Theory of a two-level artificial molecule in laterally coupled quantum Hall droplets

TL;DR

This paper develops a theoretical model of coupled quantum Hall droplets forming a two-level artificial molecule, analyzing electron interactions, edge state coupling, and singlet-triplet transitions under varying conditions.

Contribution

It introduces a novel theoretical framework for coupled quantum Hall droplets, predicting electron state transitions and interactions using configuration interaction and Hartree-Fock methods.

Findings

Prediction of singlet-triplet transitions as a function of magnetic field and electron number.

Identification of triplet transitions involving electron transfer to the center of dots.

Demonstration of edge state coupling forming a two-level artificial molecule.

Abstract

We present a theory of laterally coupled quantum Hall droplets with electron numbers (N1,N2) at filling factor $\nu=2$. We show that the edge states of each droplet are tunnel coupled and form a two-level artificial molecule. By populating the edge states with one electron each a two electron molecule is formed. We predict the singlet-triplet transitions of the effective two-electron molecule as a function of the magnetic field, the number of electrons, and confining potential using the configuration interaction method (CI) coupled with the unrestricted Hartree-Fock (URHF) basis. In addition to the singlet-triplet transitions of a 2 electron molecule involving edge states, triplet transitions involving transfer of electrons to the center of individual dots exist for $(N1 \geq 5, N2 \geq 5)$.