Origin of Magic Angular Momentum in a Quantum Dot under Strong Magnetic Field

TL;DR

This paper explores the origins of stable 'magic' angular momentum states in quantum dots under strong magnetic fields, combining numerical analysis with theoretical models to identify all such states and relate them to known quantum phenomena.

Contribution

It introduces a combined geometrical and composite fermion approach to accurately identify all magic angular momentum numbers in quantum dots.

Findings

Composite fermion picture explains small magic numbers.

Geometrical picture better for larger magic numbers.

All magic numbers can be identified by combining both models.

Abstract

This paper investigates origin of the extra stability associated with particular values (magic numbers) of the total angular momentum of electrons in a quantum dot under strong magnetic field. The ground-state energy, distribution functions of density and angular momentum, and pair correlation function are calculated in the strong field limit by numerical diagonalization of the system containing up to seven electrons. It is shown that the composite fermion picture explains the small magic numbers well, while a simple geometrical picture does better as the magic number increases. Combination of these two pictures leads to identification of all the magic numbers. Relation of the magic-number states to the Wigner crystal and the fractional quantum Hall state is discussed.