Observability of counterpropagating modes at fractional-quantum-Hall edges

TL;DR

This paper investigates the conditions for observing counterpropagating modes at fractional quantum Hall edges, deriving realistic expressions for their velocities and edge properties through microscopic calculations.

Contribution

It provides a detailed microscopic analysis of counterpropagating edge modes and their velocities, addressing previous experimental challenges in detecting these modes.

Findings

Derived expressions for the slow mode velocity based on microscopic models

Identified conditions favoring the experimental observation of counterpropagating modes

Analyzed the influence of edge width on magnetoplasmon dispersion

Abstract

When the bulk filling factor is equal to 1 - 1/m with m odd, at least one counterpropagating chiral collective mode occurs simultaneously with magnetoplasmons at the edge of fractional-quantum-Hall samples. Initial experimental searches for an additional mode were unsuccessful. In this paper, we address conditions under which its observation should be expected in experiments where the electronic system is excited and probed by capacitive coupling. We derive realistic expressions for the velocity of the slow counterpropagating mode, starting from a microscopic calculation which is simplified by a Landau-Silin-like separation between long-range Hartree and residual interactions. The microscopic calculation determines the stiffness of the edge to long-wavelength neutral excitations, which fixes the slow-mode velocity, and the effective width of the edge region, which influences the magnetoplasmon dispersion.