Edge Modes in the Hierarchical Fractional Quantum Hall Liquids with Coulomb Interaction

TL;DR

This paper investigates edge modes in hierarchical fractional quantum Hall liquids using a unified approach, revealing a dominant edge magneto-plasmon and neutral modes with specific decay properties, relevant for experimental detection.

Contribution

It introduces a unified RPA-based analysis of edge and bulk modes in hierarchical FQHL, identifying the nature and decay behavior of magneto-plasmon and neutral modes.

Findings

Edge magneto-plasmon is the system's eigen-mode.

Neutral modes decay faster than power-law and couple with electromagnetic fields.

Results are applicable to time-of-flight experiments at ν=2/3 FQHL.

Abstract

Edge modes are studied for the hierarchical fractional quantum Hall liquids (FQHL) by treating the edge and bulk in a unified fashion. Within the RPA treatment of the composite boson effective theory with Coulomb interaction, one edge magneto-plasmon is shown to be the eigen-mode of the system. This mode decays algebraically perpendicular to the edge. All the other modes decay faster than power-law, and correspond to the neutral modes. However these neutral modes generally couple with the electromagnetic field within the magnetic length from the edge. The time-of-flight experiment in the $\nu=2/3$ FQHL is discussed in terms of these results.