*Citation:* Fu, Liang, and Charles L. Kane. "Superconducting proximity effect and Majorana fermions at the surface of a topological insulator." Physical review letters 100.9 (2008): 096407.

*Web:* https://arxiv.org/abs/0707.1692

*Tags:* Physical, Foundational, Hardware, Topological-insulators, Majorana-fermions

This paper introduced the idea that topological superconductors (and hence Majorana fermions) can be synthesized at the interface between two more conventional materials in a heterostructure. The proposed heterostructure here consists of a conventional superconductor and a topological insulator. The proposal has since been simplified. The paper

> Sau, Jay D., et al. "Non-Abelian quantum order in spin-orbit-coupled semiconductors: Search for topological Majorana particles in solid-state systems." Physical Review B 82.21 (2010): 214509.

reduced the requirements to only a conventional superconductor, a semiconductor with appropriate spin-orbit coupling, and a ferromagnetic insulator. Very quickly the work

> Alicea, Jason. "Majorana fermions in a tunable semiconductor device." Physical Review B 81.12 (2010): 125318.

showed that the ferromagnetic insulator was unnecessary, as long as the semiconductor has appropriate spin orbit coupling terms. This proposal has been the basis of the vast majority of quests for topological quantum computation.

The mechanism for the topological superconductivity can be described as follows. At the surface of a topological insulator, you have topological edge states everywhere. This means that the properties of a path along the boundary only depends on the topology of the path, not the exact path taken. When put into proximity with a superconductor, the superconducting gap will extend to the boundary. That is, on the boundary electrons will still want to form Cooper pairs and there is a non-negligible energy cost associated to breaking a Cooper pair. This "gaps out" the surface states, leading to a new gapped superconductor at the interface.

The key point now is that the superconductor is a type II superconductor. This means that the Meissner effect is incomplete, so there will be localized flux tubes running through the system where the material is not superconducting. At these points, the superconductor does not gap out the surface states and hence there are zero-energy excitations whose braiding statistics behave as if they were purely in a topological insulator. That is, you have zero-energy topological excitations bound to magnetic flux tubes. These are your Majorana zero modes, and thus you have a topological superconductor.