= Fractional quantum Hall effect
{title2=$|\sigma_{xy}|=\nu e^2/h$}
{wiki}
The <fractional quantum Hall effect> is quantized transverse <sheet conductivity> at fractional <filling factors>, produced by interacting <Electrons>. The <Laughlin wavefunction> describes the sequence $\nu=1/m$, with odd $m$, including $\nu=1/3$.<Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations by Robert Laughlin>[pp. 1395–1396, ground-state construction]{ref}
For an original ideal readout example, take a <Hall bar> on the $\nu=1/3$ plateau with negligible longitudinal <sheet conductivity>. The <quantum Hall conductivity tensor inversion> gives
$$
R_H=\frac{|V_H|}{I}=\frac{h}{\nu e^2}=3R_K,
\qquad I=10\,\mathrm{nA}\quad\Longrightarrow\quad |V_H|\simeq0.774384\,\mathrm{mV}.
$$
Here $R_K$ is the <von Klitzing constant>; $R_H$ denotes transverse <electrical resistance>, rather than the bulk <Hall coefficient>. Thus a fractional <sheet conductivity> corresponds to a larger transverse <electrical resistance>. The fraction labels a collective <quantum state>: it does not mean that each <Electron> has acquired one third of its usual <electric charge>.
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