The fractional quantum hall effect

The Fractional Quantum Hall Effect (FQHE) represents a very surprising recent discovery in solid state physics. It is observed in high-mobility, two-dimensional electron systems at low temperatures (≈1 K) in intense perpendicular magnetic fields (≈200 kG) when all carriers are confined to the lowest Landau level. Under those exceptional conditions, and at fractional filling ν of this level, the Hall resistance is found to be quantized to ρxy = h/ie2, where i is a simple rational fraction. Concomitantly, the resistivity ρxx drops towards zero. So far this effect has been observed close to ν=1/3, 2/3, 4/3, 5/3, 2/5, 3/5, 4/5, and 2/7 with quantum numbers i=ν quantized, in some cases, to better than 1 part in 104. The FQHE represents the unambiguous, experimental observation of a fractional quantum number. It is presently being explained as resulting from the formation of a novel incompressible quantum liquid with fractionally charged quasi-particles, and a finite gap separating the ground state from its excitations.