Hund's Rule for Composite Fermions

TL;DR

This paper investigates the applicability of Hund's rule to composite fermions in fractional quantum Hall systems, revealing its validity in certain filling factor regions and uncovering a self-similar structure in the Landau level spectrum.

Contribution

It demonstrates that Hund's maximum-spin rule applies to composite fermions in specific regimes, providing new insights into the spin structure of fractional quantum Hall states.

Findings

Hund's rule is valid for composite fermions in certain filling factors.

A self-similar structure exists in the Landau level spectrum between filling factors 4/3 and 2/3.

The rule is not valid for electrons in the lowest Landau level.

Abstract

We consider the ``fractional quantum Hall atom" in the vanishing Zeeman energy limit, and investigate the validity of Hund's maximum-spin rule for interacting electrons in various Landau levels. While it is not valid for {\em electrons} in the lowest Landau level, there are regions of filling factors where it predicts the ground state spin correctly {\em provided it is applied to composite fermions}. The composite fermion theory also reveals a ``self-similar" structure in the filling factor range $4/3>\nu>2/3$.