Binding transition in quantum hall edge states

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 υ=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 υ=2 and υ=1/5 states only allow three-electron co-tunneling at low energies after the binding transition.