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Space, matter and topology

Nature Physics volume 12, pages 616–618 (2016)Cite this article

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An old branch of mathematics has paved the way for discovering new phases of matter.

In the early 1960s George Gamow wrote a popular book1 that contained a very suggestive observation about the effectiveness of pure mathematics in physics. As a conclusion he remarked that “only number theory and topology (analysis situs) still remain purely mathematical disciplines without any application to physics. Could it be that they will be called to help in our further understanding of the riddles of nature?” Fifty years later, the applications of topology in physics are so numerous that they cannot be covered in a short note. Gamow surely never dreamt that newly discovered phases of matter would be labelled with topological names. Topological phases, topological insulators, topological superconductors and topological semimetals — these are just a few examples of what is generally referred to as topological matter.

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Figure 1: Hopf bundle.

Niles Johnson / nilesjohnson.net

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Acknowledgements

This work was partially supported by the Spanish MINECO grant FPA2015-65745-P (MINECO/FEDER) and DGA-FSE grant 2015-E24/2.

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  1. Manuel Asorey is in the Department of Theoretical Physics, Zaragoza University, 50009 Zaragoza, Spain,

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  1. Manuel Asorey
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Asorey, M. Space, matter and topology. Nature Phys 12, 616–618 (2016). https://doi.org/10.1038/nphys3800

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