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Superlubric-Pinned Transition in Sliding Incommensurate Colloidal Monolayers

Two-dimensional (2D) crystalline colloidal monolayers sliding over a laser-induced optical lattice recently emerged as a new tool for the study of friction between ideal crystal surfaces. Here we focus in particular on static friction, the minimal sliding force necessary to depin one lattice from the other. If the colloid and the optical lattices are mutually commensurate, the colloid sliding is always pinned by static friction; but when they are incommensurate the presence or absence of pinning can be expected to depend upon the system parameters. If a 2D analogy to the mathematically established Aubry transition of one-dimensional systems were to hold, an increasing periodic corrugation strength $U_0$ should turn an initially free-sliding monolayer into a pinned state through a well-defined dynamical phase transition. We address this problem by the simulated sliding of a realistic model 2D colloidal lattice, confirming the existence of a clear and sharp superlubric-pinned transition for increasing corrugation strength. Unlike the 1D Aubry transition which is continuous, the 2D transition exhibits a definite first-order character. With no change of symmetry, the transition entails a structural character, with a sudden increase of the colloid-colloid interaction energy, accompanied by a compensating downward jump of the colloid-corrugation energy. The transition value for the corrugation amplitude $U_0$ depends upon the misalignment angle $θ$ between the optical and the colloidal lattices, superlubricity surviving until larger corrugations for angles away from the energetically favored orientation, which is itself generally slightly misaligned, as shown in recent work. The observability of the superlubric-pinned colloid transition is proposed and discussed.