Coulomb-assisted braiding of Majorana fermions in a Josephson junction array
@article{Heck2012CoulombassistedBO, title={Coulomb-assisted braiding of Majorana fermions in a Josephson junction array}, author={Bernard van Heck and A. Akhmerov and Fabian Hassler and M.Burrello and C. W. J. Beenakker}, journal={New Journal of Physics}, year={2012}, volume={14}, pages={035019} }
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 charge-neutral quasiparticles (equal to their own antiparticle), they have an effective long-range interaction through the even–odd electron number dependence of the superconducting ground state. The flux through a split Josephson junction controls this interaction via the ratio of Josephson and charging…
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References
SHOWING 1-10 OF 54 REFERENCES
Controlling non-Abelian statistics of Majorana fermions in semiconductor nanowires
- Physics
- 2011
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…
Fractionalization in Josephson junction arrays hinged by quantum spin Hall edges
- Physics
- 2010
We study a superconductor-ferromagnet-superconductor (SC-FM-SC) Josephson array deposited on top of a two-dimensional quantum spin Hall insulator. The Majorana bound state at the interface between SC…
Coulomb stability of the 4π-periodic Josephson effect of Majorana fermions
- Physics
- 2011
The Josephson energy of two superconducting islands containing Majorana fermions is a 4\pi-periodic function of the superconducting phase difference. If the islands have a small capacitance, their…
Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures.
- PhysicsPhysical review letters
- 2010
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.
Electron teleportation via Majorana bound states in a mesoscopic superconductor.
- PhysicsPhysical review letters
- 2010
This work predicts a striking nonlocal phase-coherent electron transfer process by virtue of tunneling in and out of a pair of Majorana bound states in a superconductor-quantum-spin-Hall- insulator-magnetic-insulator hybrid system.
Helical liquids and Majorana bound states in quantum wires.
- PhysicsPhysical review letters
- 2010
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.
Unpaired Majorana fermions in quantum wires
- Physics
- 2000
Certain one-dimensional Fermi systems have an energy gap in the bulk spectrum while boundary states are described by one Majorana operator per boundary point. A finite system of length L possesses…
Non-Abelian operations on Majorana fermions via single-charge control.
- PhysicsPhysical review letters
- 2011
We demonstrate that non-Abelian rotations within the degenerate ground-state manifold of a set of Majorana fermions can be realized by the addition or removal of single electrons, and propose an…
Anyonic interferometry without anyons: how a flux qubit can read out a topological qubit
- Physics
- 2010
Proposals to measure non-Abelian anyons in a superconductor by quantum interference of vortices suffer from the predominantly classical dynamics of the normal core of an Abrikosov vortex. We show how…
Non-Abelian statistics of half-quantum vortices in p-wave superconductors.
- PhysicsPhysical review letters
- 2001
From the properties of the solutions to Bogoliubov-de Gennes equations in the vortex core, the non-Abelian statistics of vortices are derived identical to that for the Moore-Read (Pfaffian) quantum Hall state.