Majorana fermion exchange in strictly one dimensional structures

Abstract

It is generally thought that adiabatic exchange of two identical particles is impossible in one spatial dimension. Here we describe a simple protocol that permits adiabatic exchange of two Majorana fermions in a one-dimensional topological superconductor wire. The exchange relies on the concept of "Majorana shuttle" whereby a $\pi$ 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 in the opposite direction. The method requires some tuning of parameters and does not, therefore, enjoy the full topological protection. The resulting exchange statistics, however, remains non-Abelian for a wide range of parameters that characterize the exchange.

arXiv comment5 pages, 4 figures, supplemental material is included

References in corpus (32)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Search for Majorana fermions in superconductors
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Majorana fermions in a tunable semiconductor device
• Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
• Superconductor-Nanowire Devices from Tunneling to the Multichannel Regime: Zero-Bias Oscillations and Magnetoconductance Crossover
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Majorana fermions in chains of magnetic atoms on a superconductor
• Spin-resolved Andreev levels and parity crossings in hybrid superconductor-semiconductor nanostructures
• Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
• Majorana Fermions in Semiconductor Nanowires: Fundamentals, Modeling, and Experiment
• Unconventional superconductivity on a topological insulator
• Coulomb-assisted braiding of Majorana fermions in a Josephson junction array
• Chiral P-Wave Order in Sr_2RuO_4
• Topological invariants for spin-orbit coupled superconductor nanowires
• Non-Abelian operations on Majorana fermions via single charge control
• AC Josephson effect in finite-length nanowire junctions with Majorana modes
• Controlling non-Abelian statistics of Majorana fermions on Majorana dimer lattices
• Majorana states in helical Shiba chains and ladders
• Manipulating Majorana fermions using supercurrents
• Josephson effect in superconducting wires supporting multiple Majorana edge states

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• Topologically protected braiding in a single wire using Floquet Majorana modes
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• Fractional Josephson Effect with and without Majorana Zero Modes
• Majorana bound states in semiconducting nanostructures
• Braiding Majorana zero modes using quantum dots
• Bosonic continuum theory of one-dimensional lattice anyons
• Topological Quantum Computing Using Nanowire Devices
• A topological Josephson junction platform for creating, manipulating, and braiding Majorana bound states
• Induced spectral gap and pairing correlations from superconducting proximity effect
• Vortex Majorana braiding in a finite time
• Robust Majorana magic gates via measurements
• Phase-tunable Majorana bound states in a topological N-SNS junction
• Bath-induced decoherence in finite-size Majorana wires at non-zero temperature
• Miraging a Majorana