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Satija, Indubala I and Wilkinson, Michael
(2020).
DOI: https://doi.org/10.1088/1751-8121/ab64a5
Abstract
The 'Hofstadter butterfly', a plot of the spectrum of an electron in a two-dimensional periodic potential with a uniform magnetic field, contains subsets which resemble small, distorted images of the entire plot. We show how the sizes of these sub-images are determined, and calculate scaling factors describing their self-similar nesting, revealing an un-expected simplicity in the fractal structure of the spectrum. We also characterise semi-infinite chains of sub-images, showing one end of the chain is a result of gap closure, and the other end is at an accumulation point.
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- Item ORO ID
- 69942
- Item Type
- Journal Item
- ISSN
- 1751-8113
- Keywords
- Hofstadter butterfly; Harper equation; Chern numbers
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Copyright Holders
- © 2020 IOP Publishing
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