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In physics, a Majorana fermion is a fermion which is its own anti-particle. No Majorana fermions are known in nature as elementary particles. The neutrino 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. The hypothetical neutralino of supersymmetric models is a Majorana fermion. 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 γj annihilates it (or, equivalently, creates the corresponding antiparticle). For a Dirac fermion the operators γ†j and γj are distinct, while for a Majorana fermion they are identical. In superconducting materials, Majorana fermions can emerge as (non-fundamental) quasiparticles.[1] 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.[2][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] So far, these are only theoretical predictions, but there is an active search for experimental observation.[8] Majorana fermions in superconductors could be used as a building block for a topological quantum computer, in view of their non-Abelian anyonic statistics.[9] See also Dirac fermion Majorana equation Majorana spinor References ^ F. Wilczek, Majorana returns, Nature Physics 5, 614 (2009). ^ N.B. Kopnin and M.M. Salomaa, Mutual friction in superfluid 3He: Effects of bound states in the vortex core, Phys. Rev. B 44, 9667 (1991). ^ G.E. Volovik, Fermion zero modes on vortices in chiral superconductors, JETP Lett. 70, 609 (1999). ^ N. Read and D. Green, Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect, Phys. Rev. B 61, 10267 (2000). ^ L. Fu and C.L. Kane, Superconducting proximity effect and Majorana fermions at the surface of a topological insulator, Phys. Rev. Lett. 100, 096407 (2008). ^ A. Yu. Kitaev, Unpaired Majorana fermions in quantum wires, Phys. Usp. (suppl.) 44, 131 (2001). ^ G. Moore and N. Read, Nonabelions in the fractional quantum Hall effect, Nucl. Phys. B 360, 362 (1991). ^ M. Franz, Race for Majorana fermions, Physics 3, 24 (2010). ^ C. Nayak, S. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80, 1083 (2008).