Subharmonic Shapiro steps of sliding colloidal monolayers in optical lattices

Abstract

Abstract. We investigate theoretically the possibility to observe dynamical mode locking, in the form of Shapiro steps, when a time-periodic potential or force modulation is applied to a two-dimensional (2D) lattice of colloidal particles that are dragged by an external force over an optically generated periodic potential. Here we present realistic molecular dynamics simulations of a 2D experimental setup, where the colloid sliding is realized through the motion of soliton lines between locally commensurate patches or domains, and where the Shapiro steps are predicted and analyzed. Interestingly, the jump between one step and the next is seen to correspond to a fixed number of colloids jumping from one patch to the next, across the soliton line boundary, during each AC cycle. In addition to ordinary "integer" steps, coinciding here with the synchronous rigid advancement of the whole colloid monolayer, our main prediction is the existence of additional smaller "subharmonic" steps due to localized solitonic regions of incommensurate layers executing synchronized slips, while the majority of the colloids remains pinned to a potential minimum. The current availability and wide parameter tunability of colloid monolayers makes these predictions potentially easy to access in an experimentally rich 2D geometrical configuration.

Dynamic mode locking in a driven colloidal system: experiments and theory

“…Recent work studied the transport properties of a system of magnetically driven colloidal particles [50]. Recent theoretical work also examines the possibility of producing mode locking steps in 2D colloidal monolayers [51,52].…”

Current trends in the physics of nanoscale friction

“…According to theory and numerical simulations [50,[144][145][146], the experiment shows the dramatic change of the static-friction threshold from a strongly pinned colloidal regime to an almost superlubric frictional sliding as a function of the overlayer/substrate lattice mismatch (see Fig. 6).…”

Influence of anharmonic convex interparticle potential and Shapiro steps in the opposite direction of driving force

“…and F (t) is a function periodic in time, with a period T = 1 ν0 , equations ( 4) and ( 8) are equivalent and ( 7) is another solution of (4). The solution is resonant if it is invariant under symmetry operation (7). The corre-sponding average velocity is then easily evaluated…”

“…Although it can be detected in many systems, the focus is on examination of dynamical mode-locking, which emerges when systems with a characteristic internal frequency are subjected to an external periodic drive [1,2]. For instance, Shapiro steps (i.e., step-like macroscopic response) are experimentally observed in various colloidal systems [3][4][5][6][7], charge-density wave systems [8][9][10], vortex lattices [11][12][13], Josephson junction arrays [14][15][16][17][18] and others. Regardless of the response function type (average velocity as a function of F dc force, IV characteristics), both pinning-sliding transition and Shapiro steps can be recognized.…”