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Majorana fermion

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2425:. These experiments resolved the predicted signatures of localized Majorana bound states – zero energy modes – at the ends of ferromagnetic (iron) chains on the surface of a superconductor (lead) with strong spin-orbit coupling. Follow up experiments at lower temperatures probed these end states with higher energy resolution and showed their robustness when the chains are buried by layers of lead. Experiments with spin-polarized STM tips have also been used, in 2017, to distinguish these end modes from trivial zero energy modes that can form due to magnetic defects in a superconductor, providing important evidence (beyond zero bias peaks) for the interpretation of the zero energy mode at the end of the chains as a Majorana bound state. More experiments finding evidence for Majorana bound states in chains have also been carried out with other types of magnetic chains, particularly chains manipulated atom-by-atom to make a spin helix on the surface of a superconductor. 55: 2410:. However, it was also pointed out that some other trivial non-topological bounded states could highly mimic the zero voltage conductance peak of Majorana bound state. The subtle relation between those trivial bound states and Majorana bound states was reported by the researchers in Niels Bohr Institute, who can directly "watch" coalescing Andreev bound states evolving into Majorana bound states, thanks to a much cleaner semiconductor-superconductor hybrid system. 7186: 2079: 2376:
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 bound states,
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and superconductors. Many proposals of a similar spirit soon followed, where it was shown that Majorana bound states can appear even without any topological insulator. An intense search to provide experimental evidence of Majorana bound states in superconductors first produced some positive results
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on the superconducting Dirac surface state of the iron-based superconductor. It was the first time that indications of Majorana particles were observed in a bulk of pure substance. However, more recent experimental studies in iron-based superconductors show that topologically trivial Caroli–de
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Dvir, Tom; Wang, Guanzhong; van Loo, Nick; Liu, Chun-Xiao; Mazur, Grzegorz P.; Bordin, Alberto; ten Haaf, Sebastiaan L. D.; Wang, Ji-Yin; van Driel, David; Zatelli, Francesco; Li, Xiang; Malinowski, Filip K.; Gazibegovic, Sasa; Badawy, Ghada; Bakkers, Erik P. A. M. (15 February 2023).
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nanowires connected to two superconducting contacts and subjected to a moderate magnetic field, another signature of Majorana bound states. Bound state with zero energy was soon detected by several other groups in similar hybrid devices, and fractional Josephson effect was observed in
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conductance edge current. Subsequent experiments by other groups, however, could not reproduce these findings. In November 2022, the article by He et al. was retracted by the editors, because "analysis of the raw and published data revealed serious irregularities and discrepancies".
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Gennes–Matricon states and Yu–Shiba–Rusinov states can exhibit qualitative and quantitative features similar to those Majorana zero modes would make. In 2020 similar results were reported for a platform consisting of europium sulfide and gold films grown on vanadium.
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Churchill, H.O.H.; Fatemi, V.; Grove-Rasmussen, K.; Deng, M.T.; Caroff, P.; Xu, H.Q.; Marcus, C.M. (6 June 2013). "Superconductor-nanowire devices from tunneling to the multichannel regime: Zero-bias oscillations and magnetoconductance crossover".
2332:: interchanging them changes the state of the system in a way that depends only on the order in which the exchange was performed. The non-abelian statistics that Majorana bound states possess allows them to be used as a building block for a 1070: 1263: 987: 4956:
He, Qing Lin; Pan, Lei; Stern, Alexander L.; Burks, Edward C.; Che, Xiaoyu; Yin, Gen; et al. (21 July 2017). "Chiral Majorana fermion modes in a quantum anomalous Hall insulator–superconductor structure".
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Kayyalha, Morteza; Xiao, Di; Zhang, Ruoxi; Shin, Jaeho; Jiang, Jue; Wang, Fei; et al. (3 January 2020). "Absence of evidence for chiral Majorana modes in quantum anomalous Hall-superconductor devices".
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The aforementioned experiments mark possible verifications of independent 2010 theoretical proposals from two groups predicting the solid state manifestation of Majorana bound states in semiconducting wires
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Lee, E.J.H.; Jiang, X.; Houzet, M.; Aguado, R.; Lieber, C.M.; Franceschi, S.D. (15 December 2013). "Spin-resolved Andreev levels and parity crossings in hybrid superconductor–semiconductor nanostructures".
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Das, A.; Ronen, Y.; Most, Y.; Oreg, Y.; Heiblum, M.; Shtrikman, H. (11 November 2012). "Zero-bias peaks and splitting in an Al-InAs nanowire topological superconductor as a signature of Majorana fermions".
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Nadj-Perge, Stevan; Drozdov, Ilya K.; Li, Jian; Chen, Hua; Jeon, Sangjun; Seo, Jungpil; et al. (2 October 2014). "Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor".
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Mourik, V.; Zuo, K.; Frolov, S.M.; Plissard, S.R.; Bakkers, E.P.A.M.; Kouwenhoven, L.P. (12 April 2012). "Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices".
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The seesaw mechanism is appealing because it would naturally explain why the observed neutrino masses are so small. However, if the neutrinos are Majorana then they violate the conservation of
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A 2017 report of the discovery of a particular kind of Majorana fermion – the chiral Majorana fermion, referred to as the 'angel particle' – is likely a false alarm, according to new research.
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Because particles and antiparticles have opposite conserved charges, Majorana fermions have zero charge, hence among the fundamental particles, the only fermions that could be Majorana are
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which carry unpaired Majorana modes. The Majoranas are then "braided" by being physically moved around each other in 2D sheets or networks of nanowires. This braiding process forms a
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Wang, Dongfei; Kong, Lingyuan; Fan, Peng; Chen, Hui; Zhu, Shiyu; Liu, Wenyao; et al. (16 August 2018). "Evidence for Majorana bound states in an iron-based superconductor".
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Deng, M.T.; Vaitiekėnas, S.; Hansen, E.B.; Danon, J.; Leijnse, M.; Flensberg, K.; et al. (2016). "Majorana bound state in a coupled quantum-dot hybrid-nanowire system".
70: 2324:. This name is more appropriate than Majorana fermion (although the distinction is not always made in the literature), because the statistics of these objects is no longer 3359:
Read, N.; Green, Dmitry (2000). "Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect".
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Deng, M.T.; Yu, C.L.; Huang, G.Y.; Larsson, M.; Caroff, P.; Xu, H.Q. (28 November 2012). "Anomalous zero-bias conductance peak in a Nb-InSb nanowire-Nb hybrid device".
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Lutchyn, Roman M.; Sau, Jay D.; Das Sarma, S. (August 2010). "Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures".
2551:. Though the codes typically have no Hamiltonian to provide suppression of errors, fault-tolerance would be provided by the underlying quantum error correcting code. 1112: 2852:
Tello, Vladimir; Nemevơek, Miha; Nesti, Fabrizio; Senjanović, Goran; Vissani, Francesco (2011). "Left-right symmetry: From LHC to neutrinoless double beta decay".
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Nayak, Chetan; Simon, Steven H.; Stern, Ady; Freedman, Michael; Sarma, Sankar Das (27 March 2008). "Non-Abelian anyons and topological quantum computation".
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In 2008, Fu and Kane provided a groundbreaking development by theoretically predicting that Majorana bound states can appear at the interface between
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Nayak, Chetan; Simon, Steven H.; Stern, Ady; Freedman, Michael; Das Sarma, Sankar (2008). "Non-Abelian anyons and topological quantum computation".
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at the end points of superconducting wires or line defects are an alternative, purely electrical, source. An altogether different source uses the
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temperature), and none are Majorana fermions. The nature of neutrinos is not settled – they may turn out to be either Dirac or Majorana fermions.
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Banerjee, A.; Bridges, C.A.; Yan, J.-Q.; et al. (4 April 2016). "Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet".
2646: 2109:, the neutrino fields would naturally behave as six Majorana fields, with three of them expected to have very high masses (comparable to the 1191: 3578:
Fu, Liang; Kane, Charles L. (2009). "Josephson current and noise at a superconductor/quantum-spin-Hall-insulator/superconductor junction".
