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{{short description|Electromagnetic effect in physics}}
{{AI-generated|date=October 2025}}
The '''fractional quantum Hall effect''' (fractional QHE or '''FQHE''') is the observation of precisely quantized plateaus in the [[Quantum Hall effect|Hall conductance]] of [[Two-dimensional electron gas|2-dimensional (2D) electrons]] at [[Decimals|fractional values]] of <math>e^2/h</math>, where ''e'' is the [[electron charge]] and ''h'' is the [[Planck constant]]. 
At the same time, longitudinal resistance drops to zero (for low enough temperatures) as for the [[Quantum Hall Effect|integer QHE]].
It is a property of a collective state in which electrons bind magnetic flux lines to make new [[quasiparticle]]s, and [[excited state|excitations]] have a [[fractionalization|fractional]] [[elementary charge]] and possibly also fractional statistics. The 1998 [[Nobel Prize in Physics]] was awarded to [[Robert Laughlin]], [[Horst Störmer]], and [[Daniel Tsui]] "for their discovery of a new form of quantum fluid with fractionally charged excitations".<ref>{{Cite web|url=https://www.nobelprize.org/nobel_prizes/physics/laureates/1998/|title=The Nobel Prize in Physics 1998|website=www.nobelprize.org|access-date=2018-03-28}}</ref><ref name=ptoday1998>{{cite journal|last=Schwarzschild|first=Bertram|title=Physics Nobel Prize Goes to Tsui, Stormer and Laughlin for the Fractional Quantum Hall Effect|journal=Physics Today|year=1998|volume=51|issue=12|doi=10.1063/1.882480|url=http://www.physicstoday.org/resource/1/phtoad/v51/i12/p17_s1|archive-url=https://archive.today/20130415185712/http://www.physicstoday.org/resource/1/phtoad/v51/i12/p17_s1|archive-date=15 April 2013|access-date=20 April 2012|bibcode=1998PhT....51l..17S|pages=17–19}}</ref> 
The microscopic origin of the FQHE is a major research topic in [[condensed matter physics]].

== Descriptions==
{{unsolved|physics|2=What mechanism explains the existence of the ''&nu;''=5/2 state in the fractional quantum Hall effect?}}
The fractional quantum Hall effect (FQHE) is a collective behavior in a 2D system of electrons. In particular magnetic fields, the [[2DEG|electron gas]] condenses into a remarkable liquid state, which is very delicate, requiring high quality material with a low [[charge carrier|carrier]] concentration, and extremely low temperatures. As in the integer [[quantum Hall effect]], the Hall resistance undergoes certain [[quantum Hall transitions]] to form a series of plateaus. Each particular value of the magnetic field corresponds to a filling factor (the ratio of number of electrons to [[magnetic flux quanta]] corresponding to given area)

:<math>\nu = p/q,\ </math>

where ''p'' and ''q'' are integers with no common factors. Here ''q'' turns out to be an odd number with the exception of filling factor 5/2<ref>{{cite journal |last1=Rezayi |first1=Edward H. |title=Landau Level Mixing and the Ground State of the ν = 5 / 2 Quantum Hall Effect |journal=Physical Review Letters |date=14 July 2017 |volume=119 |issue=2 |article-number=026801 |doi=10.1103/PhysRevLett.119.026801|pmid=28753327 |arxiv=1704.03026 |bibcode=2017PhRvL.119b6801R }}</ref>
and few others (7/2 or 2+3/8). The principal series of such fractions are

:<math>{1\over 3}, {2\over 5}, {3\over 7}, \mbox{etc.,} </math>

and their particle-hole conjugates

:<math>{2\over3}, {3\over 5}, {4\over 7}, \mbox{etc.} </math>

Depending on the fraction, both spin-polarised and zero-spin fractional QHE states may exist.<ref>{{cite journal |last1=Výborný |first1=K. |title=Spin in fractional quantum Hall systems |journal=Annalen der Physik |date=16 February 2007 |volume=16 |issue=2 |page=30 |doi=10.1002/andp.200610228|arxiv=cond-mat/0603451 }}</ref>
Fractionally charged quasiparticles are neither [[boson]]s nor [[fermion]]s and exhibit [[anyon]]ic statistics. The fractional quantum Hall effect continues to be influential in theories about [[topological order]]. Certain fractional quantum Hall phases appear to have the right properties for building a [[topological quantum computer]].

