Edge reconstruction of fractional quantum Hall liquids with spin degrees of freedom

TL;DR

This paper investigates how edge states in fractional quantum Hall liquids with spin are affected by various factors, revealing different edge instability mechanisms for Abelian and non-Abelian states through numerical analysis.

Contribution

It provides a detailed numerical study of edge instabilities in fractional quantum Hall liquids with spin, highlighting distinct mechanisms for Abelian and non-Abelian states.

Findings

Edge instabilities are mainly triggered by edge spin wave softening in Abelian states.

Edge magnetoplasmon softening causes instabilities in the non-Abelian 5/2 state.

Phase diagrams of edge stability are mapped out for different parameters.

Abstract

We study the interplay of confining potential, electron-electron interaction, and Zeeman splitting at the edges of fractional quantum Hall liquids, using numerical diagonalization of finite-size systems. The filling factors studied include 1/3, 5/2, 2/5, and 2/3. In the absence of Zeeman splitting and an edge, the first two have spin fully polarized ground states, while the latter two have singlet ground states. We find that with few exceptions, edge instabilities of these systems are triggered by softening of edge spin waves for Abelian fractional quantum Hall liquids (1/3, 2/5 and 2/3 liquids), and are triggered by softening of edge magnetoplasmon excitations for non-Abelian 5/2 liquid at the smoother confinement side. Phase diagrams are obtained in the accessible parameter spaces.