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

Abstract

We study transport across a point contact separating two line junctions in a ν = 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, we show that the stable fixed point corresponds to a point contact that 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 = 1/2e²/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 = 5/2e²/h) and the fully disconnected case (GH = 0).