Interband Kadanoff-Baym equations
(Two-time semiconductor Bloch equations)
- Nonequilibrium Greens functions approach to optical excitation and relaxation in semiconductors
- Selfconsistent treatment of electron number dynamics, optical response and time-dependent band renormalization
- Starting point:
for the two-time Greens functions generalized
to multi-band systems (corresponding to the two indices)
- For an explanation of the two time indices,
- Band-diagonal functions correspond to electron populations in the respective band,
off-diagonal functions describe the probability of transitions between two bands,
in analogy to two-level atoms (and the corresponding density matrix).
Renormalized Rabi energy (effective electric field)
- E ist the classical electric field - laser field plus field induced in the semiconductor
(the solution of Maxwell's equations), d is the dipole moment
- Omega denotes the renormalized Rabi frequency - the electric field modified by the Hartree-Fock
mean field due to the Coulomb interaction (V - Coulomb potential) between the laser pulse excited electrons and holes.
Collision integrals (describing scattering and correlation effects)
- The sigmas are the electron selfenergies.
- Note the non-local character of the integrals (time integration, "memory" effect)
- The sigmas are generalized scattering rates due to correlation effects between electrons and electrons, phonons, impurities etc.
- Here we consider, as an example, scattering due to collisions between electrons and holes, including band-off-diagonal effects (scattering with excitons)
- V_s is the statically screened Coulomb potential, pi - the longitudinal
Basic idea of nonequilibrium Greens functions |
Results for a fs-pulse excited semiconductor (1.2 Mb)
Here is a Collection of recent review articles on nonequilibrium Greens functions
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