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## "Majorana fermions in a tunable semiconductor device", Jason Alicea, 2010

*Reviewed November 27, 2023*

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

*Web:* https://arxiv.org/abs/0912.2115

*Tags:* Physical, Majorana-fermions

This paper showed that a system made from driving a magnetic field
through a semiconductor paired with an s-wave superconductor can host Majorana fermions.
This paper is part of a general approach to topological quantum computation, where one
obtains Majorana fermions not from intrinsic properties of materials but instead from
the interactions between different materials. The original work in this direction
was the breakthrough result of Fu and Kane:

>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.

which showed that the proximity effect between an s-wave superconductor and a topological insulator
could give rise to Majorana fermions. Topological insulators are complicated, and are themselves
often given by heterostructures. Such as in the prototypical work of Bernevig et al.:

> Bernevig, B. Andrei, Taylor L. Hughes, and Shou-Cheng Zhang. "Quantum spin Hall effect and topological phase transition in HgTe quantum wells." science 314.5806 (2006): 1757-1761.

Hence, there was a great desire to simplify the experimental setup.
A great paper in this direction was the work of Sau et al.:

>Sau, Jay D., et al. "Generic new platform for topological quantum computation using semiconductor heterostructures." Physical review letters 104.4 (2010): 040502.

It showed that an s-wave superconductor, a semiconductor, and a ferromagnetic insulator
could be put together to yield Majorana fermions. Jason Alicea noticed that the ferromagnetic insulator
was not a necessary part of this contraption. Namely, if one chooses the semiconductor
with a bit more care, then shooting a magnetic field through the system is enough to ensure
Majorana zero modes from just an s-wave superconductor and a semiconductor.