Transport signatures of fractional quantum Hall binding transitions

Abstract

Certain fractional quantum Hall edges have been predicted to undergo quantum phase transitions which reduce the number of edge channels and at the same time bind electrons together. However, detailed studies of experimental signatures of such a ``binding transition'' remain lacking. Here, we propose quantum transport signatures with focus on the edge at filling $\ensuremath{\nu}=9/5$. We demonstrate theoretically that in the regime of nonequilibrated edge transport, the bound and unbound edge phases have distinct conductance and noise characteristics. We also show that for a quantum point contact in the strong back-scattering (SBS) regime, the bound phase produces a minimum Fano factor ${F}_{\mathrm{SBS}}=3$ corresponding to three-electron tunneling, whereas single-electron tunneling is strongly suppressed at low energies. Together with recent experimental developments, our results will be useful for detecting binding transitions in the fractional quantum Hall regime.