Bulk and edge properties of the Chern-Simons Ginzburg-Landau theory for the fractional quantum Hall effect

TL;DR

This paper analyzes the bulk and edge properties of the Chern-Simons Ginzburg-Landau theory for the fractional quantum Hall effect, highlighting how plateau formation and edge modes emerge without impurities, and exploring spin effects and numerical results.

Contribution

It provides a detailed study of edge and bulk phenomena in the Chern-Simons Ginzburg-Landau model, including spin textures and multiple edge modes, with numerical validation.

Findings

Plateau formation occurs without impurity potential.

Edge mode velocity depends on the confining potential.

Multiple low-frequency edge modes are identified.

Abstract

The Chern-Simons Ginzburg-Landau theory for the fractional Quantum Hall effect is studied in the presence of a confining potential. We review the bulk properties of the model and discuss how the plateau formation emerges without any impurity potential. The effect is related to changes, by accumulation of charge, at the edge when the chemical potential is changed. Fluctuations about the ground state are examined and an expression is found for the velocity of the massless edge mode in terms of the confining potential. The effect of including spin is examined for the case when the system is fully polarized in the bulk. In general a spin texture may appear at the edge, and we examine this effect in the case of a small spin down component. The low frequency edge modes are examined and a third order equation is found for velocities which indicates the presence of three different modes. The discussions are illustrated by numerical studies of the ground states, both for the one- and two-component cases.