin, Germany

Physical-Technical-Institute, Politekhnicheskaya 26, 194021 St. Petersburg,
Russia
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Nonlinear carrier dynamics in semiconductor superlattices
driven by quantizing magnetic as well as dc and ac electric fields have
been the subject of intense experimental and theoretical studies. Due to the electric
field, the miniband of extended states splits into a Wannier-Stark
ladder. A parallel magnetic field gives rise to the Landau quantization
of the lateral electron motion. Consequently, the field-mediated energy spectrum
becomes completely discrete. In these molecule-like systems, quantum effects
are most prominent. We are faced with the interesting quantum-kinetic problem
to take into account both the field-induced quantization of eigenstates and their
scattering mediated decay. Our approach is developed by applying
the double-time non-equilibrium Kadanoff-Baym-Keldysh Green's function
technique in its most general form. Particular emphasis is put on the
symmetry properties of the Green's functions, which allow to simplify
the equations of motion considerably. Especially, it is demonstrated
how the theory can be formulated within an appropriate wave-number representation.
The applicability of the generalized Kadanoff-Baym ansatz is analyzed.
Our main result consists in the observation that a number of essential
physical properties appear just beyond the Kadanoff-Baym ansatz. There is
an interesting interdependence between the energy spectrum of the carriers (described by
the density of states) and their statistical properties (described by the
non-equilibrium distribution function). As a consequence even the description
of the stationary quantum transport requires the determination of a time dependent
distribution function. The related time evolution is calculated from a kinetic
equation, which emerges only beyond the Kadanoff-Baym ansatz.

The superlattice is treated under the condition of sufficiently low carrier concentration
and a wide minigap guaranteering that the carriers approximately obey Boltzmann
statistics and occupy only the lowest miniband. Based on the double-time
formulation of the Dyson equation, the retroaction of the field-induced change
of the energy spectrum on the carrier statistics is considered. A striking
peculiarity of the double-time approach consists in the appearance of current
gaps both in the electric and magnetic field dependence. The existence of these
gaps is a manifestation of the hopping character of the superlattice transport.
In addition, we identify a novel photon assisted phononless current contribution,
which has no counterparts in former density-matrix approaches and which also emerges
beyond the Kadanoff-Baym ansatz.

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