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Controlled multiple reversals of a ratchet effect


A single particle confined in an asymmetric potential demonstrates an anticipated ratchet effect by drifting along the ‘easy’ ratchet direction when subjected to non-equilibrium fluctuations1,2,3. This well-known effect can, however, be dramatically changed if the potential captures several interacting particles. Here we demonstrate that the inter-particle interactions in a chain of repelling particles captured by a ratchet potential can, in a controllable way, lead to multiple drift reversals, with the drift sign alternating from positive to negative as the number of particles per ratchet period changes from odd to even. To demonstrate experimentally the validity of this very general prediction, we performed transport measurements on a.c.-driven vortices trapped in a superconductor by an array of nanometre-scale asymmetric traps. We found that the direction of the vortex drift does undergo multiple reversals as the vortex density is increased, in excellent agreement with the model predictions. This drastic change in the drift behaviour between single- and multi-particle systems can shed some light on the different behaviour of ratchets and biomembranes4 in two drift regimes: diluted (single particles) and concentrated (interacting particles).

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Figure 1: Effective asymmetry and schematic demonstration of the ratchet mechanism.
Figure 2: Net drift velocity of the chain as a function of occupation number and pinning strength.
Figure 3: Sample geometry and phase diagram of the vortex ratchet effect.
Figure 4: Magnetoresistance and magnetic field dependence of the ratchet effect for an a.c. bias I ac = 438 µA.


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We thank A. Silhanek for the critical reading of our paper and S. Raedts for taking the AFM micrographs. This work was supported by the K.U. Leuven Research Fund GOA and FWO programmes. C.C.d.S.S. was supported by CNPq, an Agency of the Brazilian Government.

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Correspondence to Victor V. Moshchalkov.

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Supplementary information

Supplementary Figure 1.

Plots of the double-sine and double-well ratchet potentials for different parameters. (PDF 77 kb)

Supplementary Figure 2

Diagrams of the ratchet effective asymmetry for interacting particles in a double-sine potential. (PDF 117 kb)

Supplementary Video 1.

This video shows the ratchet effect for a chain with one particle per period (n = 1). In the first few seconds, the equilibrium positions are shown, and then an external oscillating force is switched on. Here and in all subsequent videos the driving force is sinusoidal and its time variation is represented by the red horizontal bar. The force amplitude is about 1% above the threshold force for depinning the whole chain. For n = 1, Fthresh = 11.2 E0/a, the chain is ratcheted to the right. (WMV 626 kb)

Supplementary Video 2.

Ratchet effect for a chain with two particles per period (n = 2, Fthresh = 6.2 E0/a). Before switching the force on, the equilibrium positions are shown and the weakly pinned particles are highlighted. Note here and in the next videos the first movements of the weakly pinned particles. They assist the depinnig of one particle by crossing the inner barrier and crowding the adjacent local well. Since for n = 2 the weakly pinned particles occupy the weaker local wells, they induce a ratchet effect to the left. (WMV 538 kb)

Supplementary Video 3.

Ratchet effect for a chain with three particles per period (n = 3, Fthresh = 4.8 E0/a). The weakly pinned particles occupy the stronger local wells, thus inducing a ratchet effect to the right. (WMV 517 kb)

Supplementary Video 4.

Ratchet effect for a chain with four particles per period (n = 4, Fthresh = 2.5 E0/a). The weakly pinned particles occupy the weaker local wells, thus inducing a ratchet effect to the left. (WMV 527 kb)

Supplementary Video 5.

Ratchet effect for a chain with five particles per period (n = 5, Fthresh = 1.35 E0/a). The weakly pinned particles occupy the stronger local wells, thus inducing a ratchet effect to the right. (WMV 534 kb)

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de Souza Silva, C., Van de Vondel, J., Morelle, M. et al. Controlled multiple reversals of a ratchet effect. Nature 440, 651–654 (2006).

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