"...Exactly 100 years later, Klaus Von Klitzing discovered a much more surprising feature of the Hall effect while examining a new kind of transistor made of crystalline silicon coated with a metal film. He was actually using the Hall effect to characterize the transistor in a high magnetic field at very low temperature. As he increased the magnetic field, instead of seeing the gradual build up of the Hall effect, he saw it jump up in little steps, reaching one plateau and then suddenly popping up to a higher one. This was a very remarkable observation of quantum effects in "big" things. The millimeter piece of semiconductor, though small, was still a million times larger than the usual environment of quantum physics. Von Klitzing's discovery won him the 1985 Nobel prize. The quantum Hall effect is now used to generate the standard of electrical resistance which is needed to calibrate sensitive electronic test equipment.

When Von Klitzing published his work, theoretical physicists scrambled to explain it with new mathematical models. Within two years, just as they were putting the finishing touches to their theories, the experimentalists came up with yet another incredible discovery. By further lowering the temperature and increasing the magnetic field, they began to measure fractional quanta. Instead of increasing in nice whole numbers like one, two and three, the quantum hall effect was now jumping up by thirds, fifths, and sevenths. The theorists went back to their blackboards to explain the fractional effects. They came up with a many-body wave function that describes the collective correlated energy states of many electrons.

Then, in 1976 the American physicist Douglas Hofstadter published a paper predicting that under even higher magnetic fields, the electrons in a crystal would become fractal. That is, the electronic energy levels would start to take on a self-similar "butterfly" pattern so that if you zoomed in at a particular energy level, you would see the same fractional breakdown as on the larger scale. Unfortunately, no magnet is powerful enough to check the theory experimentally. But George Kirczenow has found a way to verify it with a relatively small magnet; by constructing an array of ultra-clean quantum dots and observing its Hall effect.