A conformal transformation of a uniform triangular pinning array produces astructure called a conformal crystal which preserves the six-fold ordering ofthe original lattice but contains a gradient in the pinning density. Here weuse numerical simulations to show that vortices in type-II superconductorsdriven with an ac drive over gradient pinning arrays produce the mostpronounced ratchet effect over a wide range of parameters for a conformalarray, while square gradient or random gradient arrays with equivalent pinningdensities give reduced ratchet effects. In the conformal array, the largerspacing of the pinning sites in the direction transverse to the ac drivepermits easy funneling of interstitial vortices for one driving direction,producing the enhanced ratchet effect. In the square array, the transversespacing between pinning sites is uniform, giving no asymmetry in the funnelingof the vortices as the driving direction switches, while in the random array,there are numerous easy-flow channels present for either direction of drive. Wefind multiple ratchet reversals in the conformal arrays as a function of vortexdensity and ac amplitude, and correlate the features with a reversal in thevortex ordering, which is greater for motion in the ratchet direction. Theenhanced conformal pinning ratchet effect can also be realized for colloidalparticles moving over a conformal array, indicating the general usefulness ofconformal structures for controlling the motion of particles.
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