M. Leijnse and K. Flensberg. “Introduction to Topological Superconductivity and Majorana Fermions.”

Semiconductor Science and Technology27, no. 12 (2012): 124003.

M. Leijnse and K. Flensberg. “Introduction to Topological Superconductivity and Majorana Fermions.”

Semiconductor Science and Technology27, no. 12 (2012): 124003.

**Presenter**: Tejas Deshpande

**Date(s)**: 17 February 2013

**Description**: The prediction and search of this so-called Majorana “fermion” became an extremely hot topic in the condensed matter physics community immediately after the breakthrough resulting from the prediction and discovery of topological insulators. Amidst initial excitement over analogies to the Majorana fermion from high energy physics, as well as speculations of applications in quantum computing, the term “fermion” was used very cavalierly. Subsequent scrutiny, however, forced people to use the term “Majorana mode.” What’s even more interesting is that the prediction of Majorana modes in condensed matter systems was proposed long before the topological insulator revolution! The first proposal was by Read and Green in the Fractional Quantum Hall Effect (FQHE). The proposal by Kitaev to observe Majorana modes in a 1D *p*-wave superconductor soon followed. Owing to intense experimental studies on 1D nanowires, the Kitaev 1D chain is the main focus of this paper.

This is the first of the three papers covered on topological superconductivity after going over the basics of topological insulators. The most important feature of this paper is that it is short but still goes the full 360°: from the solution of the Kitaev chain to the proposal involving a Rashba spin-orbit coupled nanowire on an *s*-wave superconductor. Note that this nanowire system was the first experimental system which gave promising signatures of Majorana zero modes. Another main feature of this paper is that it gives fundamental insight into the key ingredients of topological superconductivity without overwhelming the reader by the tens of schemes to realize Majorana modes. These other schemes are covered in the following two papers.

The presentation slides for this journal club meeting can be found in the PDF file here. The PDF slides are only in the reading mode; they do not contain any animations. The original PowerPoint slides with animations can be found here. If you notice any typos or scientific inaccuracies in the slides, I would be grateful if you could bring them to my attention by sending me an email.