Editing Quantum Hall effect (section)

== Applications ==
=== Electrical resistance standards ===
The quantization of the Hall conductance (<math> G_{xy}= 1/R_{xy}  </math>) has the important property of being exceedingly precise.<ref>{{Cite journal |last=von Klitzing |first=Klaus |date=2005-09-15 |title=Developments in the quantum Hall effect |url=https://royalsocietypublishing.org/doi/10.1098/rsta.2005.1640 |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |language=en |volume=363 |issue=1834 |pages=2203–2219 |doi=10.1098/rsta.2005.1640 |pmid=16147506 |bibcode=2005RSPTA.363.2203V |issn=1364-503X|url-access=subscription }}</ref> Actual measurements of the Hall conductance have been found to be integer or fractional multiples of {{math|{{sfrac|''e''<sup>2</sup>|''h''}}}} to better than one part in a billion.<ref>{{Cite journal |last1=Janssen |first1=T J B M |last2=Williams |first2=J M |last3=Fletcher |first3=N E |last4=Goebel |first4=R |last5=Tzalenchuk |first5=A |last6=Yakimova |first6=R |last7=Lara-Avila |first7=S |last8=Kubatkin |first8=S |last9=Fal'ko |first9=V I |date=2012-06-01 |title=Precision comparison of the quantum Hall effect in graphene and gallium arsenide |url=https://iopscience.iop.org/article/10.1088/0026-1394/49/3/294 |journal=Metrologia |volume=49 |issue=3 |pages=294–306 |doi=10.1088/0026-1394/49/3/294 |issn=0026-1394|arxiv=1202.2985 |bibcode=2012Metro..49..294J }}</ref> It has allowed for the definition of a new practical [[physical unit|standard]] for [[electrical resistance]], based on the resistance quantum given by the '''von Klitzing constant''' {{math|''R''<sub>K</sub>}}. This is named after [[Klaus von Klitzing]], the discoverer of exact quantization. The quantum Hall effect also provides an extremely precise independent determination of the [[fine-structure constant]], a quantity of fundamental importance in [[quantum electrodynamics]].

{{anchor|RK-1990}}In 1990, a fixed [[conventional electrical unit|conventional value]] {{math|''R''<sub>K-90</sub> {{=}} {{physconst|RK90|ref=no}}}} was defined for use in resistance calibrations worldwide.{{physconst|RK90|ref=only}} Later, the [[2019 revision of the SI]] fixed exact values of {{math|''h''}} and {{math|''e''}}, resulting in an exact {{math|''R''<sub>K</sub> {{=}} {{sfrac|''h''|''e''<sup>2</sup>}} {{=}} {{physconst|RK|after=.}}}}