The quantum Hall effect, the quantum cousin of the classical Hall effect, is observed in ultra-clean, two-dimensional electron gasses, at low temperatures (about 1 K or less) and high magnetic fields (on the order of Teslas). Under these conditions, the electrons form so-called quantum liquids with peculiar properties. The longitudinal resistance vanishes, while the off-diagonal (Hall) conductance is (extremely well) quantized, and takes the values
σH = ν e2/h, where e2/h is the fundamental unit of conductance, and ν the filling fraction, which is an integer, or a simple fraction, such as 1/3, 1/5, 2/5, etc.
The (fractional) quantum Hall effect has become a large field of research. Here are some of the topics studied by Nordita members.
- On of the most striking aspects of the fractional quantum Hall effect (i.e., when ν is a fraction), is the existence of excitations which carry fractional charge and fractional statistics. The fractional charge has been observed in experiments, by means of shot-noise experiments, in which excitations can tunnel from one edge to the sample to the other. The theory of tunneling in the quantum Hall effect, as well as the process of charge fractionalization, is under active study at Nordita.
- In some special cases, an even more exotic form of statistics than fractional statistics, namely non-abelian statistics, might be realized in the quantum Hall effect, at filling fraction ν=5/2=2+1/2, i.e, one completely filled Landau level with spin up and down electrons, in addition to a half filled Landau level. Usually, the denominator of the filling fraction is odd, reflecting the Fermi statistics of the electrons. At ν=5/2, the electron liquids gets around this rule, by forming a so-called non-abelian quantum Hall liquid. Or, at least, this is the most likely explanation. The quantum states of particles satisfying non-abelian statistics is not fully specified by the usual quantum numbers, and position. In addition, there is an additional `internal' degree of freedom. Finding experimentally verifiable consequences of this is extremely important in uncovering the nature of the quantum Hall effect at ν=5/2. Read more about this...