Solitons on the edge of a two-dimensional electron system

Abstract

We present a study of the excitations of the edge of a two-dimensional electron droplet in a magnetic field in terms of a contour dynamics formalism. We find that, beyond the usual linear approximation, the non-linear analysis yields soliton solutions which correspond to uniformly rotating shapes. These modes are found from a perturbative treatment of a non-linear eigenvalue problem, and as solutions to a modified Korteweg-de Vries equation resulting from a local induction approximation to the nonlocal contour dynamics. We discuss applications to the edge modes in the quantum Hall effect.

4 pages, 2 eps figures (included); to appear in Phys. Rev. Letters

References in corpus (5)

• Novel Edge Excitations of Two-dimensional Electron Liquid in a Magnetic Field
• Nonlinear Modes of Liquid Drops as Solitary Waves
• The Shapes of Flux Domains in the Intermediate State of Type-I Superconductors
• Dispersion Law of Edge Waves in the Quantum Hall Effect
• $W_{1+\infty }$ Dynamics of Edge Excitations in the Quantum Hall Effect

Cited by in corpus (5)

• Physics on the edge: contour dynamics, waves and solitons in the quantum Hall effect
• Soliton excitations as emitted clusters on nuclear surfaces
• Elastic null curve flows, nonlinear $C$-integrable systems, and geometric realization of Cole-Hopf transformations
• Fingering of Electron Droplets in Nonuniform Magnetic Fields
• Model for self-organized Leidenfrost rotating polygons as cnoidal waves