Majorana Zero Modes
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In
particle physics Particle physics or high-energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the s ...
a Majorana fermion (, uploaded 19 April 2013, retrieved 5 October 2014; and also based on the pronunciation of physicist's name.) or Majorana particle is a
fermion In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin (spin 1/2, spin , Spin (physics)#Higher spins, spin , etc.) and obey the Pauli exclusion principle. These particles i ...
that is its own
antiparticle In particle physics, every type of particle of "ordinary" matter (as opposed to antimatter) is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the ...
. They were hypothesised by
Ettore Majorana Ettore Majorana ( ,, uploaded 19 April 2013, retrieved 14 December 2019 ; 5 August 1906 – disappeared 25 March 1938) was an Italian theoretical physicist who worked on neutrino masses. Majorana was a supporter of Italian Fascism and a member of ...
in 1937. The term is sometimes used in opposition to
Dirac fermion In physics, a Dirac fermion is a spin-½ particle (a fermion) which is different from its antiparticle. A vast majority of fermions fall under this category. Description In particle physics, all fermions in the standard model have distinct antipar ...
, which describes fermions that are not their own antiparticles. With the exception of
neutrino A neutrino ( ; denoted by the Greek letter ) is an elementary particle that interacts via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is so small ('' -ino'') that i ...
s, all of the
Standard Model The Standard Model of particle physics is the Scientific theory, theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions – excluding gravity) in the unive ...
elementary fermions are known to behave as Dirac fermions at low energy (lower than the electroweak symmetry breaking temperature), and none are Majorana fermions. The nature of neutrinos is not settled – they may 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 State of matter, phases, that arise from electromagnetic forces between atoms and elec ...
,
quasiparticle In condensed matter physics, a quasiparticle is a concept used to describe a collective behavior of a group of particles that can be treated as if they were a single particle. Formally, quasiparticles and collective excitations are closely relate ...
excitations can appear like bound Majorana states. 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. The Standard Model presently recognizes seventeen distinct particles—twelve fermions and five bosons. As a con ...
, 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: * Spin (physics) or particle spin, a fundamental property of elementary particles * Spin quantum number, a number which defines the value of a particle's spin * Spinning (textiles), the creation of yarn or thr ...
- 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 ...
wave equation The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light ...
(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 thi ...
), 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 numbers, then the complex conjugate of a + bi is 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 Operator (mathematics), mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. An annihilatio ...
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 ...
: 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 Supersymmetry is a Theory, theoretical framework in physics that suggests the existence of a symmetry between Particle physics, particles with integer Spin (physics), spin (''bosons'') and particles with half-integer spin (''fermions''). It propo ...
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 Operator may refer to: Mathematics * A symbol indicating a mathematical operation * Logical operator or logical connective in mathematical logic * Operator (mathematics), mapping that acts on elements of a space to produce elements of another sp ...
\gamma is : f = \tfrac (\gamma_1 + i\gamma_2), : f^\dagger = \tfrac (\gamma_1 - i\gamma_2), which can be rearranged to obtain the Majorana fermion operators as : \gamma_1 = f^\dagger + f, : \gamma_2 = i (f^\dagger - f). It is easy to see that \gamma_i=\gamma_i^\dagger is indeed fulfilled. This convention has the advantage that the Majorana operator squares to the identity, i.e. \gamma_i^2=(\gamma_i^\dagger)^2=1. Using this convention, a collection of 2n Majorana fermions (n ordinary fermions), \gamma_i (i=1,2,..,2n) obey the following anticommutation 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 with the additional structure of a distinguished subspace. As -algebras, they generalize the real number ...
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 interact only via gravity and not via any of the other fundamental interactions of the Standard Model. The term ''sterile neutrino'' is used to ...
s, if they exist. All the other elementary fermions of the
Standard Model The Standard Model of particle physics is the Scientific theory, theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions – excluding gravity) in the unive ...
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 electrically charged part of the weak interaction: Particles with half-integer weak isospin can interact with the bosons; particles with zero weak isospin do not. Weak isospin ...
, T_3 = \pm \tfrac , a charge-like quantum number. However, if they exist, the so-called "sterile neutrinos" (left-handed antineutrinos and right-handed neutrinos) would be
truly neutral particle In particle physics, a truly neutral particle is a subatomic particle that has no charge quantum number; they are their own antiparticle. In other words, it remains itself under the charge conjugation, which replaces particles with their correspon ...
s (assuming no other, unknown gauge charges exist). The sterile neutrinos introduced to explain
neutrino oscillation Neutrino oscillation is a quantum mechanics, quantum mechanical phenomenon in which a neutrino created with a specific lepton lepton number, family number ("lepton flavor": electron, muon, or tau lepton, tau) can later be Quantum measurement, mea ...
and anomalously small Standard Model
neutrino mass A neutrino ( ; denoted by the Greek letter ) is an elementary particle that interacts via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is so small ('' -ino'') that it ...
es could have Majorana masses. If they do, then at low energy (after electroweak symmetry breaking), 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 ...
) 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. A vast majority of fermions fall under this category. Description In particle physics, all fermions in the standard model have distinct antipar ...
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 particle physics, ''B'' − ''L'' (pronounced "bee minus ell") is a quantum number which is the difference between the baryon number () and the lepton number () of a quantum system. Details This quantum number is the charge of ...
.
Neutrinoless double beta decay Neutrinoless double beta decay (0νββ) is a commonly proposed and experimentally pursued theoretical radioactive decay process that would prove a Majorana particle, Majorana nature of the neutrino particle. To this day, it has not been found. ...
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 an atomic nucleus emits a beta particle (fast energetic electron or positron), transforming into an isobar of that nuclide. For example, beta decay of a neutron ...
