Global phase diagram in the quantum Hall effect

Abstract

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 T\ensuremath{\rightarrow}0, ${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{x}}$\ensuremath{\rightarrow}\ensuremath{\infty}, ${\mathrm{\ensuremath{\sigma}}}_{\mathit{x}\mathit{x}}$ and ${\mathrm{\ensuremath{\sigma}}}_{\mathit{x}\mathit{y}}$\ensuremath{\rightarrow}0, but ${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{y}}$ tends to a constant value, roughly B/nec. Each of these results has many testable experimental consequences.