Global Phase Diagram for the Quantum Hall Effect: An Experimental Picture

We study the behavior of the extended states of a two-dimensional electron system in silicon in a magnetic field, $B$. Our results show that the extended states, corresponding to the centers of different Landau levels, merge with the lowest extended state as $B\to 0$. Using our data, we construct an experimental-based “disorder vs filling factor” phase diagram for the integer quantum Hall effect (QHE). Generalizing this diagram to the case of the fractional QHE, we show that it is consistent with the recently observed direct transitions between insulator and fractional QHE at $\nu =2\mathrm{}/5$, 2/7, and 2/9.