Controlling non-Abelian statistics of Majorana fermions in semiconductor nanowires

By J. Sau, D. Clarke, S. Tewari. 2010

142 citations recorded by the source corpus.

Under appropriate external conditions a semiconductor nanowire in proximity to an s-wave superconductor can be in a topological superconducting (TS) phase. This phase supports localized zero-energy Majorana fermions at the ends of the wire. However, the non-Abelian exchange statistics of Majorana fermions is difficult verify because of the one-dimensional topology of such wires. In this paper we propose a scheme to transport Majorana fermions between the ends of different wires using tunneling, which is shown to be controllable by gate voltages. Such tunneling-generated hops of Majorana fermions can be used to exchange the Majorana fermions. The exchange process thus obtained is described by a non-Abelian braid operator that is uniquely determined by the well-controlled microscopic tunneling parameters.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/9981c31aadd9deb55a64eaf7f7e9452af3555a49

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. C. Beenakker
2. J. Alicea
3. K. Flensberg
4. N. Lindner
5. A. Stern
6. Erez Berg
7. G. Refael
8. Martin Leijnse

In Materials Chemistry

1. C. Beenakker
2. K. Flensberg
3. J. Alicea
4. A. Stern
5. N. Lindner
6. Erez Berg
7. G. Refael
8. A. Akhmerov

Citations in the corpus

• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states (2012, background): “On the other hand, in one dimension—both in the integer m 1⁄4 1 and in the fractional case—a braiding operation requires the introduction of tunneling terms between different points along the edge [38,39].”
• Flux-controlled quantum computation with Majorana fermions (2013, methodology): “The full computational power of Majoranas can be achieved by increasing the number of T-junctions.”
• Milestones toward Majorana-based quantum computing (2015, background): “Jul. 2018 Milestones Toward Majorana-Based Quantum Computing David Aasen,1 Michael Hell,2,3 Ryan V. Mishmash,1,4 Andrew Higginbotham,5,3 Jeroen Danon,3,6 Martin Leijnse,2,3 Thomas S. Jespersen,3 Joshua A. Folk,3,7,8 Charles M. Marcus,3 Karsten Flensberg,3 and Jason Alicea1,4 1Department of Physics a”