Past exam of the condensed matter physics major option course of the University of Oxford / 2018 / 6 / b

The Hall-plateau voltmeter calibration is obtained as follows. Let $D_p$ be a plateau height in displayed units after any voltage offset is removed, with identified integer plateau index $p$. The true Hall voltage is $I_x{R}_K/p$, so the calibration factor would beThe nominal current is $15\mathrm{nA}$. If several plateau heights are available, their inverse-integer ratios help identify indices and a fit of $D_p$ against $1/p$ can separate a constant offset from the gain. Reversing magnetic field and antisymmetrizing the voltage also removes an even offset. A unique absolute index should not be asserted solely from an unspecified sequence of steps.

For an established exact integer $p$ and independent current and height errors,The current alone contributes $2\%$ relative uncertainty; it is a common calibration uncertainty and does not average away by fitting more plateaux. Voltage-offset uncertainty and deviations from quantization must also be included where relevant. The $25\pm 2\mu \mathrm{m}$ width cancels because the Hall voltage divided by current is a sheet Hall resistance; it would enter the transverse electric field, not this calibration.

TODO — missing source data: the held PDF's last-page stream refers to an absent /Im6 graphic, and its recovery log reports an unknown XObject. The supplied TeX records the same source gap. No plateau heights, labels or axis values survive, so neither a numerical $D_p$ nor a unique $p$ can be read. The numerical voltmeter calibration and its complete graph-reading error cannot be supplied without that graph; the formula and known $2\%$ current contribution above are determined.