== History and developments ==
The FQHE was experimentally discovered in 1982 by [[Daniel Chee Tsui|Daniel Tsui]] and [[Horst Ludwig Störmer|Horst Störmer]], in experiments performed on  [[heterostructure]]s made out of [[gallium arsenide]] developed by [[Arthur Gossard]].

There were several major steps in the theory of the FQHE.

*'''Laughlin states and fractionally-charged [[quasiparticle]]s''': this theory, proposed by [[Robert B. Laughlin]], is based on [[Laughlin wavefunction|accurate trial wave functions]] for the [[ground state]] at fraction <math>1/q</math> as well as its quasiparticle and quasihole excitations. The excitations have fractional charge of magnitude <math>e^*={e\over q}</math>.
*'''Fractional exchange statistics of quasiparticles''': [[Bertrand Halperin]] conjectured, and Daniel Arovas, [[John Robert Schrieffer]], and [[Frank Wilczek]] demonstrated, that the fractionally charged quasiparticle excitations of the Laughlin states are [[anyon]]s with fractional statistical angle <math>\theta = {\pi \over q}</math>; the wave function acquires phase factor of <math> e^{i \theta}</math> (together with an [[Aharonov-Bohm phase factor]]) when identical quasiparticles are exchanged in a counterclockwise sense. A recent experiment seems to give a clear demonstration of this effect.<ref>{{Cite arXiv |last1=An |first1=Sanghun |last2=Jiang |first2=P. |last3=Choi |first3=H. |last4=Kang |first4=W. |last5=Simon |first5=S. H. |last6=Pfeiffer |first6=L. N. |last7=West |first7=K. W. |last8=Baldwin |first8=K. W. |date=2011 |title=Braiding of Abelian and Non-Abelian Anyons in the Fractional Quantum Hall Effect |eprint=1112.3400 |class=cond-mat.mes-hall }}</ref>
*'''Hierarchy states''': this theory was proposed by [[Duncan Haldane]], and further clarified by [[Bertrand Halperin]], to explain the observed filling fractions not occurring at the Laughlin states' <math>\nu = 1/q</math>. Starting with the Laughlin states, new states at different fillings can be formed by condensing quasiparticles into their own Laughlin states. The new states and their fillings are constrained by the fractional statistics of the quasiparticles, producing e.g. <math>\nu = 2/5</math> and <math>2/7</math> states from the Laughlin <math>\nu = 1/3</math> state. Similarly constructing another set of new states by condensing quasiparticles of the first set of new states, and so on, produces a hierarchy of states covering all the odd-denominator filling fractions. This idea has been validated quantitatively,<ref>{{cite journal|first=M.|year=1994|title=Microscopic formulation of the hierarchy of quantized Hall states|journal=[[Phys. Lett. B|Physics Letters B]]|volume=336|issue=1|pages=48–53|arxiv=cond-mat/9311062|bibcode=1994PhLB..336...48G|doi=10.1016/0370-2693(94)00957-0|last=Greiter|s2cid=119433766}}</ref> and brings out the observed fractions in a natural order. Laughlin's original plasma model was extended to the hierarchy states by [[Allan H. MacDonald]] and others.<ref>{{cite journal|first1=A.H.|first2=G.C.|first3=M.W.C.|year=1985|title=Hierarchy of plasmas for fractional quantum Hall states|journal=[[Phys. Rev. B|Physical Review B]]|volume=31|issue=8|pages=5529–5532|bibcode=1985PhRvB..31.5529M|doi=10.1103/PhysRevB.31.5529|last1=MacDonald|last2=Aers|last3=Dharma-wardana|pmid=9936538}}</ref> Using methods introduced by [[Greg Moore (physicist)|Greg Moore]] and [[Nicholas Read]],<ref>{{cite journal |last1=Moore |first1=G. |last2=Read |first2=N. |title=Nonabelions in the fractional quantum Hall effect |journal=Nucl. Phys. |date=1990 |volume=B360 |issue=2 |page=362|bibcode=1991NuPhB.360..362M |doi=10.1016/0550-3213(91)90407-O |doi-access=free }}</ref> based on [[conformal field theory]] explicit wave functions can be constructed for all hierarchy states.<ref>{{cite journal |last1=Hansson |first1=T.H. |last2=Hermanns |first2=M. |last3=Simon |first3=S.H. |last4=Viefers|first4=S.F.|author4-link= Susanne Viefers |title=Quantum Hall physics: Hierarchies and conformal field theory techniques |journal=Rev. Mod. Phys. |date=2017 |volume=89 |issue=2 |article-number=025005 |doi=10.1103/RevModPhys.89.025005|arxiv=1601.01697 |bibcode=2017RvMP...89b5005H |s2cid=118614055 }}</ref>
*'''[[Composite fermions]]''': this theory was proposed by [[Jainendra K. Jain]], and further extended by Halperin, [[Patrick A. Lee]] and Read. The basic idea of this theory is that as a result of the repulsive interactions, two (or, in general, an even number of) vortices are captured by each electron, forming integer-charged quasiparticles called composite fermions. The fractional states of the electrons are understood as the integer [[quantum Hall effect|QHE]] of composite fermions. For example, this makes electrons at filling factors 1/3, 2/5, 3/7, etc. behave in the same way as at filling factor 1, 2, 3, etc. Composite fermions have been observed, and the theory has been verified by experiment and computer calculations. Composite fermions are valid even beyond the fractional quantum Hall effect; for example, the filling factor 1/2 corresponds to zero magnetic field for composite fermions, resulting in their Fermi sea.
Tsui, Störmer, and [[Robert B. Laughlin]] were awarded the 1998 [[Nobel Prize in Physics]] for their work.