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Rokhinson, L.P.; Liu, X.; Furdyna, J.K. (2012). "Observation of the fractional ac Josephson effect: the signature of Majorana particles".
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Fu, Liang; Kane, Charles L. (2008). "Superconducting proximity effect and Majorana fermions at the surface of a topological insulatorn".
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Kim, Howon; Palacio-Morales, Alexandra; Posske, Thore; RĂłzsa, Levente; PalotĂĄs, KrisztiĂĄn; Szunyogh, LĂĄszlĂł; et al. (30 May 2018).
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events whose resultant antineutrinos immediately annihilate each other, and is only possible if neutrinos are their own antiparticles.
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Zheng, Huaixiu; Dua, Arpit; Jiang, Liang (2015). "Demonstrating non-Abelian statistics of Majorana fermions using twist defects".
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in condensed matter physics. Its existence becomes possible because a quasiparticle in a superconductor is its own antiparticle.
71: 4148:"Parity independence of the zero-bias conductance peak in a nanowire based topological superconductor-quantum dot hybrid device" 3924: 2512: 2320:. Majorana fermions can be bound to a defect at zero energy, and then the combined objects are called Majorana bound states or 1630: 2621:
Majorana, Ettore; Maiani, Luciano (2006). "A symmetric theory of electrons and positrons". In Bassani, Giuseppe Franco (ed.).
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Barkeshli, Maissam; Jian, Chao-Ming; Qi, Xiao-Liang (2013). "Twist defects and projective non-Abelian braiding statistics".
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Feldman, Benjamin E.; Randeria, Mallika T.; Li, Jian; Jeon, Sangjun; Xie, Yonglong; Wang, Zhijun; et al. (March 2017).
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The high-energy analog of the neutrinoless double beta decay process is the production of same-sign charged lepton pairs in
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are distinct, whereas for a Majorana fermion they are identical. The ordinary fermionic annihilation and creation operators
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Keung, Wai-Yee; Senjanović, Goran (1983). "Majorana neutrinos and the production of the right-handed charged gauge boson".
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Pospelov, Maxim; ter Veldhuis, Tonnis (2000). "Direct and indirect limits on the electro-magnetic form factors of WIMPs".
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Oreg, Yuval; Refael, Gil; von Oppen, Felix (October 2010). "Helical Liquids and Majorana Bound States in Quantum Wires".
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Boudjema, F.; Hamzaoui, C.; Rahal, V.; Ren, H.C. (1989). "Electromagnetic Properties of Generalized Majorana Particles".
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In February 2023 a study reported the realization of a "poor man's" Majorana that is a Majorana bound state that is not
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and their antiparticles with masses coming directly from the Higgs interaction, like the other Standard Model fermions.
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Hastings, M.B.; Geller, A. (2015). "Reduced space-time and time costs using dislocation codes and arbitrary ancillas".
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Kwon, H.-J.; Sengupta, K.; Yakovenko, V. M. (2004). "Fractional ac Josephson effect in p- and d-wave superconductors".
6071: 4765:"Toward tailoring Majorana bound states in artificially constructed magnetic atom chains on elemental superconductors" 2504: 649: 75: 72: 1947: 64: 3259:
Kopnin, N.B.; Salomaa, M.M. (1991). "Mutual friction in superfluid He: Effects of bound states in the vortex core".
2161:, there is a deep connection between these processes. In the currently most-favored explanation of the smallness of 1324: 82: 73: 5052: 3419: 2604: 80: 65: 7168: 6580: 4595: 3206: 2915:
Kayser, Boris; Goldhaber, Alfred S. (1983). "CPT and CP properties of Majorana particles, and the consequences".
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one at either end of the region of the nanowire in contact with the superconductor. Simultaneously, a group from
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in certain superconductors or superfluids can trap midgap states, which is one source of Majorana bound states.
2018: 613:, they are the collective movement of several individual particles (themselves composite) which are governed by 4213:
Wiedenmann, J.; Bocquillon, E.; Deacon, R.S.; Hartinger, S.; Herrmann, O.; Klapwijk, T.M.; et al. (2016).
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annihilates it (or, equivalently, creates the corresponding antiparticle). For a Dirac fermion the operators
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Jeon, Sangjun; Xie, Yonglong; Li, Jian; Wang, Zhijun; Bernevig, B. Andrei; Yazdani, Ali (10 November 2017).
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The difference between Majorana fermions and Dirac fermions can be expressed mathematically in terms of the
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Manna, Sujit; Wei, Peng; Xie, Yingming; Tuen Law, Kam; Lee, Patrick; Moodera, Jagadeesh (6 April 2020).
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Reich, Eugenie Samuel (28 February 2012). "Quest for quirky quantum particles may have struck gold".
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Alicea, Jason (2012). "New directions in the pursuit of Majorana fermions in solid state systems".
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Bombin, H. (14 July 2010). "Topological Order with a Twist: Ising Anyons from an Abelian Model".
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Deng, M.T.; Yu, C.L.; Huang, G.Y.; Larsson, Marcus; Caroff, P.; Xu, H.Q. (11 November 2014).
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On 16 August 2018, a strong evidence for the existence of Majorana bound states (or Majorana
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with the state arising when the rate of both processes match confirming a prediction of
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and therefore only stable for a very small range of parameters. It was obtained in a
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One of the causes of interest in Majorana bound states is that they could be used in
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Chiral Majorana fermions were claimed to be detected in 2017 by Q.L. He et al., in a
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has not (yet) been observed, but if it does exist, it can be viewed as two ordinary
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Beenakker, C.W.J. (April 2013). "Search for Majorana fermions in superconductors".
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Rodejohann, Werner (2011). "Neutrino-less double beta decay and particle physics".
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can emerge as a Majorana fermion (non-fundamental), more commonly referred to as a
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Volovik, G.E. (1999). "Fermion zero modes on vortices in chiral superconductors".
2528:. This process is done by creating so called 'twist defects' in codes such as the 1427:
is indeed fulfilled. This convention has the advantage that the Majorana operator
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Such a realization of Majoranas would allow them to be used to store and process
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The concept goes back to Majorana's suggestion in 1937 that electrically neutral
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Radescu, E.E. (1985). "On the electromagnetic properties of Majorana fermions".
2838: 2568: 2537: 1065:{\displaystyle f^{\dagger }={\tfrac {1}{\sqrt {2}}}(\gamma _{1}-i\gamma _{2})~.} 646: 455: 440: 390: 350: 300: 5914: 5803: 5725: 5544: 5404: 5329: 4863: 4124: 3611: 3237: 3028: 6883: 6777: 6767: 6749: 6639: 6540: 6475: 6192: 3762: 3392: 2739: 2598: 2529: 2417:, evidence of Majorana bound states was also observed using a low-temperature 2172:
Majorana fermions cannot possess intrinsic electric or magnetic moments, only
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Majorana, Ettore (1937). "Teoria simmetrica dell'elettrone e del positrone".
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fermions are known to behave as Dirac fermions at low energy (lower than the
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matrices. These are identical to the commutation relations for the real
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Another common convention for the normalization of the Majorana fermion
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Sarma, Sankar Das; Freedman, Michael; Nayak, Chetan (27 October 2015).
3066: 2800: 2684: 1258:{\displaystyle f^{\dagger }={\tfrac {1}{2}}(\gamma _{1}-i\gamma _{2}),} 565: 31: 6102: 4692:"Distinguishing a Majorana zero mode using spin-resolved measurements" 4660: 4181: 4070: 4008: 3900: 3190: 2607:, uploaded 19 April 2013, retrieved 5 October 2014; and also based on 609:
can appear like bound Majorana fermions. However, instead of a single
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which can be rearranged to obtain the Majorana fermion operators as
982:{\displaystyle f={\tfrac {1}{\sqrt {2}}}(\gamma _{1}+i\gamma _{2}),} 5897: 5708: 5584: 5454: 5395: 5312: 5231: 5085: 4971: 4909: 4846: 4708: 4643: 4484: 4233: 1866:{\displaystyle \sum _{ijkl}=4\sum _{ij}\gamma _{i}_{ij}\gamma _{j}} 7035: 6975: 6827: 6686: 6565: 6505: 6460: 6353: 6331: 6174: 6085: 5839: 5786: 5647: 5527: 4548: 4423: 4361: 4298: 4164: 4107: 4053: 3991: 3883: 3820: 3712: 3649: 3594: 3531: 3220: 3121: 2868: 2722: 2496: 2329: 2101:
could have Majorana masses. If they do, then at low energy (after
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Ho, Chiu Man; Scherrer, Robert J. (2013). "Anapole Dark Matter".
