FIGURE 1. The Hall effect.

The Hall voltage develops when driving a current through a conductor exposed to a perpendicular magnetic field. In classical physics, it follows a straight line. But quantum mechanics forces the electrons to occupy discrete energy levels. Whenever an integral number of these levels is filled, a plateau appears in the Hall voltage. At higher fields, when the lowest level is only partially filled, additional plateaux arise by virtue of interactions among the electrons — the fractional quantum Hall effect. This is equivalent to the integer Hall effect for 'quasi-particles' made up of an electron plus two flux quanta. But it can be taken further: add two more flux quanta to the composite quasi-particle, and you might expect new plateaux at, for instance, the fractions shown in the enlargement (schematic only; the plateaux are yet to be confirmed). Pan et al.³ have seen signs of some of these new fractional states (in boxes). With increasing sample quality the number of plateaux seems to grow, such that the Hall curve starts to show fractal characteristics.