I wonder if there are any books or resources that may address one or more of the following questions:

  • What kinds of defects are important for topology? Especially crystallographic defects.
  • How do they relate to the defect topological dimension?
  • How do they change in different crystal dimensions?

1 Answer 1


Arkadiy Simonov and Andrew Goodwin have a nice review out on the arXiv regarding designing disorder into materials, that can elicit unique topological states [1], and there is are some older reviews discussing specifically crystallography [2,3]. For a more robust mathematical treatment, this paper focuses on abstraction with a set of good physical examples [4].

  1. arXiv:1912.00366
  2. D. A. Keen, A. L. Goodwin, Nature 521, 303–309 (2015).
  3. T. R. Welberry, T. Weber Crystallography Reviews  22,  2-78  (2016)
  4. N. D. Mermin, Rev. Mod. Phys.  51,  591-648 (1979).

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