Inter-edge interactions and novel fixed points at a junction of quantum Hall line junctions

TL;DR

This paper investigates the complex inter-edge interactions at a junction of three quantum Hall line junctions, revealing new fixed points and stable configurations that depend on inter-edge repulsive interactions, with potential experimental signatures.

Contribution

It introduces novel fixed points characterized by current-splitting matrices in a three junction quantum Hall system, and identifies stable configurations influenced by inter-edge interactions.

Findings

Existence of new fixed points in a three junction quantum Hall system.

Both flower and island configurations can be stable under certain interactions.

Tunneling conductance measurements can detect the stable interaction regimes.

Abstract

We show that novel fixed points (characterized by matrices which specify the splitting of the currents at the junction) can be accessed in a system which contains a junction of three quantum Hall line junctions. For such a junction of fractional quantum Hall edge states, we find that it is possible for both the flower (single droplet) and islands (three droplets) configurations to be stable in an intermediate region, for a range of values of the inter-edge repulsive interactions. A measurement of the tunneling conductance as a function of the gate voltage controlling inter-edge repulsions can give a clear experimental signal of this region.