Jain, [[James P. Eisenstein]], and [[Mordehai Heiblum]] won the 2025 [[Wolf Prize in Physics]] "for advancing our understanding of the surprising properties of two-dimensional electron systems in strong magnetic fields".<ref>{{Cite web |last=מיכל |date=2025-03-10 |title=James P. Eisenstein |url=https://wolffund.org.il/james-p-eisenstein/ |access-date=2025-03-17 |website=Wolf Foundation |language=en-US}}</ref>

== The Composite Fermion Hierarchies ==
{{Primary sources|section|date=July 2025}}
While the [[Laughlin wavefunction]] provides an exceptionally accurate description for states at filling factors ''ν = 1/3, 1/5, ...'', a vast number of other fractional states have been experimentally observed. The vast majority of these can be understood within a single, unified framework known as the [[composite fermion]] (CF) model, introduced by [[Jainendra K. Jain]] in 1989.<ref name="Jain1989">{{cite journal |last1=Jain |first1=J. K. |title=Composite-fermion approach for the fractional quantum Hall effect |journal=Physical Review Letters |year=1989 |volume=63 |issue=2 |pages=199–202 |doi=10.1103/PhysRevLett.63.199 |pmid=10040805 |bibcode=1989PhRvL..63..199J}}</ref> This model successfully reduces the complex problem of strongly interacting electrons in a magnetic field to a simpler problem of weakly interacting quasiparticles, called composite fermions.{{cn|date=July 2025}}

The central idea of the theory is a conceptual transformation: each electron captures an even number, ''2p'', of [[magnetic flux quanta]] and binds them to itself to form a new quasiparticle, the composite fermion. This transformation has a profound effect:{{cn|date=July 2025}}
*   The Aharonov–Bohm phase acquired by a CF when it encircles another is canceled out by the phase from the attached flux quanta. This effectively "screens" the external magnetic field from the perspective of the CFs.
*   The composite fermions then move in a much weaker ''effective magnetic field'', ''B*''.
*   The problem of strongly interacting electrons at a filling factor ''ν'' is mapped onto a problem of weakly interacting composite fermions at a new, effective filling factor ''ν*''.

The relationship between the electron filling factor ''ν'' and the composite fermion filling factor ''ν*'' is given by the master equation:{{cn|date=July 2025}}

<math> \nu = \frac{\nu^*}{2p\nu^* \pm 1} </math>

where ''p'' is a positive integer (typically 1), and the ''±'' sign corresponds to the orientation of the attached flux. This single equation explains the emergence of entire sequences of FQHE states.

