Guided accumulation of active particles by topological design of a second-order skin effect

TL;DR

This paper demonstrates how a topological design based on a second-order skin effect can spontaneously guide and accumulate active particles along edges and corners without external fields, revealing a robust out-of-equilibrium topological phenomenon.

Contribution

It introduces a topological design principle using a second-order skin effect to control active matter guidance and accumulation without breaking detailed balance.

Findings

Particles are guided along edges and corners due to topological effects.

The guidance efficiency correlates with a non-zero topological invariant.

The stochastic model accurately predicts guidance behavior without fitting parameters.

Abstract

Collective guidance of out-of-equilibrium systems without using external fields is a challenge of paramount importance in active matter, ranging from bacterial colonies to swarms of self-propelled particles. Designing strategies to guide active matter and exploiting enhanced diffusion associated to its motion will provide insights for application from sensing, drug delivery to water remediation. However, achieving directed motion without breaking detailed balance, for example by asymmetric topographical patterning, is challenging. Here we engineer a two-dimensional periodic topographical design with detailed balance in its unit cell where we observe spontaneous particle edge guidance and corner accumulation of self-propelled particles. This emergent behaviour is guaranteed by a second-order non-Hermitian skin effect, a topologically robust non-equilibrium phenomenon, that we use to dynamically break detailed balance. Our stochastic circuit model predicts, without fitting parameters, how guidance and accumulation can be controlled and enhanced by design: a device guides particles more efficiently if the topological invariant characterizing it is non-zero. Our work establishes a fruitful bridge between active and topological matter, and our design principles offer a blueprint to design devices that display spontaneous, robust and predictable guided motion and accumulation, guaranteed by out-of-equilibrium topology.