Thermal transport in AB superlattices

We calculate the thermal conductivity of an AB superlattice in the cross-plane direction (perpendicular to the layers). If all of the heat is carried by phonons, the calculation has been performed often. We include the feature that one (A) or both (A and B) of the superlattice layers are electronic conductors, so they have thermal energy in the electron system as well as in the phonon system. We also assume the layers are thin, of several atomic layers, so the main thermal resistance is at the interfaces. The introduction of electron thermal energy changes the thermal conductance of the superlattice. It also changes the boundary conductance between a metal contact and the superlattice.