Strong-coupling branching of FQHL edges

TL;DR

This paper develops a theory for quasiparticle backscattering in multi-point contact systems of Fractional Quantum Hall Edges, revealing coherent splitting and new edge quasiparticle statistics in the strong-coupling regime.

Contribution

It introduces a duality-based model for strong-tunneling quasiparticle backscattering in multi-edge FQHL systems, highlighting coherent splitting and modified quasiparticle statistics.

Findings

Coherent splitting of quasiparticles at multiple contacts.

Charge and exchange statistics differ from bulk Laughlin quasiparticles.

Proper flux attachment description is essential for multiple contacts.

Abstract

We have developed a theory of quasiparticle backscattering in a system of point contacts formed between single-mode edges of several Fractional Quantum Hall Liquids (FQHLs) with in general different filling factors $\nu_j$ and one common single-mode edge $\nu_0$ of another FQHL. In the strong-tunneling limit, the model of quasiparticle backscattering is obtained by the duality transformation of the electron tunneling model. The new physics introduced by the multi-point-contact geometry of the system is coherent splitting of backscattered quasiparticles at the point contacts in the course of propagation along the common edge $\nu_0$. The ``branching ratios'' characterizing the splitting determine the charge and exchange statistics of the edge quasiparticles that can be different from those of Laughlin's quasiparticles in the bulk of FQHLs. Accounting for the edge statistics is essential for the system of more than one point contact and requires the proper description of the flux attachement to tunneling electrons.