Quantization of the Hall Effect in a J-dimensional Quasiperiodic System

The observation of the quantum Hall effect in an electronic system does not depend on the strict two-dimensionality of the system, but rather that the conductivity in the direction of the magnetic field (ozz) vanishes. This condition can be acheived in a superlattice when the Landau level spacing exceeds the zero-field miniband width of the superlattice. It is now possible to test this criterion experimentally on a quasi eriodic system to examine if the con g. resence of localized and sin the quasicrystal affects this rtion. We have experimenta system with a modulationdoped GaAs/AlGaAs Fibonacci superlattice that exhibits a spectra corresponding to a Cantor set in X-ray diffraction. No evidence for the affect of these states on the magnetotransport is seen.