Stripe and bubble ratchets on asymmetric substrates

We show that various nonmonotonic ratchet effects can arise when mesophase pattern-forming systems, which exhibit anisotropic crystal, stripe, and bubble regimes, are coupled to one-dimensional asymmetric substrates under ac driving. The patterns emerge in the absence of a substrate when the ratio of attraction to repulsion is varied for particles with competing short-range attraction and long-range repulsion potentials. In the presence of the substrate, we find that the ratchet efficiency varies nonmonotonically with increasing attraction, depending upon how well the mesophase morphology matches the substrate spacing and periodicity. For strong repulsion, there is a weak but finite ratchet effect, while at intermediate attraction, there is a robust ratchet effect in which the system forms stripes aligned with the substrate symmetry direction. For strong attraction, large bubbles appear that have weak or no ratchet effects when the bubble width exceeds the substrate lattice spacing, causing the bubble to be only weakly coupled to the substrate. For very strong attraction, small bubbles form and undergo a strong ratchet effect with an efficiency that oscillates as a function of ac drive amplitude. Although the small bubble regime is a strongly correlated regime in which each bubble contains many particles, the system behaves as if it is in a single-particle regime since the bubble width is much smaller than the substrate lattice spacing. We map out the different rectification phases as a function of the pattern morphology, substrate strength, and ac drive amplitude. The pronounced ratchet effects that we observe in some regimes can be exploited for pattern sorting in hard and soft matter systems. Published by the American Physical Society 2024