Symmetry Constraints and the Electronic Structures of a Quantum Dot with Thirteen Electrons

TL;DR

This paper investigates how symmetry constraints influence the electronic structures of a 13-electron quantum dot, identifying favorable structures and their role in determining state properties and magic numbers.

Contribution

It introduces a detailed analysis of symmetry constraints on quantum states and identifies the role of favorable structures in shaping electronic configurations.

Findings

First-state structures are dominated by competitive favorable structures.

States with favorable structures exhibit crystal-like core-ring configurations.

Magic numbers are closely linked to the identified favorable structures.

Abstract

The symmetry constraints imposing on the quantum states of a dot with 13 electrons has been investigated. Based on this study, the favorable structures (FSs) of each state has been identified. Numerical calculations have been performed to inspect the role played by the FSs. It was found that, if a first-state has a remarkably competitive FS, this FS would be pursued and the state would be crystal-like and have a specific core-ring structure associated with the FS. The magic numbers are found to be closely related to the FSs.