Majorana Fermion
   HOME

TheInfoList



OR:

A Majorana fermion (, uploaded 19 April 2013, retrieved 5 October 2014; and also based on the pronunciation of physicist's name.), also referred to as a Majorana particle, is a
fermion In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks an ...
that is its own
antiparticle In particle physics, every type of particle is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the electron is the positron (also known as an antie ...
. They were hypothesised by
Ettore Majorana Ettore Majorana (,, uploaded 19 April 2013, retrieved 14 December 2019 ; born on 5 August 1906 – possibly dying after 1959) was an Italian theoretical physicist who worked on neutrino masses. On 25 March 1938, he disappeared under mysteri ...
in 1937. The term is sometimes used in opposition to a
Dirac fermion In physics, a Dirac fermion is a spin-½ particle (a fermion) which is different from its antiparticle. The vast majority of fermions – perhaps all – fall under this category. Description In particle physics, all fermions in the standard model ...
, which describes fermions that are not their own antiparticles. With the exception of
neutrino A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
s, all of the
Standard Model The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions - excluding gravity) in the universe and classifying a ...
fermions are known to behave as Dirac fermions at low energy (lower than the
electroweak symmetry breaking In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles, the other bein ...
temperature), and none are Majorana fermions. The nature of the neutrinos is not settled – they may turn out to be either Dirac or Majorana fermions. In
condensed matter physics Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the sub ...
,
quasiparticle In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum. For exam ...
excitations can appear like bound Majorana fermions. However, instead of a single
fundamental particle In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions (quarks, leptons, antiqu ...
, they are the collective movement of several individual particles (themselves composite) which are governed by non-Abelian statistics.


Theory

The concept goes back to Majorana's suggestion in 1937 that electrically neutral
spin Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally b ...
- particles can be described by a
real-valued In mathematics, value may refer to several, strongly related notions. In general, a mathematical value may be any definite mathematical object. In elementary mathematics, this is most often a number – for example, a real number such as or an i ...
wave equation The (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and s ...
(the
Majorana equation In physics, the Majorana equation is a relativistic wave equation. It is named after the Italian physicist Ettore Majorana, who proposed it in 1937 as a means of describing fermions that are their own antiparticle. Particles corresponding to this ...
), and would therefore be identical to their antiparticle, because the wave functions of particle and antiparticle are related by
complex conjugation In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, (if a and b are real, then) the complex conjugate of a + bi is equal to a - ...
, which leaves the Majorana wave equation unchanged. The difference between Majorana fermions and Dirac fermions can be expressed mathematically in terms of the
creation and annihilation operators Creation operators 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 (usually ...
of
second quantization Second quantization, also referred to as occupation number representation, is a formalism used to describe and analyze quantum many-body systems. In quantum field theory, it is known as canonical quantization, in which the fields (typically as t ...
: The creation operator \; \gamma^_j \; creates a fermion in quantum state \; j \; (described by a ''real'' wave function), whereas the annihilation operator \; \gamma_j \; annihilates it (or, equivalently, creates the corresponding antiparticle). For a Dirac fermion the operators \; \gamma^_j \; and \gamma_j are distinct, whereas for a Majorana fermion they are identical. The ordinary fermionic annihilation and creation operators f and \; f^ \; can be written in terms of two Majorana operators \; \gamma_1 \; and \; \gamma_2 \; by : f = \tfrac (\gamma_1+i\gamma_2) \;, : f^ = \tfrac (\gamma_1-i\gamma_2) ~. In
supersymmetry In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories e ...
models,
neutralino In supersymmetry, the neutralino is a hypothetical particle. In the Minimal Supersymmetric Standard Model (MSSM), a popular model of realization of supersymmetry at a low energy, there are four neutralinos that are fermions and are electrically ...
s – superpartners of gauge bosons and Higgs bosons – are Majorana fermions.


Identities

Another common convention for the normalization of the Majorana fermion operator is : f = \tfrac (\gamma_1 + i\gamma_2) : f^\dagger = \tfrac (\gamma_1 - i\gamma_2) This convention has the advantage that the Majorana operator squares to the identity. Using this convention, a collection of \; 2n \; Majorana fermions (\; n \; ordinary fermions), \; \gamma_i \; (\; i=1,2,..,2n \;) obey the following
commutation Commute, commutation or commutative may refer to: * Commuting, the process of travelling between a place of residence and a place of work Mathematics * Commutative property, a property of a mathematical operation whose result is insensitive to th ...
identities : \ = 2 \delta_ and : \sum_ gamma_i A_ \gamma_j, \gamma_k B_ \gamma_l= 4 \, \sum_ \gamma_i ,B \gamma_j where \, A \, and \, B \, are antisymmetric matrices. These are identical to the commutation relations for the real
Clifford algebra In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As -algebras, they generalize the real numbers, complex numbers, quaternions and several other hyperc ...
in \, n \, dimensions (\, \mathrm( \mathbb ^n ) \,).


