Aharonov-Bohm Effect in the Quantum Hall Regime and fingering instability

Abstract

The shape of an electronic droplet in the quantum Hall effect is sensitive to gradients of the magnetic field, even if they are placed outside the droplet. Magnetic impurities cause a fingering instability of the edge of the droplet, similar to the Saffman-Taylor fingering instability of an interface between two immiscible phases. We discuss the fingering instability and some algebraic aspects of the electronic states in a strong nonuniform field.