=== The Principal Jain Sequences (ν < 1) ===

The most prominent FQHE states can be understood as the [[integer quantum Hall effect]] (IQHE) of composite fermions. In this scenario, the weakly interacting CFs completely fill ''n'' of their own emergent "composite fermion Landau levels," leading to an integer filling factor for them: ''ν* = n''. Substituting this into the master equation generates the '''Jain sequences''' of FQHE states:{{cn|date=July 2025}}

<math> \nu = \frac{n}{2pn \pm 1} </math>

* '''Laughlin States and the Main Sequence:''' For ''p=1'' (electrons bound to two flux quanta) and the ''+'' sign, we get the main sequence of fractions:
**   ''n=1'':  ''ν = 1 / (2*1 + 1) = 1/3'' (This recovers the primary Laughlin state)
**   ''n=2'':  ''ν = 2 / (2*2 + 1) = 2/5''
**   ''n=3'':  ''ν = 3 / (2*3 + 1) = 3/7''
    
...and so on, a sequence of states that has been extensively verified in experiments.<ref name="Jain2007">{{cite book |last1=Jain |first1=Jainendra K. |title=Composite Fermions |publisher=Cambridge University Press |year=2007 |isbn=978-0-521-86232-5}}</ref> The state ''ν=1/5'' corresponds to ''p=2'' and ''n=1''.

*   '''Particle-Hole Conjugate States:''' The second prominent sequence arises from the ''-'' sign, which is often conveniently described via [[particle-hole symmetry]]. A state at filling factor ''ν'' is closely related to a state at ''1-ν''. The particle-hole conjugates of the main sequence ''n/(2n+1)'' are:
**   For ''ν=1/3'', its conjugate is ''1 - 1/3 = 2/3''.
**   For ''ν=2/5'', its conjugate is ''1 - 2/5 = 3/5''.
**   For ''ν=1/5'' (from ''p=2''), its conjugate is ''1 - 1/5 = 4/5''.
These sequences ''ν = n/(2n-1)'' and their conjugates account for the vast majority of all observed odd-denominator FQHE states with ''ν < 1''.{{cn|date=July 2025}}

=== Higher-Order Hierarchies ===

The composite fermion model also predicts higher-order hierarchies. The composite fermions themselves are fermions and can, in principle, form their ''own'' fractional quantum Hall states. For instance, if the CFs at ''p=1'' form a ''ν* = 1/3'' Laughlin state, the resulting electron filling factor would be:<math> \nu = \frac{1/3}{2(1/3) + 1} = \frac{1/3}{5/3} = 1/5 </math>
This demonstrates how the Laughlin state at ''ν=1/5'' can be viewed as the FQHE of the quasiparticles of the ''ν=1/3'' state, a concept first proposed in the [[Haldane]]-Halperin hierarchy theory and elegantly incorporated into the CF framework.<ref name="Jain2007" />

=== The Moore–Read Pfaffian State (ν = 5/2) ===

While the [[Laughlin wavefunction]] and the [[Composite fermion|composite fermion model]] successfully describe the primary odd-denominator FQHE states, a particularly fascinating state was discovered at the even-denominator filling factor ''ν = 5/2''.<ref name="Willett1987">{{cite journal |last1=Willett |first1=R. |last2=Eisenstein |first2=J. P. |last3=Störmer |first3=H. L. |last4=Tsui |first4=D. C. |last5=Gossard |first5=A. C. |last6=English |first6=J. H. |title=Observation of an even-denominator quantum number in the fractional quantum Hall effect |journal=Physical Review Letters |year=1987 |volume=59 |issue=15 |pages=1776–1779 |doi=10.1103/PhysRevLett.59.1776 |pmid=10035326 |bibcode=1987PhRvL..59.1776W}}</ref> This state cannot be explained by the simple Laughlin theory. In 1991, [[Greg Moore (physicist)|Gregory Moore]] and [[Nicholas Read]] proposed a groundbreaking trial wavefunction, now known as the '''Moore–Read state''' or '''Pfaffian state''', which has become the leading theoretical description for this enigmatic phase.<ref name="MooreRead1991">{{cite journal |last1=Moore |first1=G. |last2=Read |first2=N. |title=Nonabelions in the fractional quantum Hall effect |journal=Nuclear Physics B |year=1991 |volume=360 |issue=2–3 |pages=362–396 |doi=10.1016/0550-3213(91)90407-O |bibcode=1991NuPhB.360..362M}}</ref>

The Moore–Read state represents a fundamentally new type of quantum fluid. Its key physical idea is that the [[composite fermion|composite fermions]] (at an effective filling factor of 1/2) do not form a simple Fermi sea, but instead form a ''p-wave paired state'', analogous to the [[Cooper pair|Cooper pairs]] in a [[p-wave superconductor]]. This pairing is the source of its unique and remarkable properties.

