Majorana fermion
Encyclopedia
In physics
, a Majorana fermion is a fermion
which is its own anti-particle. The term is used in opposition to Dirac fermion
, which describes particles that differ from their antiparticles. The concept goes back to Ettore Majorana
's 1937 discovery that neutral spin-1/2 particles can be described by a real wave equation (the Majorana equation).
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.
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) quasiparticle
s. 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. Shockley states at the end points of superconducting wires or line defects are an alternative, purely electrical, source. An altogether different source uses the fractional quantum Hall effect
as a substitute for the superconductor. So far, these are only theoretical predictions, but there is an active search for experimental observation.
Majorana fermions in superconductors could be used as a building block for a (non-universal) topological quantum computer
, in view of their non-Abelian anyon
ic statistics.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, a Majorana fermion is a fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
which is its own anti-particle. The term is used in opposition to Dirac fermion
Dirac fermion
In particle physics, a Dirac fermion is a fermion which is not its own anti-particle. It is named for Paul Dirac. All fermions in the standard model, except possibly neutrinos, are Dirac fermions...
, which describes particles that differ from their antiparticles. The concept goes back to Ettore Majorana
Ettore Majorana
Ettore Majorana was an Italian theoretical physicist who began work on neutrino masses. He disappeared suddenly in mysterious circumstances. He is noted for the eponymous Majorana equation and for Majorana fermions.-Gifted in mathematics:Majorana was born in Catania, Sicily...
's 1937 discovery that neutral spin-1/2 particles can be described by a real wave equation (the Majorana equation).
No elementary particle is known to be a Majorana fermion. However, the nature of the neutrino
Neutrino
A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...
is not yet definitely settled; it might be a Majorana fermion or it might be a Dirac fermion
Dirac fermion
In particle physics, a Dirac fermion is a fermion which is not its own anti-particle. It is named for Paul Dirac. All fermions in the standard model, except possibly neutrinos, are Dirac fermions...
. If it is a Majorana fermion, then neutrinoless double beta decay
Double beta decay
Double beta decay is a radioactive decay process where a nucleus releases two beta rays as a single process.In double-beta decay, two neutrons in the nucleus are converted to protons, and two electrons and two electron antineutrinos are emitted...
is possible; experiments are underway to search for this type of decay.
The hypothetical neutralino
Neutralino
In particle physics, the neutralino is a hypothetical particle predicted by supersymmetry. There are four neutralinos that are fermions and are electrically neutral, the lightest of which is typically stable...
of supersymmetric
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
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
Creation and annihilation operators
Creation and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. An annihilation operator lowers the number of particles in a given state by one...
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
Superconductivity
Superconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
, Majorana fermions can emerge as (non-fundamental) quasiparticle
Quasiparticle
In physics, quasiparticles are emergent phenomena that occur when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in free space...
s. 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
Fermi level
The Fermi level is a hypothetical level of potential energy for an electron inside a crystalline solid. Occupying such a level would give an electron a potential energy \epsilon equal to its chemical potential \mu as they both appear in the Fermi-Dirac distribution function,which...
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
Quantum vortex
In physics, a quantum vortex is a topological defect exhibited in superfluids and superconductors. Superfluids and superconductors are states of matter without friction. They exist only at very low temperatures. The existence of these quantum vortices was independently predicted by Richard Feynman...
in certain superconductors or superfluids can trap midgap states, so this is one source of Majorana fermions. Shockley states at the end points of superconducting wires or line defects are an alternative, purely electrical, source. An altogether different source uses the fractional quantum Hall effect
Fractional quantum Hall effect
The fractional quantum Hall effect is a physical phenomenon in which the Hall conductance of 2D electrons shows precisely quantised plateaus at fractional values of e^2/h. It is a property of a collective state in which electrons bind magnetic flux lines to make new quasiparticles, and excitations...
as a substitute for the superconductor. So far, these are only theoretical predictions, but there is an active search for experimental observation.
Majorana fermions in superconductors could be used as a building block for a (non-universal) topological quantum computer
Topological quantum computer
A topological quantum computer is a theoretical quantum computer that employs two-dimensional quasiparticles called anyons, whose world lines cross over one another to form braids in a three-dimensional spacetime . These braids form the logic gates that make up the computer...
, in view of their non-Abelian anyon
Anyon
In physics, an anyon is a type of particle that occurs only in two-dimensional systems. It is a generalization of the fermion and boson concept.-From theory to reality:...
ic statistics.