Topological sound in active-liquid metamaterials (1610.06873v2)

Abstract: Liquids composed of self-propelled particles have been experimentally realized using molecular, colloidal, or macroscopic constituents. These active liquids can flow spontaneously even in the absence of an external drive. Unlike spontaneous active flow, the propagation of density waves in confined active liquids is not well explored. Here, we exploit a mapping between density waves on top of a chiral flow and electrons in a synthetic gauge field to lay out design principles for artificial structures termed topological active metamaterials. We design metamaterials that break time-reversal symmetry using lattices composed of annular channels filled with a spontaneously flowing active liquid. Such active metamaterials support topologically protected sound modes that propagate unidirectionally, without backscattering, along either sample edges or domain walls and despite overdamped particle dynamics. Our work illustrates how parity-symmetry breaking in metamaterial structure combined with microscopic irreversibility of active matter leads to novel functionalities that cannot be achieved using only passive materials.

• The paper demonstrates that active-liquid metamaterials produce unidirectional, topologically protected sound modes robust to lattice defects.
• It employs a continuum Toner-Tu framework to model density and polarization interactions in square and Lieb lattice configurations.
• The findings suggest practical applications in dynamic acoustic isolators and one-way sound guides in soft-matter systems.

Topological Sound in Active-Liquid Metamaterials

The research presented in the paper elucidates the innovative exploration of topological sound within active-liquid metamaterials. Rather than relying on traditional passive materials, this paper manipulates self-propelled particles within metamaterial structures to achieve unique sound propagation properties, drawing analogies to the behavior of electrons in a synthetic gauge field.

Introduction and Motivation

Active liquids, composed of self-propelled particles, exhibit spontaneous flows without external forces. These active systems are of broad interest due to their potential applications in diverse fields such as materials science and biology. The work here aims to develop design principles for topological active metamaterials that feature chiral flow-induced density waves. Despite the overdamped dynamics of the constituent particles, such metamaterials enable unidirectional sound modes that are robust to defects, promising applications where control over sound propagation is critical.

Methodology and Key Results

The authors employ a continuum mechanics approach using the Toner-Tu equations tailored for a polar active liquid. This framework accounts for density and polarization field interactions to predict the behavior of sound propagation within the system. Two distinct configurations forming periodic structures—the square and Lieb lattices—were investigated to discern the effects of lattice geometry and active flow.

The findings reveal that in the Lieb lattice, time-reversal symmetry is inherently broken due to its chiral unit cell configuration, which results in a gapped spectrum for density waves. The Chern number calculations confirm that the gaps host unidirectional topologically protected sound modes. These modes exist without the requirement for inertia, distinguishing them from typical passive systems where overdamping negates wave propagation at the microscale.

Implications and Future Research

The presence of robust chiral sound modes suggests applications in designing materials that control acoustic energy flow with precision. These findings could influence the development of dynamic acoustic isolators and one-way sound guides, particularly where flexibility in design and miniaturization are required. The manifestation of topological features without inertia in active systems also extends the concept of topological matter into the domain of soft materials and colloids.

This paper opens avenues for future research into how modifications to particle propulsion or interaction might further tailor these properties. Additionally, exploration of multi-component active systems could enrich the functional diversity of these metamaterials. Further theoretical and experimental endeavors could envision active metamaterials with diverse topological edge modes, offering nuanced control over other forms of wave propagation in disparate environments.

In conclusion, the paper provides rigorous insight into how active matter systems can achieve topologically protected mechanical properties, offering a paradigm shift from passive material design strategies. The implications for computational and experimental materials science are both broad and profound, fostering advancements in the burgeoning field of active metamaterials.