  The thermal transport across metal-insulator interface can be characterized
by electron-phonon interaction through which an electron lead is coupled to a
phonon lead if phonon-phonon coupling at the interface is very weak. We
investigate the thermal conductance and rectification flowing between the
electron part and the phonon part using nonequilibrium Green's function method.
It is found that the thermal conductance has a nonmonotonic behavior as a
function of average temperature or the coupling strength between the phonon
leads in the metal part and the insulator one. The metal-insulator interface
shows evident thermal rectification effect, which can reverse with changing of
average temperature or the electron-phonon coupling.
