Majorana fermion

In condensed matter physics, quasiparticle excitations can appear like bound Majorana states.

The concept goes back to Majorana's suggestion in 1937[2] that electrically neutral spin-⁠1/2⁠ particles can be described by a real-valued wave equation (the Majorana equation), and would therefore be identical to their antiparticle, because the wave functions of particle and antiparticle are related by complex conjugation, which leaves the Majorana wave equation unchanged.

All the other elementary fermions of the Standard Model have gauge charges, so they cannot have fundamental Majorana masses: Even the Standard Model's left-handed neutrinos and right-handed antineutrinos have non-zero weak isospin,

If they do, then at low energy (after electroweak symmetry breaking), by the seesaw mechanism, the neutrino fields would naturally behave as six Majorana fields, with three of them expected to have very high masses (comparable to the GUT scale) and the other three expected to have very low masses (below 1 eV).

If right-handed neutrinos exist but do not have a Majorana mass, the neutrinos would instead behave as three Dirac fermions and their antiparticles with masses coming directly from the Higgs interaction, like the other Standard Model fermions.

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 lepton number and even of B − L. Neutrinoless double beta decay has not (yet) been observed,[3] but if it does exist, it can be viewed as two ordinary beta decay events whose resultant antineutrinos immediately annihilate each other, and is only possible if neutrinos are their own antiparticles.

[4] The high-energy analog of the neutrinoless double beta decay process is the production of same-sign charged lepton pairs in hadron colliders;[5] it is being searched for by both the ATLAS and CMS experiments at the Large Hadron Collider.

[7][8][9] Such minimal interaction with electromagnetic fields makes them potential candidates for cold dark matter.

Mathematically, the superconductor imposes electron hole "symmetry" on the quasiparticle excitations, relating the creation operator

The non-abelian statistics that Majorana bound states possess allows them to be used as a building block for a topological quantum computer.

[14][15][16] Shockley states at the end points of superconducting wires or line defects are an alternative, purely electrical, source.

[17] An altogether different source uses the fractional quantum Hall effect as a substitute for the superconductor.

[18] In 2008, Fu and Kane provided a groundbreaking development by theoretically predicting that Majorana bound states can appear at the interface between topological insulators and superconductors.

[19][20] 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[21][22] first produced some positive results in 2012.

[23][24] 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 bound states, one at either end of the region of the nanowire in contact with the superconductor.

[25] Simultaneously, a group from Purdue University and University of Notre Dame reported observation of fractional Josephson effect (decrease of the Josephson frequency by a factor of 2) in indium antimonide nanowires connected to two superconducting contacts and subjected to a moderate magnetic field,[26] another signature of Majorana bound states.

[27] Bound state with zero energy was soon detected by several other groups in similar hybrid devices,[28][29][30][31] and fractional Josephson effect was observed in topological insulator HgTe with superconducting contacts[32] The aforementioned experiments mark possible verifications of independent 2010 theoretical proposals from two groups[33][34] predicting the solid state manifestation of Majorana bound states in semiconducting wires proximitized to superconductors.

In 2014, evidence of Majorana bound states was also observed using a low-temperature scanning tunneling microscope, by scientists at Princeton University.

[37][38] 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.

[41][42] Majorana fermions may also emerge as quasiparticles in quantum spin liquids, and were observed by researchers at Oak Ridge National Laboratory, working in collaboration with Max Planck Institute and University of Cambridge on 4 April 2016.

[46][47][48] In November 2022, the article by He et al. was retracted by the editors,[49] because "analysis of the raw and published data revealed serious irregularities and discrepancies".

On 16 August 2018, a strong evidence for the existence of Majorana bound states (or Majorana anyons) in an iron-based superconductor, which many alternative trivial explanations cannot account for, was reported by Ding's and Gao's teams at Institute of Physics, Chinese Academy of Sciences and University of Chinese Academy of Sciences, when they used scanning tunneling spectroscopy 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.

In 2020 similar results were reported for a platform consisting of europium sulfide and gold films grown on vanadium.

[53] One of the causes of interest in Majorana bound states is that they could be used in quantum error correcting codes.

It was obtained in a Kitaev chain consisting of two quantum dots in a superconducting nanowire strongly coupled by normal tunneling and Andreev tunneling with the state arising when the rate of both processes match confirming a prediction of Alexei Kitaev.