Topologically cloaked magnetic colloidal transport

TL;DR

This paper demonstrates a topological magnetic cloaking method for colloidal particles, allowing them to bypass deformed regions without disturbance, extending cloaking concepts from waves to particles.

Contribution

It introduces a topological cloaking technique for magnetic colloidal transport using conformal mapping and magnetic fields, with scalable cloaking conditions.

Findings

Particles avoid cloaked regions via topological loops.

Cloaking/decloaking transition depends on the size and shape of the deformed region.

Scalable cloaking is possible if the conformal map rotates less than 45 degrees locally.

Abstract

Cloaking is a method of making obstacles undetectable. Here we cloak unit cells of a magnetic pattern squeezed into an otherwise periodic pattern from a magnetically driven colloidal flow. We apply a time-periodic external magnetic field loop to an ensemble of paramagnetic colloidal particles on the deformed periodic magnetic pattern. There exist topological loops where the particles avoid to trespass the cloaked regions by robustly traveling around the cloak. Afterwards the ensemble of particles continues with a motion identical to the motion as if the distorted region were nonexistent and the ensemble would have trespassed the undeformed region. We construct the cloak by continuously squeezing new conformally mapped unit cells between those of the originally undeformed and periodic pattern. We find a cloaking/decloaking transition as a function of the size and shape of the newly squeezed-in region. A cloak is scalable to arbitrary size if the biholomorphic map from the undistorted periodic lattice to the region outside the cloak locally rotates by less than an angle of forty five degrees. The work generalizes cloaking from waves toward particles.