Transport Signatures of Fractional Quantum Hall Binding Transitions

TL;DR

This paper predicts experimental signatures of quantum phase transitions in fractional quantum Hall edges, focusing on conductance and noise differences between bound and unbound phases at filling factor 9/5.

Contribution

It provides a theoretical framework for detecting binding transitions via transport measurements, highlighting distinct conductance, noise, and Fano-factor signatures.

Findings

Bound phase shows a minimum Fano-factor of 3 in strong back-scattering regime.

Bound and unbound phases have distinct conductance and noise characteristics.

Single electron tunneling is suppressed at low energies in the bound phase.

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 $\nu=9/5$. We demonstrate theoretically that in the regime of non-equilibrated 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 regime, the bound phase produces a minimum Fano-factor $F_{SBS}=3$ 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.