# Transport in line junctions of $\nu=5/2$ quantum Hall liquids

## TL;DR

This paper analyzes tunneling currents in line junctions of the $
u=5/2$ quantum Hall state to differentiate between various proposed edge state models, including Abelian and non-Abelian states, using momentum-resolved tunneling.

## Contribution

It provides detailed calculations of tunneling currents for multiple $
u=5/2$ state models, aiding experimental identification of the correct edge state structure.

## Key findings

- Distinct tunneling signatures for different models.
- Non-equilibrated anti-Pfaffian state shows unique resistance.
- Momentum resolved tunneling reveals edge mode properties.

## Abstract

We calculate the tunneling current through long line junctions of a $\nu=5/2$ quantum Hall liquid and i) another $\nu=5/2$ liquid, ii) an integer quantum Hall liquid and iii) a quantum wire. Momentum resolved tunneling provides information about the number, propagation directions and other features of the edge modes and thus helps distinguish several competing models of the 5/2 state. We investigate transport properties of two proposed Abelian states: $K=8 state and 331 state, and four possible non-Abelian states: Pfaffian, edge-reconstructed Pfaffian, and two versions of the anti-Pfaffian state. We also show that the non-equilibrated anti-Pfaffian state has a different resistance from other proposed states in the bar geometry.