Quantum transport theory for semiconductor nanostructures: A density-matrix formulation

A general density-matrix formulation of quantum transport phenomena in semiconductor nanostructures is presented. More specifically, contrary to the conventional single-particle correlation expansion, we shall investigate separately the effects of the adiabatic or Markov limit and of the reduction procedure. Our fully operatorial approach allows us to better identify the general properties of the scattering superoperators entering our effective quantum transport theory at various description levels, e.g., N electrons-plus-quasiparticles, N electrons only, and single-particle picture. In addition to coherent transport phenomena characterizing the transient response of the system, the proposed theoretical description allows us to study scattering induced phase coherence in steady-state conditions. As a prototypical example, we shall investigate polaronic effects in strongly biased semiconductor superlattices.