580:, which describes fermions that are not their own antiparticles. 6802: 6734: 6694: 6270: 6265: 6121: 5881:"Realization of a minimal Kitaev chain in coupled quantum dots" 4625:"High-resolution studies of the Majorana atomic chain platform" 6069:
Pal, Palash B. (2011) . "Dirac, Majorana, and Weyl fermions".
1493:{\displaystyle \gamma _{i}^{2}=(\gamma _{i}^{\dagger })^{2}=1} 546: 1180:{\displaystyle f={\tfrac {1}{2}}(\gamma _{1}+i\gamma _{2}),} 53: 4828:
JĂ€ck, Berthold; Xie, Yonglong; Yazdani, Ali (August 2021).
2763:"Neutrinoless double-β decay in SU(2) x U(1) theories" 552: 537: 534: 5748:"Why Majoranas are cool: Braiding and quantum computation" 1999:, if they exist. All the other elementary fermions of the 5568:"Majorana zero modes and topological quantum computation" 2571:
in a superconducting nanowire strongly coupled by normal
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Chatzopoulos, Damianos; et al. (12 January 2021).
3417:(2001). "Unpaired Majorana fermions in quantum wires". 2428:
Majorana fermions may also emerge as quasiparticles in
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hypothesised the existence of Majorana fermions in 1937
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quantum number. However, if they exist, the so-called "
576:
in 1937. The term is sometimes used in opposition to a
2463: 2451: 2039: 1209: 1131: 1011: 931: 2600:"Quantum Computation possible with Majorana Fermions" 2449: 2303: 2262: 2242: 2213: 2021: 1950: 1930: 1902: 1882: 1704: 1633: 1576: 1549: 1529: 1506: 1437: 1388: 1327: 1277: 1194: 1123: 1100: 996: 923: 893: 866: 839: 819: 792: 760: 733: 709: 677: 660:, which leaves the Majorana wave equation unchanged. 549: 2372:
in the Netherlands reported an experiment involving
543: 7085: 7049: 6966: 6927: 6897: 6871: 6858: 6790: 6758: 6685: 6620: 6611: 6602: 6498: 6453: 6425: 6416: 6407: 6389: 6367: 6339: 6330: 6246: 6173: 6164: 6155: 5053:"Majorana fermion detected in a quantum layer cake" 3474:"Nonabelions in the fractional quantum Hall effect" 540: 531: 2484:{\displaystyle {\tfrac {1}{2}}{\tfrac {e^{2}}{h}}} 2483: 2312: 2289: 2248: 2228: 2169:, the neutrino is “naturally” a Majorana fermion. 2075:(assuming no other, unknown gauge charges exist). 2055: 1979: 1936: 1908: 1888: 1865: 1684: 1612: 1562: 1535: 1515: 1492: 1420:{\displaystyle \gamma _{i}=\gamma _{i}^{\dagger }} 1419: 1371: 1312: 1257: 1179: 1106: 1064: 981: 906: 879: 860:can be written in terms of two Majorana operators 852: 825: 805: 778: 746: 727:wave function), whereas the annihilation operator 715: 695: 2520:Majorana bound states in quantum error correction 1980:{\displaystyle \mathrm {Cl} (\mathbb {R} ^{n})} 57: 3472:Moore, Gregory; Read, Nicholas (August 1991). 1372:{\displaystyle \gamma _{2}=i(f^{\dagger }-f).} 6133: 6003:"Unpaired Majorana fermions in quantum wires" 502: 8: 5286:Chen, Mingyang; et al. (6 March 2018). 1660: 1634: 2203:Mathematically, the superconductor imposes 1313:{\displaystyle \gamma _{1}=f^{\dagger }+f,} 6868: 6864: 6617: 6608: 6422: 6413: 6336: 6170: 6161: 6140: 6126: 6118: 2056:{\displaystyle T_{3}=\pm {\tfrac {1}{2}},} 509: 495: 38: 6084: 6018: 5977: 5896: 5838: 5785: 5707: 5646: 5601: 5583: 5526: 5481: 5471: 5453: 5412: 5394: 5337: 5311: 5230: 5149: 5084: 4970: 4908: 4845: 4804: 4707: 4642: 4547: 4483: 4422: 4360: 4297: 4258: 4232: 4189: 4163: 4106: 4052: 3990: 3937: 3882: 3819: 3711: 3699:Annual Review of Condensed Matter Physics 3648: 3593: 3530: 3499: 3432: 3374: 3319: 3219: 3120: 3065: 2867: 2799: 2721: 2509:University of Chinese Academy of Sciences 2469: 2462: 2450: 2448: 2302: 2268: 2263: 2261: 2241: 2212: 2038: 2026: 2020: 1968: 1964: 1963: 1951: 1949: 1929: 1901: 1881: 1857: 1844: 1822: 1809: 1790: 1777: 1767: 1754: 1741: 1731: 1709: 1703: 1673: 1654: 1641: 1632: 1575: 1554: 1548: 1528: 1505: 1500:. Using this convention, a collection of 1478: 1468: 1463: 1447: 1442: 1436: 1411: 1406: 1393: 1387: 1351: 1332: 1326: 1295: 1282: 1276: 1243: 1227: 1208: 1199: 1193: 1165: 1149: 1130: 1122: 1099: 1047: 1031: 1010: 1001: 995: 967: 951: 930: 922: 898: 892: 871: 865: 844: 838: 818: 797: 791: 770: 765: 759: 738: 732: 708: 687: 682: 676: 5954:"Evidence Found for a Majorana "Cousin"" 3730:10.1146/annurev-conmatphys-030212-184337 2351:as a substitute for the superconductor. 2290:{\displaystyle {\gamma ^{\dagger }(-E)}} 2709:International Journal of Modern Physics 2591: 2145:; it is being searched for by both the 41: 5952:Wright, Katherine (15 February 2023). 2555:Majorana bound states in Kitaev chains 2432:, and were observed by researchers at 779:{\displaystyle \gamma _{j}^{\dagger }} 696:{\displaystyle \gamma _{j}^{\dagger }} 2761:Schechter, J.; Valle, J.W.F. (1982). 2609:the pronunciation of physicist's name 7: 27:Fermion that is its own antiparticle 5827:Quantum Information and Computation 3778:"Majorana particle glimpsed in lab" 2402:HgTe with superconducting contacts 2385:reported observation of fractional 703:creates a fermion in quantum state 665:creation and annihilation operators 5151:10.1126/science.2020.367.6473.twis 2007:, so they cannot have fundamental 1955: 1952: 25: 2625:Ettore Majorana Scientific Papers 175:Physics beyond the Standard Model 7184: 7077:Timeline of particle discoveries 5132:Jelena Stajic (3 January 2020). 3776:Amos, Jonathan (13 April 2012). 2355:Experiments in superconductivity 645:particles can be described by a 527: 6001:Kitaev, A Yu (1 October 2001). 