Cross-talk between topological defects in different fields revealed by nematic microfluidics

Abstract

Topological defects are singularities in material fields that play a vital role across a range of systems: from cosmic microwave background polarization to superconductors and biological materials. Although topological defects and their mutual interactions have been extensively studied, little is known about the interplay between defects in different fields-especially when they coevolve-within the same physical system. Here, using nematic microfluidics, we study the cross-talk of topological defects in two different material fields-the velocity field and the molecular orientational field. Specifically, we generate hydrodynamic stagnation points of different topological charges at the center of starshaped microfluidic junctions, which then interact with emergent topological defects in the orientational field of the nematic director. We combine experiments and analytical and numerical calculations to show that a hydrodynamic singularity of a given topological charge can nucleate a nematic defect of equal topological charge and corroborate this by creating −1, −2, and −3 topological defects in four-, six-, and eight-arm junctions. Our work is an attempt toward understanding materials that are governed by distinctly multifield topology, where disparate topology-carrying fields are coupled and concertedly determine the material properties and response.multifield topology | nematic liquid crystals | topological defects | microfluidics | cross-interactions D efects are ubiquitous in nature and are at the heart of numerous physical mechanisms, including melting in 2D crystals (1), cosmic strings (2), and other topological defects in the early universe (3). Vortices are possibly the most common examples of defects in flowing media (4, 5). In a typical hydrodynamic vortex, the fluid velocity, v, rotates by 2π along any closed loop around the vortex core and has an undefined direction at the core. More generally, topological defects are singular points or lines in a distinct scalar, vector, or tensor field that can be characterized by topological invariants, including winding number (or index) for 2D, and topological charge for 3D variations of the fields (6, 7). Topological defects have been long known to mediate key processes in a wide range of settings, including knotted flow field stream lines (8), defects in light fields (9), knotted defect lines in complex fluids (10), defects in type 2 superconductors (11), spontaneous flow in active fluids (12-15), and even, conduction properties of electron nematics (16).The interaction between topological defects is governed by the defect topology and the underlying energetics. Similar to electrically charged particles, like-sign topological defects, in general, repel each other, whereas defects of opposite sign attract. However, this interaction can be additionally affected by the geometry and surface properties of the environment (17, 18) and the presence of an external stimulus (19-23). Emergence of topological defects in a field and the resulting interactions between them hav...

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