# Experimental Aspects of the Fractional Quantum Hall Effect

## Abstract

The fractional quantum Hall effect, FQHE, is one of the most exciting phenomena to be discovered recently in solid state physics. The FQHE is observed in high-mobility (µ > 10^{5}cm^{2}/Vs) two-dimensional systems at low temperatures (T < 2 K) and high magnetic fields (B > 5 T). The FQHE is phenomenologically similar to the integral quantum Hall effect, IQHE: Plateaus are observed in the Hall resistivity, p_{xy}, concomitant with minima in the diagonal resistivity, p_{xx} (see Figure 1.1). While the IQHE exists at magnetic fields corresponding to integral Landau-level filling, v, the FQHE is observed at fractional Landau-level filling v = p/q where q is always odd (v = nh/eB, n = area density, and eB/h = Landau-level degeneracy). In the T → 0 limit, for both the IQHE and the FQHE, the plateaus in p_{xy} are accurately quantized to h/ve^{2} and the minima in p_{xx} reveal the presence of zero resistance states in the two-dimensional system. This low temperature behavior indicates the existence of energy gaps above the ground state of the system. While the IQHE can be phenomenologically understood through consideration of the single particle density of states, the FQHE requires a many-body approach to account for the phenomena.

### Keywords

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### References

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