Colloidal topological insulators

Abstract

Topological insulators insulate in the bulk but exhibit robust conducting edge states protected by the topology of the bulk material. Here, we design a colloidal topological insulator and demonstrate experimentally the occurrence of edge states in a classical particle system. Magnetic colloidal particles travel along the edge of two distinct magnetic lattices. We drive the colloids with a uniform external magnetic field that performs a topologically non-trivial modulation loop. The loop induces closed orbits in the bulk of the magnetic lattices. At the edge, where both lattices merge, the colloids perform skipping orbits trajectories and hence edge-transport. We also observe paramagnetic and diamagnetic colloids moving in opposite directions along the edge between two inverted patterns; the analogue of a quantum spin Hall effect in topological insulators. We present a new, robust, and versatile way of transporting colloidal particles, enabling new pathways towards lab on a chip applications.Topologically protected quantum edge states arise from the non trivial topology (non-vanishing Chern number) of the bulk band structure [1]. If the Fermi energy is located in the gap of the bulk band structure, like in an ordinary insulator, edge currents might propagate along the edges of the bulk material. The edge currents are protected as long as perturbations to the system do not cause a band gap closure. The topological mechanism at work is not limited to quantum systems but has been shown to work equally well for classical photonic [2,3], phononic [4,5], solitonic [6], gyroscopic [7], coupled pendulums [8], and stochastic [9] waves. It is also known that the topological properties survive the particle limit when the particle size is small compared to the width of the edge. In the semi-classical picture of the quantum Hall effect, the magnetic field enforces the electrons to perform closed cyclotron orbits in the bulk of the material.

Edge transport at the boundary between topologically equivalent lattices

“…In previous work [6], we have shown that edge transport between topologically distinct lattices occurs in the form of skipped orbits [15,16,18,17,19,20]. Like the penetrating spiral orbits shown here, both forms of edge transport are truly topological and the transport is determined and protected by topological invariants.…”

“…In previous works we have shown how the motion of colloidal particles above periodic magnetic lattices can be of topological nature [3,4,5,6], and how the same topological concepts apply to both particle and "wave" systems [7,8,9,10,11,12,13,14]. Working with colloidal systems, as opposed to "wave" systems has however the advantage of a direct visualization of the motion and can therefore be more intuitive.…”

Thermally active nanoparticle clusters enslaved by engineered domain wall traps

“…( 4 ), allows exploring the assembly and dynamics for large field amplitudes, which are currently unreachable by our experimental setup. These results, however, could be readily tested with other ferromagnetic thin films able to support larger field modulations 35 . Increasing the applied field, leads to a stronger localization of nanoparticles in the trap and simultaneously strengthens the repulsion between them.…”

Reversibility, pattern formation, and edge transport in active chiral and passive disk mixtures

“…Edge currents have also been found in models with active spinners in confinement 34 , as well as in other studies of active rotators 46 . There are also studies of colloids undergoing oscillatory motion on patterned substrates where edge motion occurs along interfaces 39 .…”

“…Studies of active matter frequently employ particles that undergo run-and-tumble dynamics or driven diffusion 26 . Chiral active matter consisting of circularly moving particles or spinners 26,27 is another class of active systems that can describe biological circle swimmers [26][27][28] , selfpropelled colloids 27,29,30 , active gears [31][32][33] , interacting rotators 34,35 , circularly driven particles [36][37][38][39][40] , and collections of rotating robots 41 .…”