  We study the nonlinear interfacial thermal transport across atomic junctions
by the quantum self-consistent mean field (QSCMF) theory based on
nonequilibrium Green's function approach; the QSCMF theory we propose is very
precise and matches well with the exact results from quantum master equations.
The nonlinearity at the interface is studied by effective temperature dependent
interfacial coupling calculated from the QSCMF theory. We find that
nonlinearity can provide an extra channel for phonon transport in addition to
the phonon scattering which usually blocks heat transfer. For weak linearly
coupled interface, the nonlinearity can enhance the interfacial thermal
transport; with increasing nonlinearity or temperature, the thermal conductance
shows nonmonotonical behavior. The interfacial nonlinearity also induces
thermal rectification, which depends on the mismatch of the two leads and also
the interfacial linear coupling.
