A topological twist on materials science
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uction The notions of topology have been invoked for more than a century in the physical world in fields as diverse as condensedmatter physics, high-energy physics, and cosmology to describe the properties of matter and the universe, respectively, thus spanning the nano- and mesoscales (100 nm–1000 nm) to macroscopic (≥ a few microns) length scales.1–3 However, topology has not yet taken proper root in materials science with the question: “Do topology and geometry affect materials physical properties at the nano-/mesoscale, and, if so, how can we use them to understand and design materials from this new perspective?” One of the principal goals of this article is to address this and related questions, and materials scientists are now well poised to tap into the richness of this field due to recent advancements in measurements. Thus the goal is to identify and utilize advanced metrological techniques to probe topology and to relate the latter to the functional properties for a broad class of novel functional materials similar to what has been achieved in condensed matter physics.1 In other words, we look for analogues of identifying “edge states” in quantum Hall materials and topological insulators,4 which allows us to measure and evaluate transport properties, including surface conductivity, the Hall coefficient, and related parameters. The topology of a material goes beyond its physical shape and geometry in that it directly affects physical properties
such as electronic conduction, charge and spin transport, light transmission, and response to a magnetic field. The nontrivial aspects of topology and geometry have numerous applications in modern condensed matter physics where they play an important role in various physically and technologically interesting systems.1,4 This incipient appreciation for the importance of topology is beginning to allow researchers to engineer entirely new materials with unusual topologies that lead to either exotic or enhanced properties.5–7 Nevertheless, for most materials scientists, structural chemists, and biologists, topological methods remain obscure and unusually distant as compared to existing traditional methods. We first introduce the essentials of topological concepts (for example, handlebars or genus of a structure) by means of illustrations without invoking explicit mathematics. We then distinguish between local and global topological aspects of materials and mostly focus on nanocarbons, soft matter, and biomaterials to describe their topology, a variety of topological defects (e.g., vortices, skyrmions),1,8 and their role in controlling physical properties. To this end, we introduce many topology characterization techniques that underscore the emerging field of topological metrology. The novel and important aspects of this nascent field encompass both qualitative and quantitative trends examined experimentally through measurable quantities such as a change in Raman spectroscopy (RS) bands (e.g., G, D, and 2D) of advanced nanoscale
Sanju Gupta, Western Kentucky University, USA; sa
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