Majorana Particles in Computation

An artist's conception of the Majorana - a previously elusive subatomic particle whose existence has never been confirmed - until now. Dutch nano-scientists at the technological universities of Delft and Eindhoven, say they have found evidence of the particle. To find it, they devised miniscule circuitry around a microscopic wire in contact with a semiconductor and a superconductor. Lead researcher Leo Kouwenhoven. SOUNDBITE (English), NANOSCIENTIST OF DELFT UNIVERSITY, LEO KOUWENHOVEN, SAYING: "The samples that we use for measuring the Majorana fermions are really very small, you can see the holder of the sample, the sample is actually inside here and if you zoom in, you can actually see little wires and if you zoom in more, you see a very small nano-meter scale sample, where we detected one pair of Majoranas." When a magnetic field was applied along the the 'nanowire', electrons gathered together in synchrony as a Majorana particle. These subatomic particles could be used to encode information, turning them into data to be used inside a tiny, quantum computer. SOUNDBITE (English), NANOSCIENTIST OF DELFT UNIVERSITY, LEO KOUWENHOVEN, SAYING: "The goal is actually to develop those nano-scale devices into little circuits and actually make something like a quantum computer out of it, so they have special properties that could be very useful for computation, a particural kind of computation which we call quantum computation, which would replace actually our current computers by computers that are much more efficient than what we have now." The Majorana fermion's existence was first predicted 75 years ago by Italian Ettore Majorana. Probing the Majorana's particles could allow scientists to understand better the mysterious realm of quantum mechanics. Other groups working in solid state physics are thought to be close to making similar announcements....heralding a new era in super-powerful computer technology. Were he alive today Majorana may well be amazed at the sophisticated computer technology available to ordinary people in every day life. But compared to the revolution his particle may be about to spark, it will seem old fashioned in the not too distant future. Jim Drury, Reuters

Majorana fermion

Composition	Elementary
Statistics	Fermionic
Status	Hypothetical
Antiparticle	Itself
Theorised	Ettore Majorana, 1937

A Majorana fermion is a fermion that is its own anti-particle. The term is sometimes used in opposition to Dirac fermion, which describes particles that differ from their antiparticles. It is common that bosons (such as the photon) are their own anti-particle. It is also quite common that fermions can be their own anti-particle, such as the fermionic quasiparticles in spin-singlet superconductors (where the quasiparticles/Majorana-fermions carry spin-1/2) and in superconductors with spin-orbital coupling, such as Ir, (where the quasiparticles/Majorana-fermions do not carry well defined spins).

Contents 1 Theory 2 Elementary particle 3 Quasiparticle 4 Experiments in superconductivity 5 References

 

Theory

The concept goes back to Ettore Majorana's 1937 suggestion^[1] that neutral spin-1/2 particles can be described by a real wave equation (the Majorana equation), and would therefore be identical to their antiparticle (since the wave function of particle and antiparticle are related by complex conjugation).

The difference between Majorana fermions and Dirac fermions can be expressed mathematically in terms of the creation and annihilation operators of second quantization. The creation operator γ^†_j creates a fermion in quantum state j, while the annihilation operator γ_j annihilates it (or, equivalently, creates the corresponding antiparticle). For a Dirac fermion the operators γ^†_j and γ_j are distinct, while for a Majorana fermion they are identical.

 

Elementary particle

No elementary particle is known to be a Majorana fermion. However, the nature of the neutrino is not yet definitely settled; it might be a Majorana fermion or it might be a Dirac fermion. If it is a Majorana fermion, then neutrinoless double beta decay is possible; experiments are underway to search for this type of decay.
The hypothetical neutralino of supersymmetric models is a Majorana fermion.

 

Quasiparticle

In superconducting materials, Majorana fermions can emerge as (non-fundamental) quasiparticles.^[2] (People also name protected zero-energy mode as Majorana fermion. The discussions in the rest of this article are actually about such protected zero-energy mode, which is quite different from the propagating particle introduced by Majorana.) The superconductor imposes electron hole symmetry on the quasiparticle excitations, relating the creation operator γ(E) at energy E to the annihilation operator γ^†(−E) at energy −E. At the Fermi level E=0, one has γ=γ^† so the excitation is a Majorana fermion. Since the Fermi level is in the middle of the superconducting gap, these are midgap states. A quantum vortex in certain superconductors or superfluids can trap midgap states, so this is one source of Majorana fermions.^[3][4][5] Shockley states at the end points of superconducting wires or line defects are an alternative, purely electrical, source.^[6] An altogether different source uses the fractional quantum Hall effect as a substitute for the superconductor.^[7]

It was predicted that Majorana fermions in superconductors could be used as a building block for a (non-universal) topological quantum computer, in view of their non-Abelian anyonic statistics.^[8]

 

Experiments in superconductivity

In 2008 Fu and Kane provided a groundbreaking development by theoretically predicting that Majorana fermions can appear at the interface between topological insulators and superconductors.^[9][10] Many proposals of a similar spirit soon followed. An intense search to provide experimental evidence of Majorana fermions in superconductors^[11][12] first produced some positive results in 2012.^[13][14] A team from the Kavli Institute of Nanoscience at Delft University of Technology in the Netherlands reported an experiment involving indium antimonide nanowires connected to a circuit with a gold contact at one end and a slice of superconductor at the other. When exposed to a moderately strong magnetic field the apparatus showed a peak electrical conductance at zero voltage that is consistent with the formation of a pair of Majorana quasiparticles, one at either end of the region of the nanowire in contact with the superconductor.^[15]

This experiment from Delft marks a possible verification of independent theoretical proposals from two groups^[16][17] predicting the solid state manifestation of Majorana fermions in semiconducting wires.

