# Anomalous Topological Active Matter

## TL;DR

This paper demonstrates that active matter systems can host topologically protected sound modes analogous to quantum anomalous Hall insulators, providing new design principles for active metamaterials with potential experimental applications.

## Contribution

It introduces a continuum active matter model exhibiting topologically nontrivial sound modes, linking active flow vorticity to topological invariants, and proposes design principles for active topological metamaterials.

## Key findings

- Numerical band structure calculations show nonzero bulk topological invariants.
- Edge sound modes are demonstrated in the proposed model.
- Net vorticity must vanish in realistic active systems.

## Abstract

Active systems exhibit spontaneous flows induced by self-propulsion of microscopic constituents and can reach a nonequilibrium steady state without an external drive. Constructing the analogy between the quantum anomalous Hall insulators and active matter with spontaneous flows, we show that topologically protected sound modes can arise in a steady-state active system in continuum space. We point out that the net vorticity of the steady-state flow, which acts as a counterpart of the gauge field in condensed-matter settings, must vanish under realistic conditions for active systems. The quantum anomalous Hall effect thus provides design principles for realizing topological metamaterials. We propose and analyze the concrete minimal model and numerically calculate its band structure and eigenvectors, demonstrating the emergence of nonzero bulk topological invariants with the corresponding edge sound modes. This new type of topological active systems can potentially expand possibilities for their experimental realizations and may have broad applications to practical active metamaterials. Possible realization of non-Hermitian topological phenomena in active systems is also discussed.