At dry and clean material junctions of rigid materials the corrugation of the sliding energy landscape is dominated by variations of Pauli repulsions. These occur when electron clouds centered around atoms in adjacent layers overlap as they slide across each other. In such cases there exists a direct relation between interfacial surface (in)commensurability and superlubricity, a frictionless and wearless tribological state. The Registry Index is a purely geometrical parameter that quantifies the degree of interlayer commensurability, thus providing a simple and intuitive method for the prediction of sliding energy landscapes at rigid material interfaces. In the present study, we extend the applicability of the Registry Index to nonparallel surfaces, using a model system of nanotube motion on flat hexagonal materials. Our method successfully reproduces sliding energy landscapes of carbon nanotubes on graphene calculated using a Lennard-Jones-type and the Kolmogorov Crespi interlayer potentials. Furthermore, it captures the sliding energy corrugation of a boron nitride nanotube on hexagonal boron nitride calculated using a recently developed interlayer potential for hexagonal boron nitride (h-BN). Finally, we use the Registry Index to predict the sliding energy landscapes of the heterogeneous junctions of a carbon nanotubes on h-BN and of boron nitride nanotubes on graphene that are shown to exhibit a significantly reduced corrugation. For such rigid interfaces this is expected to be manifested by superlubric motion.
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