  The understanding of friction at nano-scales, ruled by the regular
arrangement of atoms, is surprisingly incomplete. Here we provide a unified
understanding by studying the interlocking potential energy of two infinite
contacting surfaces with arbitrary lattice symmetries, and extending it to
finite contacts. We categorize, based purely on geometrical features, all
possible contacts into three different types: a structurally lubric contact
where the monolayer can move isotropically without friction, a corrugated and
strongly interlocked contact, and a newly discovered directionally structurally
lubric contact where the layer can move frictionlessly along one specific
direction and retains finite friction along all other directions. This novel
category is energetically stable against rotational perturbations and provides
extreme friction anisotropy. The finite-size analysis shows that our
categorization applies to a wide range of technologically relevant materials in
contact, from adsorbates on crystal surfaces to layered two-dimensional
materials and colloidal monolayers.