==== Wavefunction and Construction ====

The Moore–Read wavefunction is constructed for a system of ''N'' electrons (where ''N'' must be even) and, like the Laughlin state, is built in the lowest Landau level. It has two essential components:

<math> \Psi_{\text{MR}} = \text{Pf}\left(\frac{1}{z_i - z_j}\right) \prod_{i<j} (z_i - z_j)^m </math>

1.  A standard [[Laughlin wavefunction|Laughlin–Jastrow factor]], <math>\prod(z_i - z_j)^m</math>, where ''m'' is an even integer (typically ''m=2'' for the ''ν=5/2'' state). This factor ensures that the wavefunction is antisymmetric under electron exchange (when combined with the Pfaffian's properties) and keeps the electrons apart.

2.  A '''[[Pfaffian]] term''', <math>\text{Pf}(1/(z_i - z_j))</math>. The Pfaffian is a polynomial that can be thought of as the "square root" of the determinant of a ''N x N'' anti-symmetric matrix. This mathematical object naturally encodes the pairing of particles. The term <math>1/(z_i - z_j)</math> is the wavefunction for a pair of particles with relative angular momentum ''l=1'' (a p-wave pair).

The original construction by Moore and Read was highly innovative, using techniques from [[conformal field theory]] (CFT). They showed that this wavefunction could be formally represented as a correlation function of operators in the [[Ising model]] CFT. This CFT connection provides a deep theoretical structure and allows for the properties of the quasiparticle excitations to be calculated rigorously.

==== Physical Properties and Significance ====

The Moore–Read state is not just another FQHE state; its properties are profoundly different from the Laughlin states.

*   '''Pairing of Composite Fermions''': It is the first realistic model of a topological p-wave paired state of fermions in two dimensions. This links the FQHE to concepts from superconductivity and superfluidity (like [[Helium-3]]).
*   '''Non-Abelian Anyons''': This is its most significant feature. The quasiparticle excitations of the Moore–Read state are predicted to obey '''[[non-Abelian statistics]]'''. When two Laughlin quasiparticles are exchanged, the system's wavefunction acquires a simple phase factor (Abelian statistics). In contrast, when two Moore–Read quasiparticles are exchanged, the final state of the system depends on the ''order'' in which the exchanges are performed. Braiding these non-Abelian anyons performs a rotation within a degenerate space of quantum states. The elementary excitations are often called '''Ising anyons''' due to the CFT connection.
*   '''Candidate for Topological Quantum Computation''': The existence of non-Abelian anyons makes the ''ν=5/2'' state a leading physical candidate for realizing [[fault-tolerant quantum computer|fault-tolerant topological quantum computation]]. A quantum bit ([[qubit]]) can be encoded in the degenerate ground state of several well-separated anyons, and quantum gates can be performed by physically braiding them around each other. Because the information is stored non-locally, it is intrinsically robust against local noise and errors.<ref name="Nayak2008">{{cite journal |last1=Nayak |first1=C. |last2=Simon |first2=S. H. |last3=Stern |first3=A. |last4=Freedman |first4=M. |last5=Das Sarma |first5=S. |title=Non-Abelian anyons and topological quantum computation |journal=Reviews of Modern Physics |year=2008 |volume=80 |issue=3 |pages=1083–1159 |doi=10.1103/RevModPhys.80.1083 |arxiv=0707.1889 |bibcode=2008RvMP...80.1083N}}</ref>

While the Moore–Read state is the leading theoretical candidate for the ''ν = 5/2'' plateau, conclusively demonstrating its non-Abelian nature through experiment remains a major goal of condensed matter physics. Experiments measuring [[Thermal Hall conductance|thermal Hall transport]] have provided strong evidence in favor of the Pfaffian state, but a definitive braiding experiment has not yet been achieved.
<ref name="Banerjee2018">{{cite journal |last1=Banerjee |first1=M. |last2=Heiblum |first2=M. |last3=Umansky |first3=V. |last4=Feldman |first4=D. E. |last5=Oreg |first5=Y. |last6=Stern |first6=A. |title=Observation of half-integer thermal Hall conductance |journal=Nature |year=2018 |volume=559 |issue=7713 |pages=205–210 |doi=10.1038/s41586-018-0184-1 |pmid=29867160 |arxiv=1710.00492 |bibcode=2018Natur.559..205B}}</ref>

== Evidence for fractionally-charged quasiparticles ==

Experiments have reported results that specifically support the understanding that there are fractionally-charged quasiparticles in an electron gas under FQHE conditions.