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 collider A hadron collider is a very large particle accelerator built to test the predictions of various theories in particle physics, high-energy physics or nuclear physics by colliding hadrons. A hadron collider uses tunnels to accelerate, store, and coll ...
s; it is being searched for by both the
ATLAS An atlas is a collection of maps; it is typically a bundle of world map, maps of Earth or of a continent or region of Earth. Advances in astronomy have also resulted in atlases of the celestial sphere or of other planets. Atlases have traditio ...
and
CMS CMS may refer to: Computing * Call management system * CMS-2, a programming language implemented for and used by the United States Navy * Code Morphing Software, a technology used by Transmeta * Collection management system for a museum coll ...
experiments at the
Large Hadron Collider The Large Hadron Collider (LHC) is the world's largest and highest-energy particle accelerator. It was built by the CERN, European Organization for Nuclear Research (CERN) between 1998 and 2008, in collaboration with over 10,000 scientists, ...
. 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, 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 condensed matter physics, a quasiparticle is a concept used to describe a collective behavior of a group of particles that can be treated as if they were a single particle. Formally, quasiparticles and collective excitations are closely relate ...
can emerge as a Majorana fermion (non-fundamental), more commonly referred to as a Bogoliubov quasiparticle 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 State of matter, phases, that arise from electromagnetic forces between atoms and elec ...
. 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 denoting the lack of an electron at a position where one could exist in an atom or crystal structure, atomic lattice. Since in ...
"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 subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin (spin , spin , etc.) and obey the Pauli exclusion principle. These particles include all quarks and leptons and all c ...
. 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 type of quantum computer. It utilizes anyons, a type of quasiparticle that occurs in two-dimensional systems. The anyons' world lines intertwine to form braids in a three-dimensional spacetime (one temporal ...
. 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 ...
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 (fractional QHE or FQHE) is the observation of precisely quantized plateaus in the Hall conductance of 2-dimensional (2D) electrons at fractional values of e^2/h, where ''e'' is the electron charge and ''h'' i ...
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 The Delft University of Technology (TU Delft; ) is the oldest and largest Dutch public university, public Institute of technology, technical university, located in Delft, Netherlands. It specializes in engineering, technology, computing, design, a ...
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 sy ...
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 university#United States, public Land-grant university, land-grant research university in West Lafayette, Indiana, United States, and the flagship campus of the Purdue University system. The university was founded ...
and
University of Notre Dame The University of Notre Dame du Lac (known simply as Notre Dame; ; ND) is a Private university, private Catholic research university in Notre Dame, Indiana, United States. Founded in 1842 by members of the Congregation of Holy Cross, a Cathol ...
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. The effect is named after the British physicist Brian Josephson, who predicted in 1962 ...
(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 sy ...
nanowires connected to two superconducting contacts and subjected to a moderate magnetic field, another signature of Majorana bound states. A 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 a Majorana bound state. The subtle relation between those trivial bound states and Majorana bound states was reported by researchers at the 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 The year 2014 was marked by the surge of the Western African Ebola epidemic, West African Ebola epidemic, which began in 2013, becoming the List of Ebola outbreaks, most widespread outbreak of the Ebola, Ebola virus in human history, resul ...
, evidence of Majorana bound states was also observed using a low-temperature
scanning tunneling microscope A scanning tunneling microscope (STM) is a type of scanning probe 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 ...
, by scientists at
Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...
. 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 Lead () is a chemical element; it has Chemical symbol, symbol Pb (from Latin ) and atomic number 82. It is a Heavy metal (elements), heavy metal that is density, denser than most common materials. Lead is Mohs scale, soft and Ductility, malleabl ...
) 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 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 the U.S.
Oak Ridge National Laboratory Oak Ridge National Laboratory (ORNL) is a federally funded research and development centers, federally funded research and development center in Oak Ridge, Tennessee, United States. Founded in 1943, the laboratory is sponsored by the United Sta ...
, 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/superconductor hybrid device. In this system, Majorana fermions edge mode 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 so far observed only in two-dimensional physical system, systems. In three-dimensional systems, only two kinds of elementary particles are seen: fermions and bosons. Anyons have statistical proper ...
s) in an
iron-based superconductor Iron-based superconductors (FeSC) are iron-containing chemical compounds whose superconducting properties were discovered in 2006. The first of such superconducting compounds belong to the group of oxypnictides, which was known since 1995. Until 2 ...
, 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; ) is the national academy for natural sciences and the highest consultancy for science and technology of the People's Republic of China. It is the world's largest research organization, with 106 research i ...
and
University of Chinese Academy of Sciences The University of the Chinese Academy of Sciences (UCAS; ) is a public university headquartered in Shijingshan, Beijing, Shijingshan, Beijing, China. It is affiliated with the Chinese Academy of Sciences. The university is part of the Double ...
, 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 i ...
on the superconducting Dirac surface state of the iron-based superconductor. It was the first time that indications of Majorana particles were observed in the bulk of a 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 Europium is a chemical element; it has symbol Eu and atomic number 63. It is a silvery-white metal of the lanthanide series that reacts readily with air to form a dark oxide coating. Europium is the most chemically reactive, least dense, and soft ...
sulfide and gold films grown on
vanadium Vanadium is a chemical element; it has Symbol (chemistry), symbol V and atomic number 23. It is a hard, silvery-grey, malleable transition metal. The elemental metal is rarely found in nature, but once isolated artificially, the formation of an ...
.


