Composite Edge States in the $\nu=2/3$ Fractional Quantum Hall Regime

TL;DR

This paper introduces a unified model for the $ u=2/3$ fractional quantum Hall state, analyzing its edge states and transitions, with detailed correlation function calculations and experimental implications.

Contribution

It presents a generalized $ u=2/3$ state unifying previous edge-state pictures and determines its correlation functions through Monte Carlo simulations.

Findings

Identifies a sharp transition in the ground state based on confining potential slope.

Calculates correlation functions for up to 50 electrons.

Discusses experimental implications of the transition.

Abstract

A generalized $\nu=2/3$ state, which unifies the edge-state pictures of MacDonald and of Beenakker is presented and studied in detail. Using an exact relation between correlation functions of this state and those of the Laughlin $\nu=1/3$ wave function, the correlation functions of the $\nu=2/3$ state are determined via a classical Monte Carlo calculation, for systems up to $50$ electrons. It is found that as a function of the slope of the confining potential there is a sharp transition of the ground state from one description to the other. The experimental implications are discussed.