Ground state and edge excitations of quantum Hall liquid at filling factor 2/3

TL;DR

This study numerically investigates the fractional quantum Hall state at filling factor 2/3, revealing its ground state as a particle-hole conjugate of the 1/3 Laughlin state and identifying two counter-propagating edge modes with distinct velocity responses.

Contribution

It provides a detailed microscopic analysis of the edge excitations and their velocities at filling factor 2/3, highlighting the effects of Coulomb interaction and confinement potential.

Findings

Ground state is the particle-hole conjugate of the 1/3 Laughlin state.

Identifies two counter-propagating edge modes with different velocities.

Layer thickness affects both edge mode velocities similarly.

Abstract

We present a numerical study of fractional quantum Hall liquid at Landau level filling factor $\nu=2/3$ in a microscopic model including long-range Coulomb interaction and edge confining potential, based on the disc geometry. We find the ground state is accurately described by the particle-hole conjugate of a $\nu=1/3$ Laughlin state. We also find there are two counter-propagating edge modes, and the velocity of the forward-propagating mode is larger than the backward-propagating mode. The velocities have opposite responses to the change of the background confinement potential. On the other hand changing the two-body Coulomb potential has qualitatively the same effect on the velocities; for example we find increasing layer thickness (which softens of the Coulomb interaction) reduces both the forward mode and the backward mode velocities.