StairohmQuantum Hall Effect / Resistance PlateausSticker

Stairohm manages a staircase where every step is exact.

Push a current along a thin strip of conductor in a magnetic field and the charges are pushed sideways, building a voltage across the strip. That is the Hall effect. The ratio of the sideways voltage to the current, the Hall resistance, normally rises smoothly as the field grows.

In the spring of 1980, at the High Magnetic Field Laboratory in Grenoble, Klaus von Klitzing measured specially designed transistors called MOSFETs a few degrees above absolute zero in extremely strong fields, with the electrons forced to move in an extremely thin surface layer. The Hall resistance did not ramp. It climbed in flat steps, and on each landing it sat at h/e² divided by a whole number, the first line on this page, to better than one part in ten million. With Gerhard Dorda and Michael Pepper he published it that year as a new way to measure the fine-structure constant. He received the 1985 Nobel Prize.

The landings are where the trick lives. In a strong field the electrons’ allowed energies bunch into Landau levels. Some disorder in the sample traps states between those levels, so as the field rises the Hall resistance stays put while the trapped states fill. Too much disorder washes the steps out. In 1981 Robert Laughlin explained why the step values are exact. And only while you stand on a landing does the resistance along the strip, \(R_{xx}\), drop to zero.

The steps are so reliable that h/e² now anchors the ohm. Since 20 May 2019, with h and e fixed exactly in the SI, the von Klitzing constant is exact too: 25 812.807 45… Ω, the second line.

Exact steps. Dirt helps.