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I am trying to understand why vortices in p-wave superconductors are actually non-abelian anyons and how this relates to Majorana modes.

However I am having a hard time finding proper resources (in particular since my background in superconductivity is not too strong)? These lecture notes that I found: http://www.phys.s.u-tokyo.ac.jp/curriculum/documents/2013lecture6_ver2.pdf are great in spirit but they lack some detail.

Can someone provide me with recommendations on what to read and where to start?

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I recommend the original papers,

[1]N. Read and D. Green, Phys. Rev. B 61 (2000), 10267 and

[2]D. A. Ivanov, Phys. Rev. Lett. 86 (2001), 268.

If you can understand the Bogoliubov-de Genns equation with the p wave order parameter, calculations are straightforward.

I also recommend the paper which contains the similar calculation,

[3]V. Gurarie and L. Radzihovsky, Ann. Phys. 322 (2007), 2.

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