 Resistance-versus-temperature experiment for superconductivity

The motivating observation is an abrupt disappearance of detectable electrical resistance on cooling, rather than a smooth improvement in conduction. The diagram pairs the measuring arrangement with an idealized transition. Its curves are deliberately synthetic; neither their scales nor their abrupt step are a reconstruction of measured mercury data.

In a report communicated in November 1911, Heike Kamerlingh Onnes described a mercury thread in seven connected glass U-tubes immersed in a stirred liquid-helium bath. Expansion spaces kept freezing mercury from breaking the glass or interrupting the thread. Separate leads supplied electric current and sensed electric potential difference. He compensated a troublesome thermoelectric effect and reversed the main electric current to extract the resistive signal. He reported a rapid fall between $4.21$ and $4.19\mathrm{K}$ on his stated historical temperature scale, with electrical resistance disappearing at the lower value. The apparatus and control of spurious electric potential differences are part of the discovery, not incidental details. ^[ref]

A modern version places a contacted sample and a calibrated thermometer close together in a cooling environment. Use four-terminal sensing, record the small applied electric current $I$, the sensed electric potential difference $V$, and the sample temperature $T$, then plot $R(T)=V/I$. Repeat on warming as well as cooling, and allow readings to stabilize near thermal equilibrium. Disagreement between warming and cooling is a reason to check sample–thermometer lag and reproducibility before quoting a superconducting transition temperature. Mikhailov and Kordosky's undergraduate experiment uses this strategy with liquid-nitrogen cooling. ^[ref]

Choose the measuring electric current small enough that Joule heating does not appreciably change the sample temperature, and repeat with a smaller electric current to check that the transition persists. Cancel stable offsets using the reversal described in four-terminal sensing. A reading indistinguishable from zero supplies an experimental upper bound, not a proof of exact zero electrical resistance. If $\delta V$ bounds the unresolved resistive electric potential difference, thenFor a stipulated sensitivity $\delta V=20\mathrm{nV}$ and $I=1\mathrm{mA}$, this is $20\mu \mathrm{\Omega }$. The bound applies between the sensing contacts; it is not the electrical resistance of the complete wiring. A conducting path through part of an inhomogeneous sample can also make $V$ negligible, so the Field-cooled Meissner experiment adds independent evidence about the material's magnetic response.