5051:Conover, Emily (20 July 2017). 4604:(Press release). 2 October 2014 3925:The European Physical Journal B 2513:scanning tunneling spectroscopy 2408:proximitized to superconductors 5665:10.1103/PhysRevLett.105.030403 5134:"Looking for chiral Majoranas" 5057:Science News (sciencenews.org) 4379:10.1103/PhysRevLett.105.177002 4316:10.1103/PhysRevLett.105.077001 3636:Reports on Progress in Physics 3549:10.1103/PhysRevLett.100.096407 3139:10.1016/j.physletb.2013.04.039 2886:10.1103/PhysRevLett.106.151801 2526:quantum error correcting codes 2370:Delft University of Technology 2366:Kavli Institute of Nanoscience 2349:fractional quantum Hall effect 2283: 2274: 2256:to the annihilation operator 2223: 2217: 2132:Neutrinoless double beta decay 1974: 1959: 1841: 1828: 1796: 1724: 1475: 1456: 1363: 1344: 1249: 1220: 1171: 1142: 1053: 1024: 973: 944: 1: 3667:10.1088/0034-4885/75/7/076501 3084:10.1016/S0370-2693(00)00358-0 2441:quantum anomalous Hall effect 2434:Oak Ridge National Laboratory 2419:scanning tunneling microscope 2103:electroweak symmetry breaking 593:electroweak symmetry breaking 119:Spontaneous symmetry breaking 7093:History of subatomic physics 6037:10.1070/1063-7869/44/10S/S29 3501:10.1016/0550-3213(91)90407-O 3451:10.1070/1063-7869/44/10S/S29 2639:10.1007/978-3-540-48095-2_10 2334:topological quantum computer 853:{\displaystyle f^{\dagger }} 572:. They were hypothesised by 6072:American Journal of Physics 2839:10.1103/PhysRevLett.50.1427 2505:Chinese Academy of Sciences 2097:and anomalously small S.M. 1613:{\displaystyle i=1,2,..,2n} 1563:{\displaystyle \gamma _{i}} 907:{\displaystyle \gamma _{2}} 880:{\displaystyle \gamma _{1}} 806:{\displaystyle \gamma _{j}} 747:{\displaystyle \gamma _{j}} 7232: 5915:10.1038/s41586-022-05585-1 5804:10.1103/PhysRevB.87.045130 5726:10.1103/PhysRevB.92.245139 5545:10.1103/RevModPhys.80.1083 5405:10.1038/s41467-020-20529-x 5330:10.1038/s41467-018-03404-8 4864:10.1038/s42254-021-00328-z 4125:10.1103/PhysRevB.87.241401 3956:10.1140/epjb/e2004-00066-4 3612:10.1103/PhysRevB.79.161408 3420:Physics-Uspekhi Supplement 3238:10.1103/RevModPhys.80.1083 3029:10.1103/PhysRevLett.62.852 2229:{\displaystyle \gamma (E)} 149:Standard Model mathematics 29: 7182: 6867: 5515:Reviews of Modern Physics 3763:10.1038/nature.2012.10124 3393:10.1103/PhysRevB.61.10267 3207:Reviews of Modern Physics 2740:10.1142/S0218301311020186 2534:projective representation 2501:iron-based superconductor 2364:in 2012. A team from the 2190:superconducting materials 560:), also referred to as a 7110:mathematical formulation 6705:Eta and eta prime mesons 5198:"Editorial Retraction". 3283:10.1103/PhysRevB.44.9667 2984:10.1103/PhysRevD.32.1266 2939:10.1103/PhysRevD.28.2341 2792:10.1103/PhysRevD.25.2951 2383:University of Notre Dame 2198:Bogoliubov quasiparticle 671:: The creation operator 600:condensed matter physics 30:Not to be confused with 6772:Double-charm tetraquark 5635:Physical Review Letters 5572:npj Quantum Information 5473:10.1073/pnas.1919753117 5249:10.1126/science.aao1797 5103:10.1126/science.aax6361 5024:10.1126/science.adf7575 4989:10.1126/science.aag2792 4726:10.1126/science.aan3670 4566:10.1126/science.1259327 4502:10.1126/science.aaf3961 4348:Physical Review Letters 4285:Physical Review Letters 3838:10.1126/science.1222360 3518:Physical Review Letters 3160:Wilczek, Frank (2009). 3008:Physical Review Letters 2855:Physical Review Letters 2818:Physical Review Letters 2561:topologically protected 2157:. In theories based on 2073:truly neutral particles 1429:squares to the identity 1382:It is easy to see that 1107:{\displaystyle \gamma } 137:Electroweak interaction 5857:10.26421/QIC15.11-12-6 4834:Nature Reviews Physics 4789:10.1126/sciadv.aar5251 4441:10.1038/nnano.2013.267 2485: 2361:topological insulators 2314: 2291: 2250: 2230: 2093:introduced to explain 2086: 2057: 1981: 1938: 1910: 1890: 1867: 1686: 1614: 1564: 1537: 1517: 1494: 1421: 1373: 1314: 1259: 1181: 1108: 1066: 983: 908: 881: 854: 827: 807: 780: 748: 717: 697: 615:non-Abelian statistics 583:With the exception of 141:Quantum chromodynamics 85: 7169:Wave–particle duality 7159:Relativistic particle 6296:Electron antineutrino 5979:10.1103/Physics.16.24 5383:Nature Communications 5300:Nature Communications 5018:(Retracted, see 4411:Nature Nanotechnology 4220:Nature Communications 2486: 2400:topological insulator 2393:by a factor of 2) in 2315: 2292: 2251: 2231: 2184:Majorana bound states 2155:Large Hadron Collider 2081: 2058: 1982: 1939: 1911: 1891: 1868: 1687: 1620:) obey the following 1615: 1565: 1538: 1518: 1495: 1422: 1374: 1315: 1260: 1182: 1109: 1067: 984: 909: 882: 855: 828: 808: 781: 749: 718: 698: 171:Neutrino oscillations 91:of the Standard Model 84: 7216:Quantum field theory 6399:Faddeev–Popov ghosts 6149:Particles in physics 5833:(11–12): 0962–0986. 5603:10.1038/npjqi.2015.1 2447: 2430:quantum spin liquids 2423:Princeton University 2301: 2260: 2240: 2211: 2095:neutrino oscillation 2019: 1991:Elementary particles 1948: 1928: 1900: 1880: 1702: 1631: 1574: 1547: 1543:ordinary fermions), 1527: 1504: 1435: 1386: 1325: 1275: 1192: 1121: 1098: 994: 921: 891: 864: 837: 817: 790: 758: 731: 707: 675: 611:fundamental particle 111:Quantum field theory 89:Elementary particles 7174:Particle chauvinism 7117:Subatomic particles 6095:2011AmJPh..79..485P 6029:2001PhyU...44..131K 5970:2023PhyOJ..16...24W 5907:2023Natur.614..445D 5849:2014arXiv1408.3379H 5796:2013PhRvB..87d5130B 5718:2015PhRvB..92x5139Z 5657:2010PhRvL.105c0403B 5594:2015npjQI...115001S 5537:2008RvMP...80.1083N 5464:2020PNAS..117.8775M 5322:2018NatCo...9..970C 5241:2018Sci...362..333W 5095:2020Sci...367...64K 4981:2017Sci...357..294H 4919:2016NatMa..15..733B 4856:2021NatRP...3..541J 4781:2018SciA....4.5251K 4718:2017Sci...358..772J 4653:2017NatPh..13..286F 4558:2014Sci...346..602N 4494:2016Sci...354.1557D 4478:(6319): 1557–1562. 