Relevance of inter-composite fermion interaction to the edge Tomonaga-Luttinger liquid

TL;DR

This paper investigates how residual interactions among composite fermions influence the edge states described by Tomonaga-Luttinger liquid theory, providing microscopic estimates that align with experimental data.

Contribution

It demonstrates the relevance of inter-composite fermion interactions to edge physics and refines the effective theory to include these effects.

Findings

Wen's theory accurately describes non-interacting composite fermion edges.

Residual interactions are relevant perturbations affecting the edge state.

Estimated filling factor dependence matches experimental observations.

Abstract

It is shown that Wen's effective theory correctly describes the Tomonaga-Luttinger liquid at the edge of a system of non-interacting composite fermions. However, the weak residual interaction between composite fermions appears to be a relevant perturbation. The filling factor dependence of the Tomonaga-Luttinger parameter is estimated for interacting composite fermions in a microscopic approach and satisfactory agreement with experiment is achieved. It is suggested that the electron field operator may not have a simple representation in the effective one dimensional theory.