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

TL;DR

This paper explores how magnetic field gradients and impurities induce fingering instabilities in quantum Hall droplets, revealing new insights into edge dynamics and electronic state behavior in nonuniform magnetic fields.

Contribution

It introduces the concept of fingering instability in quantum Hall droplets caused by magnetic impurities and field gradients, linking it to classical fluid instabilities.

Findings

Magnetic impurities cause fingering instability of the droplet edge.

Edge shape sensitivity to external magnetic field gradients.

Algebraic analysis of electronic states in nonuniform fields.

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.