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 ...
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 In mathematics, the braid group on strands (denoted B_n), also known as the Artin braid group, is the group whose elements are equivalence classes of Braid theory, -braids (e.g. under ambient isotopy), and whose group operation is composition of ...
. 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 t ...
within a
quantum computation A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of both particles and waves, and quantum computing takes advantage of this behavior using specialized hardware. C ...
. Though the codes typically have no Hamiltonian to provide suppression of errors, fault-tolerance would be provided by the underlying quantum error correcting code.


Majorana bound states in Kitaev chains

In February 2023 a study reported the realization of a "poor man's" Majorana that is a Majorana bound state that is not topologically protected and therefore only stable for a very small range of parameters. It was obtained in a Kitaev chain consisting of two
quantum dot Quantum dots (QDs) or semiconductor nanocrystals are semiconductor particles a few nanometres in size with optical and electronic properties that differ from those of larger particles via quantum mechanical effects. They are a central topic i ...
s 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 Alexei Yurievich Kitaev (; born August 26, 1963) is a Russian-American theoretical physicist. He is currently a professor of theoretical physics and mathematics at the California Institute of Technology. Kitaev has received multiple awards for ...
.


Topological qubits

On 19 February 2025 Microsoft announced the “
Majorana 1 Majorana 1 is a hardware device developed by Microsoft, with potential applications to quantum computing. It is the first device produced by Microsoft intended for use in quantum computing. It is an indium arsenide-aluminium hybrid device that adm ...
” processor, for use in quantum computers, claiming to feature Majorana zero modes. The work created a new class of materials called topoconductors, which use topological superconductivity to control hardware-protected topological qubits. The research paper utilized a method to determine fermion parity in Majorana zero modes in a single shot – validating a necessary ingredient for utility-scale topological quantum computation architectures based on measurement.


References


Further reading

* {{Particles Fermions Quantum field theory