Elementary particles

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
sterile neutrino Sterile neutrinos (or inert neutrinos) are hypothetical particles (neutral leptons – neutrinos) that are believed to interact only via gravity and not via any of the other fundamental interactions of the Standard Model. The term ''sterile neutrin ...
s, if they even exist. All the other elementary fermions of the
Standard Model The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions - excluding gravity) in the universe and classifying a ...
have gauge charges, so they cannot have fundamental
Majorana mass In physics, the Majorana equation is a relativistic wave equation. It is named after the Italian physicist Ettore Majorana, who proposed it in 1937 as a means of describing fermions that are their own antiparticle. Particles corresponding to this e ...
es: Even the Standard Model's left-handed neutrinos and right-handed antineutrinos have non-zero
weak isospin In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol or , with the third component written as or . It can ...
, \, T_3 = \pm \tfrac \, , a charge-like quantum number. However, if they exist, the so-called "
sterile neutrinos Sterile neutrinos (or inert neutrinos) are hypothetical particles (neutral leptons – neutrinos) that are believed to interact only via gravity and not via any of the other fundamental interactions of the Standard Model. The term ''sterile neutrin ...
" (left-handed antineutrinos and right-handed neutrinos) would be
truly neutral particle In particle physics, a truly neutral particle is a subatomic particle that is its own antiparticle. In other words, it remains itself under the charge conjugation which replaces particles with their corresponding antiparticles. All charges of a ''t ...
s (assuming no other, unknown gauge charges exist). The
sterile neutrino Sterile neutrinos (or inert neutrinos) are hypothetical particles (neutral leptons – neutrinos) that are believed to interact only via gravity and not via any of the other fundamental interactions of the Standard Model. The term ''sterile neutrin ...
s introduced to explain neutrino oscillation and anomalously small S.M.
neutrino mass A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass i ...
es could have Majorana masses. If they do, then at low energy (after
electroweak symmetry breaking In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles, the other bein ...
), by the
seesaw mechanism In the theory of grand unification of particle physics, and, in particular, in theories of neutrino masses and neutrino oscillation, the seesaw mechanism is a generic model used to understand the relative sizes of observed neutrino masses, of the ...
, 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 The grand unification energy \Lambda_, or the GUT scale, is the energy level above which, it is believed, the electromagnetic force, weak force, and strong force become equal in strength and unify to one force governed by a simple Lie group. The exa ...
) 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 fermion In physics, a Dirac fermion is a spin-½ particle (a fermion) which is different from its antiparticle. The vast majority of fermions – perhaps all – fall under this category. Description In particle physics, all fermions in the standard model ...
s 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 In particle physics, lepton number (historically also called lepton charge) is a conserved quantum number representing the difference between the number of leptons and the number of antileptons in an elementary particle reaction. Lepton number ...
and even of
B − L In high-energy physics, ''B'' − ''L'' (pronounced "bee minus ell") is the difference between the baryon number (''B'') and the lepton number (''L''). Details This quantum number is the charge of a global/gauge U(1) symmetry in so ...
.
Neutrinoless double beta decay The neutrinoless double beta decay (0νββ) is a commonly proposed and experimentally pursued theoretical radioactive decay process that would prove a Majorana nature of the neutrino particle. To this day, it has not been found. The discovery o ...
has not (yet) been observed, but if it does exist, it can be viewed as two ordinary
beta decay In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For ...
events whose resultant antineutrinos immediately annihilate each other, and is only possible if neutrinos are their own antiparticles. The high-energy analog of the neutrinoless double beta decay process is the production of same-sign charged lepton pairs in hadron colliders; it is being searched for by both the
ATLAS An atlas is a collection of maps; it is typically a bundle of maps of Earth or of a region of Earth. Atlases have traditionally been bound into book form, but today many atlases are in multimedia formats. In addition to presenting geographic ...
and
CMS CMS may refer to: Computing * Call management system * CMS-2 (programming language), used by the United States Navy * Code Morphing Software, a technology used by Transmeta * Collection management system for a museum collection * Color manag ...
experiments at the
Large Hadron Collider The Large Hadron Collider (LHC) is the world's largest and highest-energy particle collider. It was built by the European Organization for Nuclear Research (CERN) between 1998 and 2008 in collaboration with over 10,000 scientists and hundred ...
. In theories based on left–right symmetry, there is a deep connection between these processes. In the currently most-favored explanation of the smallness of
neutrino mass A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass i ...
, the
seesaw mechanism In the theory of grand unification of particle physics, and, in particular, in theories of neutrino masses and neutrino oscillation, the seesaw mechanism is a generic model used to understand the relative sizes of observed neutrino masses, of the ...
, the neutrino is “naturally” a Majorana fermion. Majorana fermions cannot possess intrinsic electric or magnetic moments, only toroidal moments. Such minimal interaction with electromagnetic fields makes them potential candidates for
cold dark matter In cosmology and physics, cold dark matter (CDM) is a hypothetical type of dark matter. According to the current standard model of cosmology, Lambda-CDM model, approximately 27% of the universe is dark matter and 68% is dark energy, with only a sm ...
.