In 1995, the fractional charge of Laughlin quasiparticles was measured directly in a quantum antidot electrometer at [[State University of New York at Stony Brook|Stony Brook University]], [[New York (state)|New York]].<ref>{{cite journal|first1=V.J.|first2=B.|year=1995|title=Resonant Tunneling in the Quantum Hall Regime: Measurement of Fractional Charge|journal=[[Science (journal)|Science]]|volume=267|issue=5200|pages=1010–2|bibcode=1995Sci...267.1010G|doi=10.1126/science.267.5200.1010|last1=Goldman|last2=Su|pmid=17811442|s2cid=45371551}}
*{{cite web |date=2003 |title=Direct Observation of Fractional Charge |website=Stony Brook University |url=http://quantum.physics.sunysb.edu/index.html|archive-url=https://web.archive.org/web/20031007040231/http://quantum.physics.sunysb.edu/index.html |archive-date=2003-10-07 }}</ref> In 1997, two groups of physicists at the [[Weizmann Institute of Science]] in [[Rehovot]], Israel, and at the [[Commissariat à l'énergie atomique]] laboratory near [[Paris]],<ref>
{{cite journal
 |author=L. Saminadayar |author2=D. C. Glattli |author3=Y. Jin |author4=B. Etienne
 |year=1997
 |title=Observation of the e/3 fractionally charged Laughlin quasiparticle
 |journal=[[Physical Review Letters]]
 |volume=79|issue=13
 |pages=2526–2529
 |doi=10.1103/PhysRevLett.79.2526
|arxiv=cond-mat/9706307
 |bibcode=1997PhRvL..79.2526S
 |s2cid=119425609
 }}</ref> detected such quasiparticles carrying an [[electric current]], through measuring quantum [[shot noise]]<ref>
{{cite web|date=24 October 1997|title=Fractional charge carriers discovered|url=https://physicsworld.com/a/fractional-charge-carriers-discovered/ |access-date=2010-02-08|work=[[Physics World]]}}</ref><ref>
{{cite journal
 |author1=R. de-Picciotto |author2=M. Reznikov |author3=M. Heiblum |author4=V. Umansky |author5=G. Bunin |author6=D. Mahalu |year=1997
 |title=Direct observation of a fractional charge
 |journal=[[Nature (journal)|Nature]]
 |volume=389 |page=162
 |doi=10.1038/38241
|bibcode = 1997Natur.389..162D
 |issue=6647|arxiv=cond-mat/9707289|s2cid=4310360 }}</ref>
Both of these experiments have been confirmed with certainty.{{citation needed|date=March 2024}}

A more recent experiment,<ref>
{{cite journal
|doi=10.1126/science.1099950
|author=J. Martin
|author2=S. Ilani
|author3=B. Verdene
|author4= J. Smet
|author5=V. Umansky
|author6=D. Mahalu
|author7=D. Schuh
|author8=G. Abstreiter
|author9=A. Yacoby 
|title =Localization of Fractionally Charged Quasi Particles 
|journal= [[Science (journal)|Science]] 
|volume=305 |pages=980–3
|year=2004 
|bibcode = 2004Sci...305..980M
 |pmid=15310895
|issue=5686|s2cid=2859577
}}</ref>  measures the quasiparticle charge. In 2020, interferometry experiments conducted by two different groups, at Paris<ref>{{Cite journal |last1=Bartolomei |first1=H. |last2=Kumar |first2=M. |last3=Bisognin |first3=R. |last4=Marguerite |first4=A. |last5=Berroir |first5=J.-M. |last6=Bocquillon |first6=E. |last7=Plaçais |first7=B. |last8=Cavanna |first8=A. |last9=Dong |first9=Q. |last10=Gennser |first10=U. |last11=Jin |first11=Y. |last12=Fève |first12=G. |date=2020-04-10 |title=Fractional statistics in anyon collisions |url=https://www.science.org/doi/10.1126/science.aaz5601 |journal=Science |volume=368 |issue=6487 |pages=173–177 |doi=10.1126/science.aaz5601|pmid=32273465 |arxiv=2006.13157 |bibcode=2020Sci...368..173B }}</ref> and Purdue,<ref>{{Cite journal |last1=Nakamura |first1=J. |last2=Liang |first2=S. |last3=Gardner |first3=G. C. |last4=Manfra |first4=M. J. |date=September 2020 |title=Direct observation of anyonic braiding statistics |url=https://www.nature.com/articles/s41567-020-1019-1 |journal=Nature Physics |language=en |volume=16 |issue=9 |pages=931–936 |doi=10.1038/s41567-020-1019-1 |issn=1745-2481|arxiv=2006.14115 |bibcode=2020NatPh..16..931N }}</ref> were both able to probe and confirm the braiding statistics of anyons.

