Theory of the spin singlet filling factor $\nu=2$ quantum Hall droplet

TL;DR

This paper develops a theoretical framework for understanding the electronic properties, stability, and spin transitions of a $ u=2$ spin-singlet quantum Hall droplet in quantum dots, aligning with recent experimental observations.

Contribution

It introduces a comprehensive theory combining Hartree-Fock, exact diagonalisation, and spin-density functional methods to analyze the stability and spin transitions of the $ u=2$ quantum Hall droplet.

Findings

Identification of a critical electron number $N_c$ where the droplet transitions to a spin-polarized phase.

Prediction of characteristic Coulomb blockade spectra patterns for the stable $ u=2$ droplet.

Demonstration of current amplitude reversal associated with the spin transition, matching experimental data.

Abstract

A theory of electronic properties of a spin-singlet quantum Hall droplet at filling factor $\nu=2$ in a parabolic quantum dot is developed. The excitation spectrum and the stability of the droplet due to the transfer of electrons into the second Landau level at low magnetic fields and due to spin flip at the edge at higher magnetic fields is determined using Hartree-Fock, exact diagonalisation, and spin-density functional methods. We show that above a critical number of electrons $N_c$ the unpolarised $\nu=2$ quantum Hall droplet ceases to be a ground state in favor of spin-polarised phases. We determine the characteristic pattern in the addition and current-amplitude Coulomb blockade spectra associated with the stable $\nu=2$ droplet. We show that the spin transition of the droplet at a critical number of electrons is accompanied by the reversal of the current amplitude modulation at the $\nu=2$ line, as observed in recent experiments.