Randomness at the Edge: Theory of Quantum Hall transport at filling $\nu=2/3$

TL;DR

This paper develops a theory for quantum Hall edge transport at filling factor 2/3, showing that disorder induces a phase transition to a phase with quantized conductance and a neutral mode, aligning theory with experimental observations.

Contribution

It introduces an exact solution for the disordered edge phase at filling 2/3, revealing a quantized Hall conductance and the existence of an upstream neutral mode.

Findings

Disorder induces a phase transition to a new edge phase.

The new phase exhibits quantized Hall conductance of 2/3.

Presence of an upstream neutral mode alters tunneling temperature dependence.

Abstract

Current Luttinger liquid edge state theories for filling $\nu=2/3$ predict a non-universal Hall conductance, in disagreement with experiment. Upon inclusion of random edge tunnelling we find a phase transition into a new disordered-dominated edge phase. An exact solution of the random model in this phase gives a quantized Hall conductance of 2/3 and a neutral mode propagating upstream. The presence of the neutral mode changes the predicted temperature dependence for tunnelling through a point contact from $T^{2/\nu -2}$ to $T^2$.