Physics:Quantum Majorana fermion
Majorana fermion is a ScholarlyWiki page in the Quantum Collection about fermionic fields or excitations that are identical to their own antiparticles.
Overview
A Majorana fermion is a fermion that is identical to its own antiparticle. The concept was introduced by Ettore Majorana in 1937 as a possible solution of the relativistic wave equation for neutral spin- particles.
No elementary particle has been conclusively established to be a Majorana fermion. Neutrinos are the main candidates in particle physics, because they are electrically neutral and have nonzero mass. In condensed-matter physics, Majorana-like quasiparticle excitations can appear as emergent modes in certain superconducting systems; these are usually called Majorana zero modes or Majorana bound states.
Key ideas
For ordinary charged fermions, a particle and its antiparticle are distinct because they carry opposite electric charge. An electron and a positron, for example, cannot be the same particle. A Majorana fermion must therefore be neutral with respect to charges that would distinguish it from its antiparticle.
In field-theory language, a Majorana field satisfies a reality condition that relates the field to its charge conjugate:
This compact equation expresses the central idea: the particle described by the field is the same as the antiparticle described by the charge-conjugate field.
Particle physics
The most important open question is whether neutrinos are Majorana fermions or Dirac fermions. If neutrinos are Majorana particles, then lepton number is not an exact conserved quantity. One possible experimental signature is neutrinoless double beta decay, a rare nuclear process in which two neutrons decay into two protons and two electrons without emitting antineutrinos.
Observation of neutrinoless double beta decay would show that neutrinos have a Majorana component. Experiments have not yet produced a confirmed observation, so the Majorana nature of neutrinos remains an open problem.
Majorana zero modes
In condensed-matter systems, the phrase "Majorana fermion" often refers to emergent quasiparticle modes rather than fundamental elementary particles. A Majorana zero mode can appear at defects, vortices, or boundaries of certain topological superconductors. Such a mode is described mathematically by an operator that is equal to its own Hermitian conjugate:
Pairs of Majorana zero modes can combine to form an ordinary fermionic degree of freedom. Because the information can be stored nonlocally across separated modes, these systems are studied for possible use in topological quantum information.
Relation to superconductivity
Superconductivity provides a natural setting for Majorana-like excitations because particle number is not conserved in the same way as in an ordinary metal. The Bogoliubov quasiparticles of a superconductor mix electron and hole degrees of freedom. Under special topological conditions, this mixing can produce localized zero-energy modes with Majorana properties.
Proposed platforms include semiconductor nanowires coupled to superconductors, magnetic atom chains on superconducting surfaces, vortices in topological superconductors, and certain fractionalized quantum Hall or spin-liquid settings. Experimental interpretation is challenging because ordinary low-energy states can sometimes mimic Majorana signatures.
Relation to anyons
Majorana zero modes are related to non-Abelian anyons. Exchanging systems that host such modes can transform the quantum state in a way that depends on the braid history. This is different from ordinary bosonic or fermionic exchange, and it motivates proposals for topological quantum computation.
The distinction between an elementary Majorana fermion and a Majorana zero mode is important. The first is a possible fundamental particle or field. The second is an emergent quasiparticle excitation in a many-body system. Both share the mathematical idea of being self-conjugate, but they belong to different physical contexts.
See also
Table of contents (217 articles)
Index
Full contents
References
- Majorana, Ettore (1937). "Teoria simmetrica dell'elettrone e del positrone". Il Nuovo Cimento 14: 171-184. doi:10.1007/BF02961314.
- Wilczek, Frank (2009). "Majorana returns". Nature Physics 5: 614-618. doi:10.1038/nphys1380.
- Alicea, Jason (2012). "New directions in the pursuit of Majorana fermions in solid state systems". Reports on Progress in Physics 75 (7): 076501. doi:10.1088/0034-4885/75/7/076501.
- Elliott, Steven R.; Franz, Marcel (2015). "Colloquium: Majorana fermions in nuclear, particle, and solid-state physics". Reviews of Modern Physics 87 (1): 137-163. doi:10.1103/RevModPhys.87.137.
Source attribution: Physics:Quantum Majorana fermion