It is important to note that the solid state manifestations of Majorana fermions are emergent low-energy localized modes of the system (quasiparticles) which are not fundamental new elementary particles as originally envisioned by Majorana (or as the neutrino would be if it turns out to be a Majorana fermion), but are effective linear combinations of half-electrons and half-holes which are topological anyonic objects obeying non-Abelian statistics.^[8] The terminology "Majorana fermion" is thus not a good nomenclature for these solid state Majorana modes.

 

References

1. ^ E. Majorana (1937). "Teoria simmetrica dell’elettrone e del positrone" (in Italian). Nuovo Cimento 14: 171. English translation.
2. ^ F. Wilczek (2009). "Majorana returns". Nature Physics 5 (9): 614. Bibcode 2009NatPh...5..614W. DOI:10.1038/nphys1380.
3. ^ N.B. Kopnin; Salomaa (1991). "Mutual friction in superfluid ³He: Effects of bound states in the vortex core". Physical Review B 44 (17): 9667. Bibcode 1991PhRvB..44.9667K. DOI:10.1103/PhysRevB.44.9667.
4. ^ G.E. Volovik (1999). "Fermion zero modes on vortices in chiral superconductors". JETP Letters 70 (9): 609. Bibcode 1999JETPL..70..609V. DOI:10.1134/1.568223.
5. ^ N. Read; Green (2000). "Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect". Physical Review B 61 (15): 10267. Bibcode 2000PhRvB..6110267R. DOI:10.1103/PhysRevB.61.10267.
6. ^ A. Yu. Kitaev (2001). "Unpaired Majorana fermions in quantum wires". Physics-Uspekhi (supplement) 44 (131): 131. Bibcode 2001PhyU...44..131K. DOI:10.1070/1063-7869/44/10S/S29.
7. ^ G. Moore; Read (1991). "Nonabelions in the fractional quantum Hall effect". Nuclear Physics B 360 (2–3): 362. Bibcode 1991NuPhB.360..362M. DOI:10.1016/0550-3213(91)90407-O.
8. ^ ^{a b} C. Nayak, S. Simon, A. Stern, M. Freedman, and S. Das Sarma (2008). "Non-Abelian anyons and topological quantum computation". Reviews of Modern Physics 80: 1083.
9. ^ L. Fu; C. L. Kane (2008). "Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator". Physical Review Letters 10 (9): 096407. DOI:10.1103/PhysRevLett.100.096407.
10. ^ L. Fu; C. L. Kane (2009). "Josephson current and noise at a superconductor/quantum-spin-Hall-insulator/superconductor junction". Physical Review B 79 (16): 161408. DOI:10.1103/PhysRevB.79.161408.
11. ^ J. Alicea. New directions in the pursuit of Majorana fermions in solid state systems. arXiv:1202.1293.
12. ^ C. W. J. Beenakker. Search for Majorana fermions in superconductors. arXiv:1112.1950.
13. ^ E. S. Reich (28 February 2012). "Quest for quirky quantum particles may have struck gold". Nature News. DOI:10.1038/nature.2012.10124.
14. ^ Jonathan Amos (13 April 2012). "Majorana particle glimpsed in lab". BBC News. Retrieved 15 April 2012.
15. ^ V. Mourik; K. Zuo; S.M. Frolov; S.R. Plissard; E.P.A.M. Bakkers; L.P. Kouwenhoven (12 April 2012). "Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices". Science. arXiv:1204.2792. DOI:10.1126/science.1222360.
16. ^ R. Lutchyn; J. Sau; S. Das Sarma (2010). "Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures". Physical Review Letters 105 (7): 077001. Bibcode 2010PhRvL.105g7001L. DOI:10.1103/PhysRevLett.105.077001.
17. ^ Y. Oreg; G. Refael; F. von Oppen (2010). "Helical Liquids and Majorana Bound States in Quantum Wires". Physical Review Letters 105 (17): 177002. DOI:10.1103/PhysRevLett.105.177002.

The Majorana experiment will search for neutrinoless double-beta decay of 76Ge. The discovery of this process would imply that the neutrino is a Majorana fermion (its own anti-particle) and allow a measurement of the effective Majorana neutrino mass. The first stage of the experiment, the Majorana Demonstrator, will consist of 60kg of germanium crystal detectors in three cryostats. Half of these will be made from natural germanium and half from germanium enriched in 76Ge. The goals of the Demonstrator are to test a claim for measurement of neutrinoless double beta-decay by Klapdor-Kleingrothaus et al. (2006), to demonstrate a low enough background to justify the construction of a larger tonne-scale experiment, and to demonstrate the scalability of the technology to the tonne scale. The experiment will be located at the 4850 ft level of the Sanford Laboratory in Lead, South Dakota. See: The Majorana neutrinoless double beta-decay experiment

See Also: Sounding Off on the Dark Matter Issue