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

Maria Guix,Lucas S Palacios,Serguei Tchoumakov,Samuel Sánchez,Ignacio Pagonabarraga,Adolfo G Grushin

doi:10.1038/s41467-021-24948-2

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.

Highlights

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 selfpropelled particles
The last decades of research in condensed matter physics have revealed that exceptionally robust electronic motion occurs at the boundaries of a class of insulators known as topological insulators[1,2]
These ideas extend beyond solid-state physics, and predict guided boundary motion in systems including photonic[3], acoustic, and mechanical systems[4]

Summary

Introduction

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 selfpropelled particles. In a one-dimensional (1D) chain of hopping particles, the first-order non-Hermitian skin effect arises from the asymmetry between left and right hopping probabilities, which results in an accumulation of a macroscopic number of modes, of the order of the system size, on one side of the system. The non-Hermitian skin effect dynamically breaks this detailed balance on the top and bottom edges, and we use it to guide and accumulate self-propelled Janus particles.

Results

Conclusion