4433:2014NatNa...9...79L 4371:2010PhRvL.105q7002O 4308:2010PhRvL.105g7001L 4251:10.1038/ncomms10303 4243:2016NatCo...710303W 4174:2014NatSR...4E7261D 4117:2013PhRvB..87x1401C 4063:2012NatPh...8..887D 4001:2012NanoL..12.6414D 3948:2004EPJB...37..349K 3893:2012NatPh...8..795R 3830:2012Sci...336.1003M 3814:(6084): 1003–1007. 3722:2013ARCMP...4..113B 3659:2012RPPh...75g6501A 3604:2009PhRvB..79p1408F 3541:2008PhRvL.100i6407F 3492:1991NuPhB.360..362M 3443:2001PhyU...44..131K 3385:2000PhRvB..6110267R 3369:(15): 10267–10297. 3330:1999JETPL..70..609V 3275:1991PhRvB..44.9667K 3230:2008RvMP...80.1083N 3183:2009NatPh...5..614W 3131:2013PhLB..722..341H 3076:2000PhLB..480..181P 3021:1989PhRvL..62..852B 2976:1985PhRvD..32.1266R 2931:1983PhRvD..28.2341K 2878:2011PhRvL.106o1801T 2831:1983PhRvL..50.1427K 2784:1982PhRvD..25.2951S 2732:2011IJMPE..20.1833R 2677:1937NCim...14..171M 2549:quantum computation 2545:quantum information 2421:, by scientists at 2391:Josephson frequency 2322:Majorana zero modes 2159:left–right symmetry 2153:experiments at the 1523:Majorana fermions ( 1473: 1452: 1416: 775: 692: 669:second quantization 658:complex conjugation 5184:. 3 January 2020. 4152:Scientific Reports 3162:"Majorana returns" 2685:10.1007/bf02961314 2567:consisting of two 2481: 2479: 2460: 2330:non-abelian anyons 2313:{\displaystyle -E} 2310: 2287: 2246: 2226: 2087: 2053: 2048: 1977: 1934: 1906: 1886: 1863: 1817: 1723: 1682: 1610: 1560: 1533: 1516:{\displaystyle 2n} 1513: 1490: 1459: 1438: 1417: 1402: 1369: 1310: 1255: 1218: 1177: 1140: 1104: 1062: 1022: 979: 942: 904: 877: 850: 823: 803: 776: 761: 744: 713: 693: 678: 86: 18:Majorana particles 7198: 7197: 7154:Massless particle 6962: 6961: 6958: 6957: 6923: 6922: 6786: 6785: 6598: 6597: 6594: 6593: 6546:Magnetic monopole 6494: 6493: 6385: 6384: 6326: 6325: 6306:Muon antineutrino 6291:Electron neutrino 6103:10.1119/1.3549729 5891:(7948): 445–450. 5774:Physical Review B 5696:Physical Review B 5448:(16): 8775–8782. 5225:(6412): 333–335. 5180:(Press release). 4965:(6348): 294–299. 4702:(6364): 772–776. 4661:10.1038/nphys3947 4542:(6209): 602–607. 4182:10.1038/srep07261 4101:(24): 241401(R). 4095:Physical Review B 4071:10.1038/nphys2479 4009:10.1021/nl303758w 3985:(12): 6414–6419. 3901:10.1038/nphys2429 3581:Physical Review B 3479:Nuclear Physics B 3362:Physical Review B 3269:(17): 9667–9677. 3262:Physical Review B 3191:10.1038/nphys1380 3108:Physics Letters B 3053:Physics Letters B 2963:Physical Review D 2918:Physical Review D 2825:(19): 1427–1430. 2778:(11): 2951–2954. 2771:Physical Review D 2661:Translated from: 2648:978-3-540-48091-4 2577:Andreev tunneling 2511:, when they used 2478: 2459: 2395:indium antimonide 2389:(decrease of the 2379:Purdue University 2374:indium antimonide 2249:{\displaystyle E} 2091:sterile neutrinos 2069:sterile neutrinos 2047: 1997:sterile neutrinos 1937:{\displaystyle n} 1909:{\displaystyle B} 1889:{\displaystyle A} 1805: 1705: 1536:{\displaystyle n} 1217: 1139: 1058: 1021: 1020: 941: 940: 826:{\displaystyle f} 716:{\displaystyle j} 654:Majorana equation 562:Majorana particle 519: 518: 167:Hierarchy problem 163:Strong CP problem 16:(Redirected from 7223: 7188: 7164:Virtual particle 6935:Mesonic molecule 6869: 6865: 6710:Bottom eta meson 6618: 6609: 6581:Wâ€Č and Zâ€Č bosons 6571:Sterile neutrino 6556:Majorana fermion 6423: 6414: 6337: 6316:Tau antineutrino 6171: 6162: 6142: 6135: 6128: 6119: 6114: 6088: 6057: 6056: 6022: 6020:cond-mat/0010440 6013:(10S): 131–136. 5998: 5992: 5991: 5981: 5949: 5943: 5942: 5900: 5875: 5869: 5868: 5842: 5822: 5816: 5815: 5789: 5769: 5763: 5762: 5760: 5758: 5744: 5738: 5737: 5711: 5691: 5685: 5684: 5650: 5630: 5624: 5623: 5605: 5587: 5563: 5557: 5556: 5530: 5521:(3): 1083–1159. 5510: 5504: 5503: 5485: 5475: 5457: 5433: 5427: 5426: 5416: 5398: 5366: 5360: 5359: 5341: 5315: 5283: 5277: 5276: 5234: 5214: 5208: 5207: 5195: 5189: 5188: 5170: 5164: 5163: 5153: 5129: 5123: 5122: 5088: 5067: 5061: 5060: 5048: 5042: 5041: 5037:Retraction Watch 5016: 4974: 4953: 4947: 4946: 4927:10.1038/nmat4604 4912: 4896:Nature Materials 4890: 4884: 4883: 4849: 4825: 4819: 4818: 4808: 4769:Science Advances 4760: 4754: 4753: 4711: 4687: 4681: 4680: 4646: 4620: 4614: 4613: 4611: 4609: 4592: 4586: 4585: 4551: 4528: 4522: 4521: 4487: 4467: 4461: 4460: 4426: 4405: 4399: 4398: 4364: 4342: 4336: 4335: 4301: 4279: 4273: 4272: 4262: 4236: 4210: 4204: 4203: 4193: 4167: 4143: 4137: 4136: 4110: 4089: 4083: 4082: 4056: 4035: 4029: 4028: 3994: 3974: 3968: 3967: 3941: 3939:cond-mat/0210148 3919: 3913: 3912: 3886: 3864: 3858: 3857: 3823: 3801: 3795: 3794: 3792: 3790: 3773: 3767: 3766: 3748: 3742: 3741: 3715: 3706:(113): 113–136. 3693: 3687: 3686: 3652: 3630: 3624: 3623: 3597: 3575: 3569: 3568: 3534: 3512: 3506: 3505: 3503: 3486:(2–3): 362–396. 3469: 3463: 3462: 3436: 3434:cond-mat/0010440 3427:(131): 131–136. 3411: 3405: 3404: 3378: 3376:cond-mat/9906453 3356: 3350: 3349: 3338:10.1134/1.568223 3323: 3321:cond-mat/9909426 3301: 3295: 3294: 3256: 3250: 3249: 3223: 3214:(3): 1083–1159. 