# Controlling non-Abelian statistics of Majorana fermions in semiconductor nanowires

@article{Sau2011ControllingNS, title={Controlling non-Abelian statistics of Majorana fermions in semiconductor nanowires}, author={Jay Deep Sau and David J. Clarke and Sumanta Tewari}, journal={Physical Review B}, year={2011}, volume={84} }

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…

## 113 Citations

Tunable Majorana fermion from Landau quantization in 2D topological superconductors

- Physics
- 2016

We study the generation of Majorana fermions in a two-dimensional topological superconductor placed in a transverse magnetic field B. A topological insulator/superconductor heterostructure and a…

Search for Majorana Fermions in Superconductors

- Physics
- 2011

Majorana fermions (particles that are their own antiparticle) may or may not exist in nature as elementary building blocks, but in condensed matter they can be constructed out of electron and hole…

Coulomb-assisted braiding of Majorana fermions in a Josephson junction array

- Physics
- 2012

We show how to exchange (braid) Majorana fermions in a network of superconducting nanowires by control over Coulomb interactions rather than tunneling. Even though Majorana fermions are…

Topological superconductivity in spin-orbit-coupled semiconducting nanowires

- PhysicsSemiconductors and Semimetals
- 2021

Abstract We present a pedagogical review of topological superconductivity and its consequences in spin-orbit-coupled semiconductor/superconductor heterostructures. We start by reviewing the…

Majorana Fermions and Topology in Superconductors

- Physics
- 2016

Topological superconductors are novel classes of quantum condensed phases, characterized by topologically nontrivial structures of Cooper pairing states. On the surfaces of samples and in vortex…

New scheme for braiding Majorana fermions

- Physics, MedicineScience and technology of advanced materials
- 2014

A way to braid MFs without moving vortices is proposed and non-Abelian statistics is achieved by monitoring the time evolution of MF wave-functions.

Adaptive tuning of Majorana fermions in a quantum dot chain

- Physics
- 2013

We suggest a way to overcome the obstacles that disorder and high density of states pose to the creation of unpaired Majorana fermions in one-dimensional systems. This is achieved by splitting the…

Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device

- Physics
- 2012

We report on the observation of excitation of Majorana fermions in a Nb-InSb nanowire quantum dot-Nb hybrid system. The InSb nanowire quantum dot is formed between the two Nb contacts by weak…

Proposal for the detection and braiding of Majorana fermions in a quantum spin Hall insulator

- Physics
- 2013

We show how a quantum dot with a ballistic single-channel point contact to a superconductor can be created by means of a gate electrode at the edge of a quantum spin Hall insulator (such as an…

Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states

- Physics
- 2012

We study the non-abelian statistics characterizing systems where counter-propagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity-coupling to superconductors…

## References

) argued that a similar result holds based on consevation of iγ 1 γ 2 γ 3 which follows from conservation of fermion parity . 33 J . Bardeen

- Phys . Rev . Lett .
- 2010