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  %title
%  {\bfseries Influence of electron--phonon--interaction
%    on the interband polarization 
%    applying a non-Markovian treatment of scattering terms}
  {\bfseries 
     Electron--phonon quantum kinetic effects 
     in the linear optical properties 
     of semiconductors 
    }
  \vspace*{\baselineskip}\\
  %authors
  Th. Kl\"ahn, G. Manzke and K. Henneberger\vspace*{\baselineskip}\\
  %address
  \textit{Universit\"at Rostock, Fachbereich Physik, D-18051 Rostock,
    Germany}\\
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%                     ABSTRACT
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The progress in describing non--equilibrium states
made during the last years was promoted
by using several sophisticated ideas and techniques
within the scope of  Green's function(GF) formalism.
Applying these concepts to the theoretical description
of excited semiconductors and their interaction
with external perturbations, 
e.g. a laser field,
leads to the system of Semiconductor Bloch Equations (SBE),
which describes the temporal evolution of 
the two--band density matrix.

Considering the linear response of
an excited semiconductor in quasie--quilibrium
the SBE are reduced to the kinetic equation
for the interband polarization,
which gives directly the optical susceptibility.
Nonlinear optical properties, 
are caused by many-body effects 
specified within scattering terms.

In [1] we have demonstrated the influence of memory effects
on scattering terms by a microscopic quantum--kinetic description of
Coulomb scattering using the
free generalized Kadanoff-Baym Ansatz(FGKB)
which expresses 
the two--band GF matrix, depending on two times,
in terms of the two--band density matrix.
Performing a Fourier transformation
the numerical effort
for solving the SBE can be strongly reduced.
Within this approach the energetic position and the
lineshape of the exciton, as well as Mott transition and 
shift of the bandedge with increasing density 
could be successful described in accordance with
experiments in GaAs.

Our work aims to an improved description of
II--VI semiconductors, e.g. ZnSe, where due to a 
stronger electron--phonon coupling an additional
scattering channel becomes relevant.
The polarization caused by LO--phonons is
incorporated into the longitudinal
dielectric function.
The latter is responsible for screening
of the Coulomb interaction[2]
and leads to coupled plasmon--phonon modes.

In contrast to the strong polaron renormalizations of the single
carriers we find in ZnSe for low excitation (small number of thermalized 
carriers, upto $n=1\cdot 10^{14}cm^{-3}$) no influence of phonons 
on the excitonic properties, while plasmons give rise to a small
increase of the linewidth in comparison to the unexcited semiconductor. 
Comparing with earlier approaches,
which have neglected the energy-dependence of the many-body effects
and applied instead Boltzmann-like scattering terms, we 
demonstrate the strong influence of quantum-kinetic effects.

With increasing carrier density the interplay of plasmon- and
phonon-scattering changes drastically. For carrier densities of          
$n=1\cdot 10^{16}cm^{-3}$ (near the Mott transition of the exciton) the
influence of phonons is much larger than that of plasmons in both the
energy-dependent dephasing and spectral changes of the exciton. The
diagonal dephasing will be increased by a factor 3 if phonon scattering
is included, which results in a much stronger bleaching of the
exciton. Finally the phonon scattering leads to a pronounced lowering of the
critical density, where the excitonic features vanish (Mott
transition). 
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\newline
\noindent
[1] J. S. N\"agerl, B. Stabenau, G. B\"ohne,  S. Dreher, R. G. Ulbrich,
G. Manzke, and \\
\hspace*{5mm} K. Henneberger, Phys. Rev. {\bf B 63}, 235202 (2001).
\newline
\noindent
[2] K. Henneberger et al. in 
{\it Progress in Nonequilibrium Greens Functions}, p.179,\\
\hspace*{5mm} M.Bonitz(ed.), World Scientific, Singapore(2000)
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