Issue 6, 2021

Gauge invariant and gauge dependent aspects of topological walking colloidal bipeds

Abstract

Paramagnetic colloidal spheres assemble to colloidal bipeds of various length in an external magnetic field. When the bipeds reside above a magnetic pattern and we modulate the direction of the external magnetic field, the rods perform topologically distinct classes of protected motion above the pattern. The topological protection allows each class to be robust against small continuous deformations of the driving loop of the external field. We observe motion of the rod from a passive central sliding and rolling motion for short bipeds toward a walking motion with both ends of the rod alternately touching down on the pattern for long bipeds. The change of character of the motion occurs in form of discrete topological transitions. The topological protection makes walking a form of motion robust against the breaking of the non symmorphic symmetry. In patterns with non symmorphic symmetry walking is reversible. In symmorphic patterns lacking a glide plane the walking can be irreversible or reversible involving or not involving ratchet jumps. Using different gauges allows us to unravel the active and passive aspects of the topological walks.

Graphical abstract: Gauge invariant and gauge dependent aspects of topological walking colloidal bipeds

Supplementary files

Article information

Article type
Paper
Submitted
16 Sep 2020
Accepted
10 Dec 2020
First published
11 Dec 2020

Soft Matter, 2021,17, 1663-1674

Gauge invariant and gauge dependent aspects of topological walking colloidal bipeds

M. Mirzaee-Kakhki, A. Ernst, D. de las Heras, M. Urbaniak, F. Stobiecki, A. Tomita, R. Huhnstock, I. Koch, A. Ehresmann, D. Holzinger and T. M. Fischer, Soft Matter, 2021, 17, 1663 DOI: 10.1039/D0SM01670E

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