  Recently, it has been shown that in graded systems, thermal rectification
(TR) effect may remain in the thermodynamical limit. Here, by taking the
one-dimensional rotor lattice as an illustrating model, we investigate how the
graded structure may affect the TR efficiency. In particular, we consider the
case where the interaction is assigned with nonlinear polynomial functions. It
is found that TR is robust in the thermodynamical limit and meanwhile its
efficiency may considerably depend on the details of the graded structure. This
finding suggests that it is possible to enhance the TR effect by taking into
account the nonlinear graded structure even in large systems.
