Binding Transition in Quantum Hall Edge States

TL;DR

This paper investigates phase transitions in topologically unstable Abelian quantum Hall edge states, revealing electron-binding phenomena that alter edge conductance and enable only multi-electron co-tunneling after the transition.

Contribution

It introduces the concept of binding transitions in T-unstable QH edge states, showing how they modify edge excitations and tunneling processes, a novel insight into edge state stability.

Findings

Binding transitions reduce the number of gapless edge modes.

Single-electron tunneling becomes gapped after transition.

Multi-electron co-tunneling remains gapless, e.g., three-electron co-tunneling at ν=9/5.

Abstract

We study a class of Abelian quantum Hall (QH) states which are topologically unstable (T-unstable). We find that the T-unstable QH states can have a phase transition on the edge which causes a binding between electrons and reduces the number of gapless edge branches. After the binding transition, the single-electron tunneling into the edge gains a finite energy gap, and only certain multi-electron co-tunneling (such as three-electron co-tunneling for $\nu=9/5$ edges) can be gapless. Similar phenomenon also appear for edge state on the boundary between certain QH states. For example edge on the boundary between $\nu=2$ and $\nu=1/5$ states only allow three-electron co-tunneling at low energies after the binding transition.