Localization problem of a two-dimensional lattice in a random magnetic field

Electron dynamics in inhomogeneous magnetic fields

This review explores the dynamics of two-dimensional electrons in magnetic potentials that vary on scales smaller than the mean free path. The physics of microscopically inhomogeneous magnetic fields relates to important fundamental problems in the fractional quantum Hall effect, superconductivity, spintronics and graphene physics and spins out promising applications which will be described here. After introducing the initial work done on electron localization in random magnetic fields, the experimental methods for fabricating magnetic potentials are presented. Drift-diffusion phenomena are then described, which include commensurability oscillations, magnetic channelling, resistance resonance effects and magnetic dots. We then review quantum phenomena in magnetic potentials including magnetic quantum wires, magnetic minibands in superlattices, rectification by snake states, quantum tunnelling and Klein tunnelling. The third part is devoted to spintronics in inhomogeneous magnetic fields. This covers spin filtering by magnetic field gradients and circular magnetic fields, electrically induced spin resonance, spin resonance fluorescence and coherent spin manipulation.

Antilocalization in a 2D electron gas in a random magnetic field

We construct a supersymmetric field theory for the problem of a two-dimensional electron gas in a random, static magnetic field. We find a new term in the free energy in addition to those present in the conventional unitary sigma model, whose presence relies on the long-range nature of the disorder correlations. Under a perturbative renormalization group analysis of the free energy, the new term contributes to the scaling function at one-loop order and leads to antilocalization.