# Unpaired Majorana fermions in quantum wires

@article{Kitaev2000UnpairedMF,
title={Unpaired Majorana fermions in quantum wires},
author={Alexei Y. Kitaev},
journal={Physics-Uspekhi},
year={2000},
volume={44},
pages={131-136}
}
• A. Kitaev
• Published 2000
• Physics
• Physics-Uspekhi
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 two ground states with an energy difference proportional to exp(-L/l0) and different fermionic parities. Such systems can be used as qubits since they are intrinsically immune to decoherence. The property of a system to have boundary Majorana fermions is expressed as a condition on the bulk electron… Expand
2,107 Citations

#### Figures from this paper

Majorana Zero-Energy Modes in a Magnetic Field-Free Quantum Wire
We report on a proposal for engineering a one-dimensional topological superconductor hosting Majorana zero-energy modes pinned at the edges of a spin-orbit coupled and electron-electron interactingExpand
Many-particle Majorana bound states: Derivation and signatures in superconducting double quantum dots
• Physics
• 2014
We consider two interacting quantum dots coupled by standard s-wave superconductors. We derive an effective Hamiltonian, and show that over a wide parameter range a degenerate ground state can beExpand
Majorana zero modes in the interacting fermion chain without pairing
The ground state behavior of the spinless fermion chain with an interaction between fermions at neighboring sites is studied for free open boundaries. For the strong enough repulsion boundary gaplessExpand
Majorana modes in multiband superconducting quantum wires
We calculate analytically the spectrum of the Andreev bound states in a half-infinite superconducting wire with an arbitrary number of bands crossing the chemical potential. The normal state of theExpand
Controlling Fusion of Majorana Fermions in one-dimensional systems by Zeeman Field
• Physics
• 2013
We propose to realize Majorana fermions (MFs) on an edge of a two-dimensional topological insulator in the proximity with s-wave superconductors and in the presence of transverse exchange field h. ItExpand
Search for Majorana Fermions in Superconductors
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 holeExpand
Landau-Zener transitions for Majorana fermions
One-dimensional systems obtained as low-energy limits of hybrid superconductor-topological insulator devices provide means of production, transport, and destruction of Majorana bound states (MBSs) byExpand
Finite temperature effects on Majorana bound states in chiral $p$-wave superconductors
• Physics
• SciPost Physics
• 2019
We study Majorana modes bound to vortex cores in a chiral \bm{p}𝐩-wave superconductor at temperatures non-negligible compared to the superconducting gap. Thermal occupation of Caroli deExpand
Majorana Fermions in Superconducting Quantum Wires
The appearance of Majorana fermions in one dimensional p-wave superconductors was first predicted by A. Kitaev in his well known paper [Kitaev, 2000]. One expected signature of such zero-energyExpand
Probing Majorana edge states with a flux qubit
• Physics
• 2011
A pair of counter-propagating Majorana edge modes appears in chiral p-wave superconductors and in other superconducting systems belonging to the same universality class. These modes can be describedExpand

#### References

SHOWING 1-10 OF 11 REFERENCES
Midgap edge states and pairing symmetry of quasi-one-dimensional organic superconductors
• Physics
• 2001
The singlet s-, d- and triplet p-wave pairing symmetries in quasi-one-dimensional organic superconductors can be experimentally discriminated by probing the Andreev bound states at the sample edges.Expand
Fermionic quantum computation
We define a model of quantum computation with local fermionic modes (LFMs) — sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of mExpand
Non-Abelian statistics of half-quantum vortices in p-wave superconductors.
• D. Ivanov
• Physics, Medicine
• Physical 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. Expand
A Modular Functor Which is Universal¶for Quantum Computation
• Mathematics, Physics
• 2000
Abstract:We show that the topological modular functor from Witten–Chern–Simons theory is universal for quantum computation in the sense that a quantum circuit computation can be efficientlyExpand
Threshold Accuracy for Quantum Computation
• Mathematics, Physics
• 1996
We have previously (quant-ph/9608012) shown that for quantum memories and quantum communication, a state can be transmitted over arbitrary distances with error $\epsilon$ provided each gate has errorExpand
P/NP, and the quantum field computer
• M. Freedman
• Computer Science, Medicine
• Proc. Natl. Acad. Sci. USA
• 1998
This work proposes that each physical theory supports computational models whose power is limited by the physical theory, and suggests that some physical system whose effective Lagrangian contains a non-Abelian topological term might be manipulated to serve as an analog computer capable of solving NP or even #P-hard problems in polynomial time. Expand
Fault-tolerant quantum computation with constant error
• Mathematics, Computer Science
• STOC '97
• 1997
This paper shows how to perform fault tolerant quantum computation when the error probability, q, is smaller than some constant threshold, q.. the cost is polylogarithmic in time and space, and no measurements are used during the quantum computation. Expand
Quantum computations: algorithms and error correction
Contents §0. Introduction §1. Abelian problem on the stabilizer §2. Classical models of computations2.1. Boolean schemes and sequences of operations2.2. Reversible computations §3. QuantumExpand
Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetry
• Phys. Rev. B
• 2000
Fault - Tolerant Quantum Computation with Constant Error Rate ” Quantum Computations : Algorithms and Error Correction ” , Russian Math . Surveys
• A modular functor which is universal for quantum computation ”