Global phase diagram in the quantum Hall effect

We report recent progress in determining the global behavior of the two-dimensional electron gas in a high magnetic field. Specifically, we have: (i) derived a law of corresponding states which allows us to construct a global phase diagram and calculate many interrelations between transport coefficients; (ii) derived a selection rule governing the allowed continuous transitions between pairs of quantum Hall liquid states; and (iii) identified the insulating state, which we have named the Hall insulator, as a state in which, as the temperature T0, xx, xx and xy0, but xy tends to a constant value, roughly B/nec. Each of these results has many testable experimental consequences. © 1992 The American Physical Society.