Electron Spin in Quantum Hall Effect in AlxGa1-xAs: D. C. Tsui's data

The Hall resistivity in the layers of AlxGa1-xAs/Al0.32Ga0.68As is found to show plateaus at certain fractions which depend on the effective charge. The Hall resistivity formula rho(xy)=h/e(2) has been modified to rho(xy)=h/[(1/2)ge(2)] so that the effective charge of the electron becomes, e*=(1/2)ge. The plateaus occur at the effective charge determined by g = (2j+1)/(2l+1). Some of the plateaus are explained to arise from the g values while some others require the use of Landau levels. The flux quantization is modified to include the effect of spin. When the samples are doped with aluminium, the clusters of Al atoms occur in the GaAs resulting into electron clusters in which the spin is NS with S=1/2 and N=101. The electron clusters form a temperature dependent plateau in the Hall resistivity.