About the quantum-kinetic derivation of boundary conditions for quasiparticle Boltzmann equations at interfaces
Quite a many electron transport problems in condensed matter physics are analyzed with a quasiparticle Boltzmann equation. For sufficiently slowly varying weak external potentials it can be derived from the basic equations of quantum kinetics, provided quasiparticles can be defined and lead to a pole in the quantum-mechanical propagators. The derivation breaks down, however, in the vicinity of an interface which constitutes an abrupt strong perturbation of the system. In this contribution we discuss in a tutorial manner a particular technique to systematically derive, for a planar, nonideal interface, matching conditions for the quasi-particle Boltzmann equation. The technique is based on pseudizing the transport problem by two auxiliary interface-free systems and matching Green functions at the interface. Provided quasiparticles exist in the auxiliary systems, the framework can be put onto the semiclassical level and the desired boundary conditions result. For ideal interfaces, the conditions can be guessed from flux conservation, but for complex interfaces this is no longer the case. The technique presented in this work is geared towards such interfaces.