Majorana bound states

In superconducting materials, a
quasiparticle In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum. For exam ...
can emerge as a Majorana fermion (non-fundamental), more commonly referred to as a
Bogoliubov quasiparticle In condensed matter physics, a Bogoliubov quasiparticle or Bogoliubon is a quasiparticle that occurs in superconductors. Whereas superconductivity is characterized by the condensation of Cooper pairs into the same ground quantum state, Bogoliubov qu ...
in condensed matter physics. Its existence becomes possible because a quasiparticle in a superconductor is its own antiparticle. Mathematically, the superconductor imposes
electron hole In physics, chemistry, and electronic engineering, an electron hole (often simply called a hole) is a quasiparticle which is the lack of an electron at a position where one could exist in an atom or atomic lattice. Since in a normal atom or ...
"symmetry" on the quasiparticle excitations, relating the creation operator \gamma(E) at energy E to the annihilation operator at energy -E. Majorana fermions can be bound to a defect at zero energy, and then the combined objects are called Majorana bound states or Majorana zero modes. 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
fermionic In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and ...
. Instead, the Majorana bound states are an example of non-abelian anyons: 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
topological quantum computer A topological quantum computer is a theoretical quantum computer proposed by Russian-American physicist Alexei Kitaev in 1997. It employs quasiparticles in two-dimensional systems, called anyons, whose world lines pass around one another to for ...
. A
quantum vortex In physics, a quantum vortex represents a quantized flux circulation of some physical quantity. In most cases, quantum vortices are a type of topological defect exhibited in superfluids and superconductors. The existence of quantum vortices was fi ...
in certain superconductors or superfluids can trap midgap states, which is one source of Majorana bound states. 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 The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2-dimensional (2D) electrons shows precisely quantized plateaus at fractional values of e^2/h. It is a property of a collective state in which elec ...
as a substitute for the superconductor.


