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"Introduction to topological superconductivity and Majorana fermions", Martin Leijnse, Jarsten Flensberg, 2012

Reviewed November 17, 2023

Citation: Leijnse, Martin, and Karsten Flensberg. "Introduction to topological superconductivity and Majorana fermions." Semiconductor Science and Technology 27.12 (2012): 124003.

Web: https://arxiv.org/abs/1206.1736

Tags: Expository, Pedagogical, Hardware

This article gives a lovely introduction to Majorana fermions from superconductivity. The bulk of the paper is spent discussing the Kitaev quantum wire model, a toy model for p-wave superconductivity which exhibits Majorana fermions. There is then a discussion about how to perform computations via braiding and fusion.

A beautiful aspect of this article is that they then go on to connect their discussion to the most promising current direction in p-wave superconductivity, which is exploiting the proximity effect between a p-wave superconductor and a topological insulator. This seems like a great introduction to the field for people who are very familiar with superconductivity, and the mathematical aspects of materials science.

A more direct introduction to Kitaev's quantum wire model can be found in Gil Rafel's notes. Those notes are a lot more fun, but there are many typos, giving the notes an overall feel of being "sketchy".