Hermitian and non-Hermitian topology in active matter

TL;DR

This paper reviews the emerging intersection of active matter and topological band theory, highlighting how non-Hermitian topology can describe nonequilibrium phenomena in biological and active systems.

Contribution

It introduces the extension of band topology concepts to nonequilibrium, non-Hermitian active matter systems, revealing new topological phenomena beyond passive materials.

Findings

Active matter exhibits exotic topological phenomena not seen in passive systems.

Extension of band topology to non-Hermitian systems explains robust edge modes in active matter.

Active systems serve as a platform for exploring novel topological effects in nonlinear and nonequilibrium regimes.

Abstract

Self-propulsion is a quintessential aspect of biological systems, which can induce nonequilibrium phenomena that have no counterparts in passive systems. Motivated by biophysical interest together with recent advances in experimental techniques, active matter has been a rapidly developing field in physics. Meanwhile, over the past few decades, topology has played a crucial role to understand certain robust properties appearing in condensed matter systems. For instance, the nontrivial topology of band structures leads to the notion of topological insulators, where one can find robust gapless edge modes protected by the bulk band topology. We here review recent progress in an interdisciplinary area of research at the intersection of these two fields. Specifically, we give brief introductions to active matter and band topology in Hermitian systems, and then explain how the notion of band topology can be extended to nonequilibrium (and thus non-Hermitian) systems including active matter. We review recent studies that have demonstrated the intimate connections between active matter and topological materials, where exotic topological phenomena that are unfeasible in passive systems have been found. A possible extension of the band topology to nonlinear systems is also briefly discussed. Active matter can thus provide an ideal playground to explore topological phenomena in qualitatively new realms beyond conservative linear systems.