Experiments in superconductivity

In 2008, Fu and Kane provided a groundbreaking development by theoretically predicting that Majorana bound states can appear at the interface between
topological insulators A topological insulator is a material whose interior behaves as an electrical insulator while its surface behaves as an electrical conductor, meaning that electrons can only move along the surface of the material. A topological insulator is an ...
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 in 2012. A team from the Kavli Institute of Nanoscience at
Delft University of Technology Delft University of Technology ( nl, Technische Universiteit Delft), also known as TU Delft, is the oldest and largest Dutch public technical university, located in Delft, Netherlands. As of 2022 it is ranked by QS World University Rankings among ...
in the Netherlands reported an experiment involving
indium antimonide Indium antimonide (InSb) is a crystalline compound made from the elements indium (In) and antimony (Sb). It is a narrow- gap semiconductor material from the III- V group used in infrared detectors, including thermal imaging cameras, FLIR systems ...
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. Simultaneously, a group from
Purdue University Purdue University is a public land-grant research university in West Lafayette, Indiana, and the flagship campus of the Purdue University system. The university was founded in 1869 after Lafayette businessman John Purdue donated land and money ...
and
University of Notre Dame The University of Notre Dame du Lac, known simply as Notre Dame ( ) or ND, is a private Catholic research university in Notre Dame, Indiana, outside the city of South Bend. French priest Edward Sorin founded the school in 1842. The main campu ...
reported observation of fractional
Josephson effect In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mech ...
(decrease of the Josephson frequency by a factor of 2) in
indium antimonide Indium antimonide (InSb) is a crystalline compound made from the elements indium (In) and antimony (Sb). It is a narrow- gap semiconductor material from the III- V group used in infrared detectors, including thermal imaging cameras, FLIR systems ...
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
topological insulator A topological insulator is a material whose interior behaves as an electrical insulator while its surface behaves as an electrical conductor, meaning that electrons can only move along the surface of the material. A topological insulator is an ...
HgTe with superconducting contacts 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 proximitized to superconductors. 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. In
2014 File:2014 Events Collage.png, From top left, clockwise: Stocking up supplies and personal protective equipment (PPE) for the Western African Ebola virus epidemic; Citizens examining the ruins after the Chibok schoolgirls kidnapping; Bundles of wat ...
, evidence of Majorana bound states was also observed using a low-temperature
scanning tunneling microscope A scanning tunneling microscope (STM) is a type of microscope used for imaging surfaces at the atomic level. Its development in 1981 earned its inventors, Gerd Binnig and Heinrich Rohrer, then at IBM Zürich, the Nobel Prize in Physics in 1986. ...
, by scientists at
Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...
. These experiments resolved the predicted signatures of localized Majorana bound states – zero energy modes – at the ends of chains 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. Majorana fermions may also emerge as quasiparticles in
quantum spin liquid In condensed matter physics, a quantum spin liquid is a phase of matter that can be formed by interacting quantum spins in certain magnetic materials. Quantum spin liquids (QSL) are generally characterized by their long-range quantum entangleme ...
s, and were observed by researchers at
Oak Ridge National Laboratory Oak Ridge National Laboratory (ORNL) is a U.S. multiprogram science and technology national laboratory sponsored by the U.S. Department of Energy (DOE) and administered, managed, and operated by UT–Battelle as a federally funded research and ...
, working in collaboration with Max Planck Institute and University of Cambridge on 4 April 2016. Chiral Majorana fermions were claimed to be detected in 2017 by Q.L. He et al., in a
quantum anomalous Hall effect Quantum anomalous Hall effect (QAHE) is the "quantum" version of the anomalous Hall effect. While the anomalous Hall effect requires a combination of magnetic polarization and spin-orbit coupling to generate a finite Hall voltage even in the abse ...
/superconductor hybrid device. In this system, Majorana fermions edge mode will give a rise to a \tfrac \tfrac 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". On 16 August 2018, a strong evidence for the existence of Majorana bound states (or Majorana
anyon In physics, an anyon is a type of quasiparticle that occurs only in two-dimensional systems, with properties much less restricted than the two kinds of standard elementary particles, fermions and bosons. In general, the operation of exchangi ...
s) in an
iron-based superconductor Iron-based superconductors (FeSC) are iron-containing chemical compounds whose superconducting properties were discovered in 2006. In 2008, led by recently discovered iron pnictide compounds (originally known as oxypnictides), they were in the firs ...
, 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 The Chinese Academy of Sciences (CAS); ), known by Academia Sinica in English until the 1980s, is the national academy of the People's Republic of China for natural sciences. It has historical origins in the Academia Sinica during the Republ ...
and
University of Chinese Academy of Sciences The University of the Chinese Academy of Sciences (UCAS; ) is a public university for graduate education, under the direct leadership of the Chinese Academy of Sciences (CAS). The predecessors of UCAS are the Graduate University of the Chinese ...
, when they used
scanning tunneling spectroscopy Scanning tunneling spectroscopy (STS), an extension of scanning tunneling microscopy (STM), is used to provide information about the density of electrons in a sample as a function of their energy. In scanning tunneling microscopy, a metal tip is ...
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 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.


Majorana bound states in quantum error correction

One of the causes of interest in Majorana bound states is that they could be used in quantum error correcting codes. This process is done by creating so called 'twist defects' in codes such as the
toric code The toric code is a topological quantum error correcting code, and an example of a stabilizer code, defined on a two-dimensional spin lattice. It is the simplest and most well studied of the quantum double models. It is also the simplest example o ...
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
projective representation In the field of representation theory in mathematics, a projective representation of a group ''G'' on a vector space ''V'' over a field ''F'' is a group homomorphism from ''G'' to the projective linear group \mathrm(V) = \mathrm(V) / F^*, where G ...
of the
braid group A braid (also referred to as a plait) is a complex structure or pattern formed by interlacing two or more strands of flexible material such as textile yarns, wire, or hair. The simplest and most common version is a flat, solid, three-strande ...
. Such a realization of Majoranas would allow them to be used to store and process
quantum information Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both th ...
within a
quantum computation Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
. Though the codes typically have no Hamiltonian to provide suppression of errors, fault-tolerance would be provided by the underlying quantum error correcting code.


References


Further reading

* {{Particles Fermions Quantum field theory