Majorana fermion exchange in strictly one-dimensional structures

@article{Chiu2015MajoranaFE,
  title={Majorana fermion exchange in strictly one-dimensional structures},
  author={Ching-Kai Chiu and Mojtaba Mashhadi Mohammadzadeh Vazifeh and Marcel Franz},
  journal={EPL},
  year={2015},
  volume={110},
  pages={10001}
}
It is generally thought that the adiabatic exchange of two identical particles is impossible in one spatial dimension. Here we describe a simple protocol that permits the adiabatic exchange of two Majorana fermions in a one-dimensional topological superconductor wire. The exchange relies on the concept of "Majorana shuttle" whereby a π domain wall in the superconducting order parameter which hosts a pair of ancillary majoranas delivers one zero mode across the wire while the other one tunnels… 

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References

SHOWING 1-10 OF 55 REFERENCES
Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures.
TLDR
The measurement of the supercurrent through the junction allows one to discern topologically distinct phases and observe a topological phase transition by simply changing the in-plane magnetic field or the gate voltage, which will be a direct demonstration of the existence of Majorana particles.
Majorana fermions in a tunable semiconductor device
The experimental realization of Majorana fermions presents an important problem due to their non-Abelian nature and potential exploitation for topological quantum computation. Very recently Sau et
Manipulating Majorana fermions using supercurrents
Topological insulator edges and spin-orbit-coupled quantum wires in proximity to s-wave superconductors can be tuned through a topological quantum phase transition by a Zeeman field. Here we show
Coulomb-assisted braiding of Majorana fermions in a Josephson junction array
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
Helical liquids and Majorana bound states in quantum wires.
TLDR
It is argued that zero-energy Majorana bound states are formed in various situations when such wires are situated in proximity to a conventional s-wave superconductor when the external magnetic field, the superconducting gap, or the chemical potential vary along the wire.
Unconventional superconductivity on a topological insulator.
TLDR
It is found that the excitation spectrum becomes gapless for any spin-triplet pairing, such that both subgap bound states and Andreev reflection is strongly suppressed.
Josephson effect in superconducting wires supporting multiple Majorana edge states
We study superconducting-normal-superconducting (SNS) Josephson junctions in one-dimensional topological superconductors which support more than one Majorana end mode. The variation of the energy
Superconducting proximity effect and majorana fermions at the surface of a topological insulator.
TLDR
It is shown that linear junctions between superconductors mediated by the topological insulator form a nonchiral one-dimensional wire for Majorana fermions, and that circuits formed from these junctions provide a method for creating, manipulating, and fusing Majorana bound states.
Proposal for realizing Majorana fermions in chains of magnetic atoms on a superconductor
We propose an easy-to-build easy-to-detect scheme for realizing Majorana fermions at the ends of a chain of magnetic atoms on the surface of a superconductor. Model calculations show that such chains
Generic new platform for topological quantum computation using semiconductor heterostructures.
TLDR
The heterostructure proposed is a semiconducting thin film sandwiched between an s-wave superconductor and a magnetic insulator which can be used as the platform for topological quantum computation by virtue of the existence of non-Abelian Majorana fermions.
...
1
2
3
4
5
...