Effect of inter-edge Coulomb interactions on transport through a point contact in a \nu = 5/2 quantum Hall state

TL;DR

This paper investigates how inter-edge Coulomb interactions influence electron transport in a rac{5}{2}illing quantum Hall state, revealing a stable fixed point with unique conductance properties and specific temperature-dependent behaviors.

Contribution

It introduces a detailed analysis of Coulomb interactions in a rac{5}{2}illing quantum Hall system, identifying a novel stable fixed point with partial transmission and backscattering.

Findings

Stable fixed point with half-filled level fully transmitting

Hall conductance at the fixed point is 1/2 e^2/h

Predicted non-universal temperature power laws for approach to fixed point

Abstract

We study transport across a point contact separating two line junctions in a \nu = 5/2 quantum Hall system. We analyze the effect of inter-edge Coulomb interactions between the chiral bosonic edge modes of the half-filled Landau level (assuming a Pfaffian wave function for the half-filled state) and of the two fully filled Landau levels. In the presence of inter-edge Coulomb interactions between all the six edges participating in the line junction, the stable fixed point corresponds to a point contact which is neither fully opaque nor fully transparent. Remarkably, this fixed point represents a situation where the half-filled level is fully transmitting, while the two filled levels are completely backscattered; hence the fixed point Hall conductance is given by G_H = {1/2} e^2/h. We predict the non-universal temperature power laws by which the system approaches the stable fixed point from the two unstable fixed points corresponding to the fully connected case (G_H = {5/2} e^2/h) and the fully disconnected case (G_H = 0).