3201: 3195: 3194: 3166: 3157: 3151: 3150: 3124: 3102: 3096: 3095: 3069: 3060:(1–2): 181–186. 3047: 3041: 3040: 3002: 2996: 2995: 2970:(5): 1266–1268. 2957: 2951: 2950: 2925:(9): 2341–2344. 2912: 2906: 2905: 2871: 2849: 2843: 2842: 2812: 2806: 2805: 2803: 2767: 2758: 2752: 2751: 2725: 2716:(9): 1833–1930. 2703: 2697: 2696: 2665:Il Nuovo Cimento 2660: 2628: 2618: 2612: 2601: 2596: 2490: 2488: 2487: 2482: 2480: 2474: 2473: 2464: 2461: 2452: 2387:Josephson effect 2319: 2317: 2316: 2311: 2296: 2294: 2293: 2288: 2286: 2273: 2272: 2255: 2253: 2252: 2247: 2235: 2233: 2232: 2227: 2178:cold dark matter 2174:toroidal moments 2167:seesaw mechanism 2143:hadron colliders 2107:seesaw mechanism 2062: 2060: 2059: 2054: 2049: 2040: 2031: 2030: 1986: 1984: 1983: 1978: 1973: 1972: 1967: 1958: 1943: 1941: 1940: 1935: 1922:Clifford algebra 1915: 1913: 1912: 1907: 1895: 1893: 1892: 1887: 1872: 1870: 1869: 1864: 1862: 1861: 1852: 1851: 1827: 1826: 1816: 1795: 1794: 1785: 1784: 1772: 1771: 1759: 1758: 1749: 1748: 1736: 1735: 1722: 1691: 1689: 1688: 1683: 1681: 1680: 1659: 1658: 1646: 1645: 1619: 1617: 1616: 1611: 1569: 1567: 1566: 1561: 1559: 1558: 1542: 1540: 1539: 1534: 1522: 1520: 1519: 1514: 1499: 1497: 1496: 1491: 1483: 1482: 1472: 1467: 1451: 1446: 1426: 1424: 1423: 1418: 1415: 1410: 1398: 1397: 1378: 1376: 1375: 1370: 1356: 1355: 1337: 1336: 1319: 1317: 1316: 1311: 1300: 1299: 1287: 1286: 1264: 1262: 1261: 1256: 1248: 1247: 1232: 1231: 1219: 1210: 1204: 1203: 1186: 1184: 1183: 1178: 1170: 1169: 1154: 1153: 1141: 1132: 1113: 1111: 1110: 1105: 1071: 1069: 1068: 1063: 1056: 1052: 1051: 1036: 1035: 1023: 1016: 1012: 1006: 1005: 988: 986: 985: 980: 972: 971: 956: 955: 943: 936: 932: 913: 911: 910: 905: 903: 902: 886: 884: 883: 878: 876: 875: 859: 857: 856: 851: 849: 848: 832: 830: 829: 824: 812: 810: 809: 804: 802: 801: 785: 783: 782: 777: 774: 769: 753: 751: 750: 745: 743: 742: 723:(described by a 722: 720: 719: 714: 702: 700: 699: 694: 691: 686: 644: 642: 641: 638: 635: 568:that is its own 559: 558: 555: 554: 551: 548: 545: 542: 539: 536: 533: 523:Majorana fermion 511: 504: 497: 103:Particle physics 56: 47:particle physics 39: 21: 7231: 7230: 7226: 7225: 7224: 7222: 7221: 7220: 7201: 7200: 7199: 7194: 7178: 7132:Nuclear physics 7081: 7045: 6981:Davydov soliton 6954: 6919: 6893: 6854: 6782: 6754: 6681: 6590: 6490: 6449: 6403: 6381: 6363: 6322: 6242: 6151: 6146: 6068: 6065: 6063:Further reading 6060: 6007:Physics-Uspekhi 6000: 5999: 5995: 5951: 5950: 5946: 5877: 5876: 5872: 5824: 5823: 5819: 5771: 5770: 5766: 5756: 5754: 5752:topocondmat.org 5746: 5745: 5741: 5693: 5692: 5688: 5632: 5631: 5627: 5565: 5564: 5560: 5512: 5511: 5507: 5435: 5434: 5430: 5378: 5374: 5368: 5367: 5363: 5295: 5291: 5285: 5284: 5280: 5216: 5215: 5211: 5197: 5196: 5192: 5172: 5171: 5167: 5144:(6473): 36–38. 5131: 5130: 5126: 5079:(6473): 64–67. 5069: 5068: 5064: 5050: 5049: 5045: 5017: 4955: 4954: 4950: 4892: 4891: 4887: 4827: 4826: 4822: 4775:(5): eaar5251. 4762: 4761: 4757: 4689: 4688: 4684: 4622: 4621: 4617: 4607: 4605: 4594: 4593: 4589: 4530: 4529: 4525: 4469: 4468: 4464: 4407: 4406: 4402: 4344: 4343: 4339: 4281: 4280: 4276: 4212: 4211: 4207: 4145: 4144: 4140: 4091: 4090: 4086: 4047:(12): 887–895. 4037: 4036: 4032: 3976: 3975: 3971: 3921: 3920: 3916: 3877:(11): 795–799. 3866: 3865: 3861: 3803: 3802: 3798: 3788: 3786: 3775: 3774: 3770: 3750: 3749: 3745: 3695: 3694: 3690: 3632: 3631: 3627: 3577: 3576: 3572: 3514: 3513: 3509: 3471: 3470: 3466: 3413: 3412: 3408: 3358: 3357: 3353: 3303: 3302: 3298: 3258: 3257: 3253: 3203: 3202: 3198: 3164: 3159: 3158: 3154: 3104: 3103: 3099: 3049: 3048: 3044: 3004: 3003: 2999: 2959: 2958: 2954: 2914: 2913: 2909: 2851: 2850: 2846: 2814: 2813: 2809: 2765: 2760: 2759: 2755: 2705: 2704: 2700: 2662: 2649: 2620: 2619: 2615: 2599: 2597: 2593: 2589: 2557: 2522: 2465: 2445: 2444: 2357: 2345:Shockley states 2299: 2298: 2264: 2258: 2257: 2238: 2237: 2209: 2208: 2186: 2099:neutrino masses 2083:Ettore Majorana 2022: 2017: 2016: 2009:Majorana masses 1993: 1962: 1946: 1945: 1926: 1925: 1898: 1897: 1878: 1877: 1853: 1840: 1818: 1786: 1773: 1763: 1750: 1737: 1727: 1700: 1699: 1669: 1650: 1637: 1629: 1628: 1622:anticommutation 1572: 1571: 1550: 1545: 1544: 1525: 1524: 1502: 1501: 1474: 1433: 1432: 1389: 1384: 1383: 1347: 1328: 1323: 1322: 1291: 1278: 1273: 1272: 1239: 1223: 1195: 1190: 1189: 1161: 1145: 1119: 1118: 1096: 1095: 1089: 1043: 1027: 997: 992: 991: 963: 947: 919: 918: 894: 889: 888: 867: 862: 861: 840: 835: 834: 815: 814: 793: 788: 787: 756: 755: 734: 729: 728: 705: 704: 673: 672: 639: 636: 633: 632: 630: 623: 574:Ettore Majorana 530: 526: 515: 486: 485: 186: 178: 177: 173: 169: 165: 160: 152: 151: 147: 143: 139: 134: 126: 125: 123:Higgs mechanism 121: 117: 113: 109: 105: 100: 92: 83: 54: 35: 28: 23: 22: 15: 12: 11: 5: 7229: 7227: 7219: 7218: 7213: 7203: 7202: 7196: 7195: 7191:Physics portal 7183: 7180: 7179: 7177: 7176: 7171: 7166: 7161: 7156: 7151: 7146: 7145: 7144: 7134: 7129: 7124: 7119: 7114: 7113: 7112: 7105:Standard Model 7102: 7101: 7100: 7089: 7087: 7083: 7082: 7080: 7079: 7074: 7072:Quasiparticles 7069: 7064: 7059: 7053: 7051: 7047: 7046: 7044: 7043: 7038: 7033: 7028: 7023: 7018: 7013: 7008: 7003: 6998: 6993: 6988: 6983: 6978: 6972: 6970: 6968:Quasiparticles 6964: 6963: 6960: 6959: 6956: 6955: 6953: 6952: 6947: 6942: 6937: 6931: 6929: 6925: 6924: 6921: 6920: 6918: 6917: 6912: 6907: 6901: 6899: 6895: 6894: 6892: 6891: 6886: 6881: 6875: 6873: 6862: 6856: 6855: 6853: 