Negative-positive oscillation in interfacial friction of a In2Se3 -graphene heterojunction

According to the classic law of Da Vinci-Amontons, a friction force $f$ was found to increase macroscopically with an external normal load $N(f=\ensuremath{\mu}N)$, with a positive definite friction coefficient \ensuremath{\mu}. Here we employ first-principles calculations to predict that, when sliding the ferroelectric two-dimensional ${\mathrm{In}}_{2}{\mathrm{Se}}_{3}$ over graphene, the differential friction coefficient \ensuremath{\mu}, measured by the slope of the corrugation in the sliding potential energy barrier subject to load $N$, displays an overall positive feather when the dipole is aligned toward the ${\mathrm{In}}_{2}{\mathrm{Se}}_{3}$-graphene interface; however, \ensuremath{\mu} exhibits intriguing negative-positive oscillation with increasing $N$ when the dipole is aligned outward from the interface. Such striking observations can be rationalized by the van der Waals and electrostatic interaction-induced competition between the downward shift of the sliding barrier by the ${\mathrm{p}}_{\mathrm{x}}$- and ${p}_{y}$-like levels and the upward shift of the barrier by the ${p}_{\mathrm{z}}$ states, which is accompanied by an oscillation of the ${\mathrm{In}}_{2}{\mathrm{Se}}_{3}$-graphene interfacial charge redistribution subject to the external load. The present findings are expected to play an instrumental role in the design of high-performance solid lubricants.