Edge spin excitations and reconstructions of integer quantum Hall liquids

TL;DR

This paper investigates how electron-electron interactions influence edge spin excitations and reconstructions in integer quantum Hall liquids, revealing bosonic edge spin waves and instabilities related to confinement strength.

Contribution

It provides a detailed analysis of edge spin structures and instabilities in integer quantum Hall states using exact diagonalization and trial wave functions, highlighting new edge phenomena.

Findings

Edge spin waves are the low-energy excitations in u=1 ferromagnetic states.

Instabilities occur due to softening of edge spin waves with changing confinement.

Ground states in certain regimes are compact states with varying total spin.

Abstract

We study the effect of electron-electron interaction on the charge and spin structures at the edge of integer quantum Hall liquids, under three different kinds of confining potentials. Our exact diagonalization calculation for small systems indicates that the low energy excitations of \nu=1 ferromagnetic state are bosonic edge spin waves. Instabilities of the ferromagnetic state with altering confinement strength result from the softening of these edge spin waves, and formation of edge spin textures. In \nu\lesssim 2 regime, exact diagonalization on edge electron systems indicates that compact Hartree-Fock states with different total spin always become ground states in some regions of parameter space, and the ground states appear in between two compact states are their edge spin waves. The initial \nu=2 instability is toward the compact state with total spin 1. Larger systems are studied using a microscopic trial wave functions, and some quantitative predictions on the edge instabilities for a certain type of confining potential are reached in the thermodynamic limit.