  We have investigated the lattice thermal transport across the asymmetric tilt
grain boundary between armchair and zigzag graphene by nonequilibrium molecular
dynamics (NEMD). We have observed significant temperature drop and ultra-low
temperature-dependent thermal boundary resistance. More importantly, we find an
unexpected thermal rectification phenomenon. The thermal conductivity and
Kapitza conductance is direction-dependent. The effect of thermal rectification
could be amplified by increasing the difference of temperature imposed on two
sides. Our results propose a promising kind of thermal rectifier and phonon
diodes based on polycrystalline graphene without delicate manipulation of the
atomic structure.