6852: 6847: 6842: 6841: 6840: 6835: 6830: 6825: 6820: 6815: 6805: 6800: 6794: 6792: 6788: 6787: 6784: 6783: 6781: 6780: 6775: 6764: 6762: 6760:Exotic hadrons 6756: 6755: 6753: 6752: 6747: 6742: 6737: 6732: 6727: 6722: 6717: 6712: 6707: 6702: 6697: 6691: 6689: 6683: 6682: 6680: 6679: 6674: 6669: 6664: 6659: 6654: 6653: 6652: 6647: 6642: 6637: 6626: 6624: 6615: 6606: 6600: 6599: 6596: 6595: 6592: 6591: 6589: 6588: 6586:X and Y bosons 6583: 6578: 6573: 6568: 6563: 6558: 6553: 6548: 6543: 6538: 6533: 6528: 6523: 6518: 6513: 6508: 6502: 6500: 6496: 6495: 6492: 6491: 6489: 6488: 6478: 6473: 6468: 6463: 6457: 6455: 6451: 6450: 6448: 6447: 6442: 6437: 6431: 6429: 6420: 6411: 6405: 6404: 6402: 6401: 6395: 6393: 6387: 6386: 6383: 6382: 6380: 6379: 6373: 6371: 6365: 6364: 6362: 6361: 6359:W and Z bosons 6356: 6351: 6345: 6343: 6334: 6328: 6327: 6324: 6323: 6321: 6320: 6319: 6318: 6313: 6308: 6303: 6298: 6293: 6283: 6278: 6273: 6268: 6263: 6258: 6252: 6250: 6244: 6243: 6241: 6240: 6235: 6230: 6225: 6220: 6215: 6213:Strange (quark 6210: 6205: 6200: 6195: 6190: 6185: 6179: 6177: 6168: 6159: 6153: 6152: 6147: 6145: 6144: 6137: 6130: 6122: 6116: 6115: 6079:(5): 485–498. 6064: 6061: 6059: 6058: 5993: 5944: 5870: 5817: 5764: 5739: 5702:(24): 245139. 5686: 5625: 5558: 5505: 5428: 5376: 5372: 5361: 5293: 5289: 5278: 5209: 5190: 5165: 5124: 5062: 5043: 4948: 4903:(7): 733–740. 4885: 4840:(8): 541–554. 4820: 4755: 4682: 4637:(3): 286–291. 4630:Nature Physics 4615: 4587: 4523: 4462: 4400: 4355:(17): 177002. 4337: 4274: 4205: 4138: 4084: 4041:Nature Physics 4030: 3969: 3932:(3): 349–361. 3914: 3870:Nature Physics 3859: 3796: 3768: 3743: 3688: 3625: 3588:(16): 161408. 3570: 3507: 3464: 3406: 3351: 3314:(9): 609–614. 3296: 3251: 3196: 3177:(9): 614–618. 3170:Nature Physics 3152: 3115:(8): 341–346. 3097: 3067:hep-ph/0003010 3042: 3015:(8): 852–854. 2997: 2952: 2907: 2862:(15): 151801. 2844: 2807: 2753: 2698: 2671:(4): 171–184. 2667:(in Italian). 2647: 2613: 2590: 2588: 2585: 2556: 2553: 2521: 2518: 2477: 2472: 2468: 2458: 2455: 2356: 2353: 2341:quantum vortex 2309: 2306: 2285: 2282: 2279: 2276: 2271: 2267: 2245: 2225: 2222: 2219: 2216: 2185: 2182: 2115:Dirac fermions 2052: 2046: 2043: 2037: 2034: 2029: 2025: 2001:Standard Model 1992: 1989: 1976: 1971: 1966: 1961: 1957: 1954: 1933: 1905: 1885: 1874: 1873: 1860: 1856: 1850: 1847: 1843: 1839: 1836: 1833: 1830: 1825: 1821: 1815: 1812: 1808: 1804: 1801: 1798: 1793: 1789: 1783: 1780: 1776: 1770: 1766: 1762: 1757: 1753: 1747: 1744: 1740: 1734: 1730: 1726: 1721: 1718: 1715: 1712: 1708: 1693: 1692: 1679: 1676: 1672: 1668: 1665: 1662: 1657: 1653: 1649: 1644: 1640: 1636: 1609: 1606: 1603: 1600: 1597: 1594: 1591: 1588: 1585: 1582: 1579: 1557: 1553: 1532: 1512: 1509: 1489: 1486: 1481: 1477: 1471: 1466: 1462: 1458: 1455: 1450: 1445: 1441: 1414: 1409: 1405: 1401: 1396: 1392: 1380: 1379: 1368: 1365: 1362: 1359: 1354: 1350: 1346: 1343: 1340: 1335: 1331: 1320: 1309: 1306: 1303: 1298: 1294: 1290: 1285: 1281: 1266: 1265: 1254: 1251: 1246: 1242: 1238: 1235: 1230: 1226: 1222: 1216: 1213: 1207: 1202: 1198: 1187: 1176: 1173: 1168: 1164: 1160: 1157: 1152: 1148: 1144: 1138: 1135: 1129: 1126: 1103: 1088: 1085: 1073: 1072: 1061: 1055: 1050: 1046: 1042: 1039: 1034: 1030: 1026: 1019: 1015: 1009: 1004: 1000: 989: 978: 975: 970: 966: 962: 959: 954: 950: 946: 939: 935: 929: 926: 901: 897: 874: 870: 847: 843: 822: 800: 796: 773: 768: 764: 741: 737: 712: 690: 685: 681: 622: 619: 589:Standard Model 517: 516: 514: 513: 506: 499: 491: 488: 487: 484: 483: 478: 473: 468: 463: 458: 453: 448: 443: 438: 433: 428: 423: 418: 413: 408: 403: 398: 393: 388: 383: 378: 373: 368: 363: 358: 353: 348: 343: 338: 333: 328: 323: 318: 313: 308: 303: 298: 293: 288: 283: 278: 273: 268: 263: 258: 253: 248: 243: 238: 233: 228: 223: 218: 213: 208: 203: 198: 193: 187: 184: 183: 180: 179: 161: 158: 157: 154: 153: 135: 132: 131: 128: 127: 107:Standard Model 101: 98: 97: 94: 93: 87: 50: 49: 43:Standard Model 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 7228: 7217: 7214: 7212: 7209: 7208: 7206: 7193: 7192: 7187: 7181: 7175: 7172: 7170: 7167: 7165: 7162: 7160: 7157: 7155: 7152: 7150: 7149:Exotic matter 7147: 7143: 7140: 7139: 7138: 7137:Eightfold way 7135: 7133: 7130: 7128: 7127:Antiparticles 7125: 7123: 7120: 7118: 7115: 7111: 7108: 7107: 7106: 7103: 7099: 7096: 7095: 7094: 7091: 7090: 7088: 7084: 7078: 7075: 7073: 7070: 7068: 7065: 7063: 7060: 7058: 7055: 7054: 7052: 7048: 7042: 7039: 7037: 7034: 7032: 7029: 7027: 7024: 7022: 7019: 7017: 7014: 7012: 7009: 7007: 7004: 7002: 6999: 6997: 6994: 6992: 6989: 6987: 6984: 6982: 6979: 6977: 6974: 6973: 6971: 6969: 6965: 6951: 6948: 6946: 6943: 6941: 6938: 6936: 6933: 6932: 6930: 6926: 6916: 6913: 6911: 6908: 6906: 6903: 6902: 6900: 6896: 6890: 6887: 6885: 6882: 6880: 6877: 6876: 6874: 6870: 6866: 6863: 6861: 6857: 6851: 6848: 6846: 6843: 6839: 6836: 6834: 6831: 6829: 6826: 6824: 6821: 6819: 6816: 6814: 6811: 6810: 6809: 6806: 6804: 6801: 6799: 6798:Atomic nuclei 6796: 6795: 6793: 6789: 6779: 6776: 6773: 6769: 6766: 6765: 6763: 6761: 6757: 6751: 6748: 6746: 6743: 6741: 6738: 6736: 6733: 6731: 6730:Upsilon meson 6728: 6726: 6723: 6721: 6718: 6716: 6713: 6711: 6708: 6706: 6703: 6701: 6698: 6696: 6693: 6692: 6690: 6688: 6684: 6678: 6675: 6673: 6670: 6668: 6665: 6663: 6662:Lambda baryon 6660: 6658: 6655: 6651: 6648: 6646: 6643: 6641: 6638: 6636: 6633: 6632: 6631: 6628: 6627: 6625: 6623: 6619: 6616: 6614: 6610: 6607: 6605: 6601: 6587: 