Atomic-scale friction observed with a two-dimensional frictional-force microscope

Using the two-dimensional frictional-force microscope, we studied the two-dimensional nature of the atomic-scale friction between a ${\mathrm{Si}}_3$ ${\mathrm{N}}_4$ tip and the cleaved ${\mathrm{MoS}}_2$ surface. As a result, we confirmed the existence of two-dimensionally discrete friction with the lattice periodicity of the ${\mathrm{MoS}}_2$ surface. In addition to the well-known stick-slip behavior, we found the appearance of friction with square-wave behavior which works across the scanning direction, although it is contradictory to the assumption of classical friction. We found that this friction is due to spatially discrete adhesion and jumps with the lattice periodicity, which is explained by the two-dimensional stick-slip model not only qualitatively but also quantitatively. We also observed the fluctuation of the discrete jumps. Further, using the two-dimensional stick-slip model with an effective adhesive radius, we explain the sawtooth and square-wave behaviors due to each discrete jump in more detail.