Ring Arrays in Quantum Dots: Nagaoka Ferromagnetism or something new?

Nagaoka ferromagnetism (NF) is a long-predicted example of itinerant ferromagnetism in the Hubbard model and has been studied theoretically for many years. NF occurs when there is one hole in a half-filled band and a large onsite Coulomb repulsion, which does not arise naturally in materials. Quantum dots systems like dopant arrays in Si, can be fabricated with atomically precise complex geometries to create highly controllable systems. This makes them good candidates to study itinerate ferromagnetism in different array geometries. Here we describe theoretical simulations done for rings and arrays of rings at different hole densities for a quantum dot system, such as the dopant arrays studied at NIST. We find a new type of itinerate ferromagnetism at fixed electron number that depends on the number of rings in the system, as well as the emergence and disappearance of such ferromagnetism when disorder is present. This ferromagnetism on a ring could co-exist with NF in special cases like hexagonal systems, and the exact mechanism is under investigation. Our results define possible experiments to hunt for different forms of saturated ferromagnetism, which may be used as a simple (but physically interesting) test case for solid-state analog quantum simulators.