Topological Soft Matter

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Background

As topological materials in hard-condensed matter are opening new paths towards quantum computing, the soft matter community can offer its own point of view on topology. On the one hand, soft materials can be used as tools to better understand topology in other harder-to-observe systems, because of the larger length-scales typically involved. On the other hand, topology in soft matter intertwines with other topics such as self-assembly, geometry, active matter and metamaterials. Topology influences the way the materials spontaneously assemble, the three-dimensional shapes they take and the way they interact with the environment, therefore it affects the biological world. Finally, soft materials can also be used as models for topological insulators, where the mechanical deformation modes play the role of the charges, and a phononic band-gap behaves as the electronic band-gap of hard materials.

The goal of this Research Topic is to bring together different visions of soft-matter scientists interested in topology, both in the theoretical and in the practical aspects.

The topics can be articulated into four main, related, sub-categories:

1- Liquid crystals: liquid crystals are special “topological” materials because they form topological defects, which are easily visible and controllable with appropriate boundary conditions and external fields. Topological defects in liquid crystals can be used as model systems for other fields of physics, from spin systems to cosmology. They can also be used for nonlinear optics, due to the rapid variation of the refractive index of the material, or as special sites for molecular or colloidal assembly, due to the concentration of the elastic distortion.

2- Soft matter models of topological insulators and other physical systems: a good amount of new research in soft matter is now devoted to the so-called mechanical metamaterials, where the deformability of the materials is intrinsically linked to its geometry and topology. These systems can be designed to sustain only certain modes of deformations and to create topologically-protected modes that cannot propagate in the bulk materials. Similarly, it is possible to use soft matter to study properties of molecular crystals and phase transitions.

3- Foldable soft matter: one of the current challenges in soft matter is to design 2-dimensional (2D) systems that can fold into 3D structures, and to understand how nature has perfected these mechanisms throughout evolution. Physicists and materials scientists are looking for strategies to encode Gaussian curvature in a flat sheet. This opens new paths for soft robotics and bio-mimicking actuators.

4- Active matter: in active materials, both living and not living, topological defects can move and be the driving force for order-disorder transitions. This can be applied to biological systems, such as cells or tissues, where defects affect the biology of cells or deform the shape of vesicles, just to make a few examples. In these life-like systems topology strongly influences self-assembly and dynamics.

Keywords: Soft matter, topology, liquid crystals, active matter, folding

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