Topological active matter

Abstract

In active matter systems, individual constituents convert energy into non-conservative forces or motion at the microscale, leading to morphological features and transport properties that do not occur in equilibrium and that are robust against certain perturbations. In recent years, a fruitful method for analysing these features has been to use tools from topology. In this Review, we focus 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 that are robust thanks to a common mathematical origin: the presence of topological invariants. Beyond active matter, our Review underscores the role of topological excitations in non-equilibrium settings of relevance, from open quantum systems to living matter. Active matter encompasses various non-equilibrium 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. Topology plays a defining role in understanding robust features in active media whose basic constituents convert energy into non-conservative forces and motion. Topological defects in active media can acquire self-propulsion and non-reciprocal interactions. Local stresses and flows generated by active defects can have biological functionality in living systems. When detailed balance is broken, unidirectional density waves emerge that are protected against scattering by the presence of topological invariants in the band structure of the media. Non-Hermitian band theory naturally arises in active materials because energy is both consumed and dissipated, resulting in the presence of skin modes and odd viscoelasticity. The full potential of these ideas extends from the fundamental understanding of topology in non-equilibrium systems to applications including materials design and tissue mechanics. Topology plays a defining role in understanding robust features in active media whose basic constituents convert energy into non-conservative forces and motion. Topological defects in active media can acquire self-propulsion and non-reciprocal interactions. Local stresses and flows generated by active defects can have biological functionality in living systems. When detailed balance is broken, unidirectional density waves emerge that are protected against scattering by the presence of topological invariants in the band structure of the media. Non-Hermitian band theory naturally arises in active materials because energy is both consumed and dissipated, resulting in the presence of skin modes and odd viscoelasticity. The full potential of these ideas extends from the fundamental understanding of topology in non-equilibrium systems to applications including materials design and tissue mechanics.