John Chalker

Abstract:

We study localization in layered, three-dimensional conductors in strong magnetic fields. We demonstrate the existence of three phases - insulator, metal and quantized Hall conductor - in the two-dimensional parameter space obtained by varying the Fermi energy and the interlayer coupling strength. Transport in the quantized Hall conductor occurs via extended surface states. These surface states constitute a subsystem at a novel critical point, which we describe using a new, directed network model.

Abstract:

We present an interpretation of recent cyclotron resonance experiments on the two-dimensional electron gas in GaAs/AlGaAs heterostructures. We show that the observed dependence of the resonance spectrum on Landau level occupancy and temperature arises from the interplay of three factors: spin-splitting of the cyclotron frequency; thermal population of the two spin states; and coupling of the resonances for each spin orientation by Coulomb interactions. In addition, we derive an $f$-sum rule which allows spin polarisation to be determined directly from resonance spectra.

Abstract:

A single model is presented which represents both of the two apparently unrelated localisation problems of the title. The phase diagram of this model is examined using scaling ideas and numerical simulations. It is argued that the localisation length in a spin-degenerate Landau level diverges at two distinct energies, with the same critical behaviour as in a spin-split Landau level, and that all states of a charged particle moving in two dimensions, in a random magnetic field with zero average, are localised.