Editing Fractional quantum Hall effect (section)

== 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 |page=026801 |doi=10.1103/PhysRevLett.119.026801|arxiv=1704.03026 }}</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]].