The registry index: a quantitative measure of materials' interfacial commensurability.

Nanoscale tribology is an active and rapidly developing area of research that poses fundamental scientific questions that, if answered, may offer great technological potential in the fields of friction, wear, and lubrication. When considering nanoscale material's junctions, surface commensurability often plays a crucial rule in dictating the tribological properties of the interface. This Review surveys recent theoretical work in this area, with the aim of providing a quantitative measure of the crystal lattice commensurability at interfaces between rigid materials and relating it to the tribological properties of the junction. By considering a variety of hexagonal layered materials, including graphene, hexagonal boron nitride, and molybdenum disulfide, we show how a simple geometrical parameter, termed the "registry index" (RI), can capture the interlayer sliding energy landscape as calculated using advanced electronic structure methods. The predictive power of this method is further demonstrated by showing how the RI is able to fully reproduce the experimentally measured frictional behavior of a graphene nanoflake sliding over a graphite surface. It is shown that generalizations towards heterogeneous junctions and non-planar structures (e.g., nanotubes) provide a route for designing nanoscale systems with unique tribological properties, such as robust superlubricity. Future extension of this method towards nonparallel interfaces, bulk-material junctions, molecular surface diffusion barriers, and dynamic simulations are discussed.