Composite fermion theory of correlated electrons in semiconductor quantum dots in high magnetic fields

TL;DR

This paper develops a perturbative approach based on composite-fermion theory to accurately describe correlated electron states in semiconductor quantum dots under high magnetic fields, improving understanding of their complex quantum phases.

Contribution

It introduces a systematic perturbative scheme using correlated basis functions to enhance wave function and energy calculations for low-lying states in quantum dots.

Findings

Achieves nearly exact results for ground state wave functions and energies.

Effectively resolves competing orders in complex cases.

Provides a systematic method for improving quantum state descriptions.

Abstract

Interacting electrons in a semiconductor quantum dot at strong magnetic fields exhibit a rich set of states, including correlated quantum fluids and crystallites of various symmetries. We develop in this paper a perturbative scheme based on the correlated basis functions of the composite-fermion theory, that allows a systematic improvement of the wave functions and the energies for low-lying eigenstates. For a test of the method, we study systems for which exact results are known, and find that practically exact answers are obtained for the ground state wave function, ground state energy, excitation gap, and the pair correlation function. We show how the perturbative scheme helps resolve the subtle physics of competing orders in certain anomalous cases.