6584: 6582: 6579: 6577: 6574: 6572: 6569: 6567: 6564: 6562: 6559: 6557: 6554: 6552: 6549: 6547: 6544: 6542: 6539: 6537: 6534: 6532: 6529: 6527: 6524: 6522: 6521:Dual graviton 6519: 6517: 6514: 6512: 6509: 6507: 6504: 6503: 6501: 6497: 6486: 6482: 6479: 6477: 6474: 6472: 6469: 6467: 6464: 6462: 6459: 6458: 6456: 6452: 6446: 6443: 6441: 6438: 6436: 6433: 6432: 6430: 6428: 6424: 6421: 6419: 6418:Superpartners 6415: 6412: 6410: 6406: 6400: 6397: 6396: 6394: 6392: 6388: 6378: 6375: 6374: 6372: 6370: 6366: 6360: 6357: 6355: 6352: 6350: 6347: 6346: 6344: 6342: 6338: 6335: 6333: 6329: 6317: 6314: 6312: 6309: 6307: 6304: 6302: 6301:Muon neutrino 6299: 6297: 6294: 6292: 6289: 6288: 6287: 6284: 6282: 6279: 6277: 6274: 6272: 6269: 6267: 6264: 6262: 6259: 6257: 6254: 6253: 6251: 6249: 6245: 6239: 6236: 6234: 6233:Bottom (quark 6231: 6229: 6226: 6224: 6221: 6219: 6216: 6214: 6211: 6209: 6206: 6204: 6201: 6199: 6196: 6194: 6191: 6189: 6186: 6184: 6181: 6180: 6178: 6176: 6172: 6169: 6167: 6163: 6160: 6158: 6154: 6150: 6143: 6138: 6136: 6131: 6129: 6124: 6123: 6120: 6112: 6108: 6104: 6100: 6096: 6092: 6087: 6082: 6078: 6074: 6073: 6067: 6066: 6062: 6054: 6050: 6046: 6042: 6038: 6034: 6030: 6026: 6021: 6016: 6012: 6008: 6004: 5997: 5994: 5989: 5985: 5980: 5975: 5971: 5967: 5963: 5959: 5955: 5948: 5945: 5940: 5936: 5932: 5928: 5924: 5920: 5916: 5912: 5908: 5904: 5899: 5894: 5890: 5886: 5882: 5874: 5871: 5866: 5862: 5858: 5854: 5850: 5846: 5841: 5836: 5832: 5828: 5821: 5818: 5813: 5809: 5805: 5801: 5797: 5793: 5788: 5783: 5780:(4): 045130. 5779: 5775: 5768: 5765: 5753: 5749: 5743: 5740: 5735: 5731: 5727: 5723: 5719: 5715: 5710: 5705: 5701: 5697: 5690: 5687: 5682: 5678: 5674: 5670: 5666: 5662: 5658: 5654: 5649: 5644: 5641:(3): 030403. 5640: 5636: 5629: 5626: 5621: 5617: 5613: 5609: 5604: 5599: 5595: 5591: 5586: 5581: 5577: 5573: 5569: 5562: 5559: 5554: 5550: 5546: 5542: 5538: 5534: 5529: 5524: 5520: 5516: 5509: 5506: 5501: 5497: 5493: 5489: 5484: 5479: 5474: 5469: 5465: 5461: 5456: 5451: 5447: 5443: 5439: 5432: 5429: 5424: 5420: 5415: 5410: 5406: 5402: 5397: 5392: 5388: 5384: 5380: 5365: 5362: 5357: 5353: 5349: 5345: 5340: 5335: 5331: 5327: 5323: 5319: 5314: 5309: 5305: 5301: 5297: 5282: 5279: 5274: 5270: 5266: 5262: 5258: 5254: 5250: 5246: 5242: 5238: 5233: 5228: 5224: 5220: 5213: 5210: 5205: 5201: 5194: 5191: 5187: 5183: 5179: 5175: 5169: 5166: 5161: 5157: 5152: 5147: 5143: 5139: 5135: 5128: 5125: 5120: 5116: 5112: 5108: 5104: 5100: 5096: 5092: 5087: 5082: 5078: 5074: 5066: 5063: 5058: 5054: 5047: 5044: 5039: 5038: 5033: 5029: 5025: 5021: 5014: 5010: 5006: 5002: 4998: 4994: 4990: 4986: 4982: 4978: 4973: 4968: 4964: 4960: 4952: 4949: 4944: 4940: 4936: 4932: 4928: 4924: 4920: 4916: 4911: 4906: 4902: 4898: 4897: 4889: 4886: 4881: 4877: 4873: 4869: 4865: 4861: 4857: 4853: 4848: 4843: 4839: 4835: 4831: 4824: 4821: 4816: 4812: 4807: 4802: 4798: 4794: 4790: 4786: 4782: 4778: 4774: 4770: 4766: 4759: 4756: 4751: 4747: 4743: 4739: 4735: 4731: 4727: 4723: 4719: 4715: 4710: 4705: 4701: 4697: 4693: 4686: 4683: 4678: 4674: 4670: 4666: 4662: 4658: 4654: 4650: 4645: 4640: 4636: 4632: 4631: 4626: 4619: 4616: 4603: 4602: 4597: 4591: 4588: 4583: 4579: 4575: 4571: 4567: 4563: 4559: 4555: 4550: 4545: 4541: 4537: 4536: 4527: 4524: 4519: 4515: 4511: 4507: 4503: 4499: 4495: 4491: 4486: 4481: 4477: 4473: 4466: 4463: 4458: 4454: 4450: 4446: 4442: 4438: 4434: 4430: 4425: 4420: 4416: 4412: 4404: 4401: 4396: 4392: 4388: 4384: 4380: 4376: 4372: 4368: 4363: 4358: 4354: 4350: 4349: 4341: 4338: 4333: 4329: 4325: 4321: 4317: 4313: 4309: 4305: 4300: 4295: 4292:(7): 077001. 4291: 4287: 4286: 4278: 4275: 4270: 4266: 4261: 4256: 4252: 4248: 4244: 4240: 4235: 4230: 4226: 4222: 4221: 4216: 4209: 4206: 4201: 4197: 4192: 4187: 4183: 4179: 4175: 4171: 4166: 4161: 4157: 4153: 4149: 4142: 4139: 4134: 4130: 4126: 4122: 4118: 4114: 4109: 4104: 4100: 4096: 4088: 4085: 4080: 4076: 4072: 4068: 4064: 4060: 4055: 4050: 4046: 4042: 4034: 4031: 4026: 4022: 4018: 4014: 4010: 4006: 4002: 3998: 3993: 3988: 3984: 3980: 3973: 3970: 3965: 3961: 3957: 3953: 3949: 3945: 3940: 3935: 3931: 3927: 3926: 3918: 3915: 3910: 3906: 3902: 3898: 3894: 3890: 3885: 3880: 3876: 3872: 3871: 3863: 3860: 3855: 3851: 3847: 3843: 3839: 3835: 3831: 3827: 3822: 3817: 3813: 3809: 3808: 3800: 3797: 3785: 3784: 3779: 3772: 3769: 3764: 3760: 3756: 3755: 3747: 3744: 3739: 3735: 3731: 3727: 3723: 3719: 3714: 3709: 3705: 3701: 3700: 3692: 3689: 3684: 3680: 3676: 3672: 3668: 3664: 3660: 3656: 3651: 3646: 3643:(7): 076501. 3642: 3638: 3637: 3629: 3626: 3621: 3617: 3613: 3609: 3605: 3601: 3596: 3591: 3587: 3583: 3582: 3574: 3571: 3566: 3562: 3558: 3554: 3550: 3546: 3542: 3538: 3533: 3528: 3525:(9): 096407. 3524: 3520: 3519: 3511: 3508: 3502: 3497: 3493: 3489: 3485: 3481: 3480: 3475: 3468: 3465: 3460: 3456: 3452: 3448: 3444: 3440: 3435: 3430: 3426: 3422: 3421: 3416: 3415:Kitaev, A. 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34:. 20:)

Index

Majorana particles
Majoron
Standard Model
particle physics
Elementary particles
Particle physics
Standard Model
Quantum field theory
Gauge theory
Spontaneous symmetry breaking
Higgs mechanism
Electroweak interaction
Quantum chromodynamics
CKM matrix
Standard Model mathematics
Strong CP problem
Hierarchy problem
Neutrino oscillations
Physics beyond the Standard Model
Rutherford
Thomson
Chadwick
Bose
Sudarshan
Davis Jr
Anderson
Fermi
Dirac
Feynman
Rubbia

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