Simple electron-electron scattering in non-equilibrium Green's function   simulations
  In this work we include electron-electron interaction beyond Hartree-Fock level in our non-equilibrium Green's function approach by a crude form of GW through the Single Plasmon Pole Approximation. This is achieved by treating all conduction band electrons as a single effective band screening the Coulomb potential. We describe the corresponding self-energies in this scheme for a multi-subband system. In order to apply the formalism to heterostructures we discuss the screening and plasmon dispersion in both 2D and 3D systems. Results are shown for a four well quantum cascade laser with different doping concentration where comparisons to experimental findings can be made. 
David O. Winge, Martin Francki\'e, Claudio Verdozzi, Andreas Wacker   and Mauro F. Pereira
cond-mat.mes-hall