Topological active matter

Abstract

Active matter encompasses different nonequilibrium systems in which individual constituents convert energy into non-conservative forces or motion at the microscale. This review provides an elementary introduction to the role of topology in active matter through experimentally relevant examples. Here, the focus lies on topological defects and topologically protected edge modes with an emphasis on the distinctive properties they acquire in active media. These paradigmatic examples represent two physically distinct classes of phenomena whose robustness can be traced to a common mathematical origin: the presence of topological invariants. These invariants are typically integer numbers that cannot be changed by continuous deformations of the relevant order parameters or physical parameters of the underlying medium. We first explain the mechanisms whereby topological defects self propel and proliferate in active nematics, leading to collective states which can be manipulated by geometry and patterning. Possible implications for active microfluidics and biological tissues are presented. We then illustrate how the propagation of waves in active fluids and solids is affected by the presence of topological invariants characterizing their dispersion relations. We discuss the relevance of these ideas for the design of robotic metamaterials and the properties of active granular and colloidal systems. Open theoretical and experimental challenges are presented as future research prospects.

23 pages, 3 figures, 4 boxes

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Cited by in corpus (122)

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• Tailored Topological Edge Waves via Chiral Hierarchical Metamaterials
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• Non-Hermitian spectral flows and Berry-Chern monopoles
• Motility Induced Phase Separation and Frustration in Active Matter Swarmalators
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• Roadmap for Animate Matter
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• Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect
• Non-reciprocal breathing solitons
• On the Effective Mass of Mechanical Lattices with Microstructure
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• Anderson localization of walking droplets
• Many-defect solutions in planar nematics: interactions, spiral textures and boundary conditions
• A topological fluctuation theorem
• Spiking at the edge
• Nonreciprocal interactions induce frequency shifts in superradiant lasers
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• Photoinduced non-reciprocal magnetism
• The XY model with vision cone: non-reciprocal vs. reciprocal interactions
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• Symmetry-driven Phononic Metamaterials
• Topology of Discrete Quantum Feedback Control
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• Cells around the corner
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• Aligning Active Particles Py Package
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• Topology of the simplest gene switch
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• Chiral Active Matter
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• Mechanical activity and odd elasticity of passive, 2D chiral metamaterials
• Towards kinetic equations of open systems of active soft matter