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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 $\nu =1/3$.^[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 givesHere $R_K$ 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.

The von Klitzing constant is $R_K=h/e^2=25812.807459\dots \Omega$. The current SI fixes the Planck constant $h=6.62607015\times 10^{-34}\mathrm{J}\mathrm{s}$ and elementary charge $e=1.602176634\times 10^{-19}\mathrm{C}$ exactly, so $R_K$ is exact; the displayed decimal is truncated. It differs from the historical conventional value $R_{K\text{-}90}=25812.807\Omega$.^[ref]

As an original ideal example, $N=2$ and electric current $I=1\mu \mathrm{A}$ give $|V_H|=I{R}_K/2\simeq 12.9064\mathrm{mV}$. Changing the Hall bar's width changes the transverse electric field required for this electric potential difference, while the ideal ratio $|V_H|/I$ remains $R_K/2$.