  Negative differential resistance in electronic conduction has been
extensively studied, but it is not the case for its thermal counterpart,
namely, negative differential thermal resistance (NDTR). We present a classical
Landauer formula in which the nonlinearity is incorporated by the
self-consistent phonon theory in order to study the heat flux across a chain
consisting of two weakly coupled lattices. Two typical nonlinear models of hard
and soft on-site potentials are discussed, respectively. It is shown that the
nonlinearity has strong impacts on the occurring of NDTR. As a result, a
transition from the absence to the presence of NDTR is observed. The origin of
NDTR consists in the competition between the temperature difference, which acts
as an external field, and the temperature-dependent thermal boundary
conductance. Finally, the onset of the transition is clearly illustrated for
this model. Our analytical calculation agrees reasonably well with numerical
simulations.
