Quantum Hall States at $\nu=\frac{2}{k+2}$

TL;DR

This paper investigates the edge states and thermal properties of specific fractional quantum Hall states at filling factors rac{2}{k+2}, revealing an emergent SU(2) algebra and distinctive heat flow characteristics that differentiate them from other states.

Contribution

It uncovers the emergent SU(2) algebra in the edge modes and analyzes thermal Hall conductance to distinguish these states from competing models.

Findings

Emergent SU(2)$_k$ algebra in edge modes.

Opposite direction heat flow along edges.

Distinct thermal Hall conductance for rac{2}{k+2} states.

Abstract

We study the $\nu=\frac{2}{k+2}$ quantum Hall states which are particle-hole conjugates of the $\nu=\frac{k}{k+2}$ Read-Rezayi states. We find that equilibration between the different modes at the edge of such a state leads to an emergent SU(2)$_k$ algebra in the counter-propagating neutral sector. Heat flow along the edges of these states will be in the opposite direction of charge flow. In the $k=3$ case, which may be relevant to $\nu=2+{2/5}$, the thermal Hall conductance and the exponents associated with quasiparticle and electron tunneling distinguish this state from competing states such as the hierarchy/Jain state.