== Impact ==
{{expand section|date=April 2019}}
The FQH effect shows the limits of [[Lev Landau|Landau]]'s [[symmetry breaking]] theory. Previously it was held that the symmetry breaking theory could explain all the important concepts and properties of forms of matter. According to this view, the only thing to be done was to apply the [[symmetry breaking]] theory to all different kinds of phases and [[phase transition]]s.<ref>{{cite journal |vauthors=Rychkov VS, Borlenghi S, Jaffres H, Fert A, Waintal X |title=Spin torque and waviness in magnetic multilayers: a bridge between Valet-Fert theory and quantum approaches |journal=Phys. Rev. Lett. |volume=103 |issue=6 |article-number=066602 |date=August 2009 |pmid=19792592|doi=10.1103/PhysRevLett.103.066602|bibcode=2009PhRvL.103f6602R|arxiv = 0902.4360 |s2cid=209013 }}</ref> From this perspective, the importance of the FQHE discovered by
Tsui, Stormer, and Gossard is notable for contesting old perspectives.

The existence of FQH liquids suggests that there is much more to discover beyond the present [[symmetry breaking]] paradigm in condensed matter physics.
Different FQH states all have the same symmetry
and cannot be described by symmetry breaking theory.
The associated [[fractional charge]], [[fractional statistics]], [[Non-abelian gauge theory|non-Abelian]] statistics,
[[chiral]] edge states, etc. demonstrate the power and the fascination of [[emergence]] in many-body systems.
Thus FQH states represent new states of matter that contain a
completely new kind of order—[[topological order]].
For example, properties once deemed isotropic for all materials may be anisotropic in 2D planes.
The new type of orders represented by FQH states greatly enrich our
understanding of quantum phases and [[quantum phase transitions]].

== See also ==
* [[Hall probe]]
* [[Laughlin wavefunction]]
* [[Macroscopic quantum phenomena]]
* [[Quantum anomalous Hall effect]]
* [[Quantum Hall Effect]]
* [[Quantum spin Hall effect]]
* [[Topological order]]
* [[Fractional Chern insulator]]

==Notes==
{{reflist}}

==References==
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 |volume=48 |page=1559
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|bibcode=1982PhRvL..48.1559T
 |issue=22
|doi-access=free}}
* {{cite journal
 |author=H.L. Stormer
 |year=1999
 |title=Nobel Lecture: The fractional quantum Hall effect
 |journal=[[Reviews of Modern Physics]]
 |volume=71 |pages=875–889
 |doi=10.1103/RevModPhys.71.875
|bibcode=1999RvMP...71..875S
 |issue=4
|doi-access=free
 }}
* {{cite journal
 |author=R.B. Laughlin
 |year=1983
 |title=Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
 |journal=[[Physical Review Letters]]
 |volume=50 |pages=1395–1398
 |doi=10.1103/PhysRevLett.50.1395
|bibcode=1983PhRvL..50.1395L
 |issue=18
}}

{{DEFAULTSORT:Fractional Quantum Hall Effect}}
[[Category:Hall effect]]
[[Category:Correlated electrons]]
[[Category:Quantum phases]]
[[Category:Mesoscopic physics]]
[[Category:Unsolved problems in physics]]
[[Category:Unexplained phenomena]]