Superlubric-pinned transition in sliding incommensurate colloidal monolayers

Abstract

Two-dimensional (2D) crystalline colloidal monolayers sliding over a laser-induced optical lattice providing the periodic "corrugation" potential 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, like in one-dimensional (1D) systems. If a 2D analogy to the mathematically established Aubry transition of one-dimensional systems were to hold, an increasing periodic corrugation strength U0 should turn an initially free-sliding, superlubric colloid into a pinned state, where the static friction force goes from zero to finite 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 a jump of static friction. 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 U0 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.

Finite-temperature phase diagram and critical point of the Aubry pinned-sliding transition in a two-dimensional monolayer

“…Results are expressed in terms of the same system of units defined in Table I of Ref. 17. In these units, very roughly inspired by experimental systems, 6 T ∼ 0.04 corresponds to room temperature.…”

“…As was the case at T = 0, the moiré pattern conserves its shape and symmetry across the unpinned-pinned transition, but the central domains enclosed by the honeycombshaped network of domain walls undergo a sharp structural transformation. 17 At pinning, the portion of 2D lattice inside each hexagon rotates transforming from misaligned and incommensurate to approximately aligned and commensurate with the underlying periodic potential. This transformation can be followed by calculating the average local lattice orientation of the colloidal monolayer defined as…”

Subharmonic Shapiro steps of sliding colloidal monolayers in optical lattices

“…In these mismatched systems we must first of all identify the corrugation amplitude at which, as was mentioned above, a pinning/depinning transition takes place in the absence of AC modulation (∆ 0 = 0). In the limit of infinitesimal applied force, this transition was recently discovered and characterized by Mandelli et al [31]. Ignoring here the weak 14/15 commensurability and taking this to represent a truly incommensurate case, this is the 2D analog of the celebrated 1D "Aubry transition" [29,38,31] here taking place at V 0 crit ≃ 0.4 [39].…”

“…For example, a 2D colloid lattice incommensurate with a weak periodic corrugation is an unpinned system which can slide "superlubrically" without static friction, and will exhibit no Shapiro steps. The same incommensurate lattice must however become pinned when the corrugation amplitude exceeds a first-order depinning-pinning transition threshold value [31], and here Shapiro steps can exist. This is the situation which we concentrate upon here.…”

Current trends in the physics of nanoscale friction

“…While nucleation dynamics rules the depinning mechanism of a stiff commensurate colloidal monolayer [144], for an incommensurate interface the presence/absence of pinning depends upon the system parameters; when an increasing substrate corrugation turns an initially free-sliding network of solitons into a colloid pinned state, the static friction force crosses a well-defined, Aubry-like, dynamical phase transition, from zero to finite [49,147]. The transition value for the critical corrugation depends significantly upon the relative colloid/substrate orientation, which, energetically, is always slightly misaligned, as shown in recent work [148].…”