The defining characteristic of the fractional quantum Hall effect is outwardly simple: At low enough temperatures and high enough magnetic fields, and in clean enough samples, the Hall conductance as a function of magnetic field features plateaus at exact rational fractions of e2/h.

When Daniel Tsui, Horst Stormer, and Arthur Gossard first discovered the effect in 1981, all the fractions they found had odd denominators: 13, 25, 37, … 23, 35, 47, …, and so on. Within a year Robert Laughlin had devised his famous wavefunction that encapsulates the many-body interactions responsible for the effect.

Then in 1986 Stormer’s graduate student Robert Willett discovered an even-denominator plateau at 52. The need to go beyond Laughlin’s wavefunction was immediately clear. Because electrons obey Fermi–Dirac statistics, any...

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