Magnetic properties of moir\'e quantum dot arrays

TL;DR

This paper explores the magnetic behavior of moiré quantum dot arrays, revealing finite spin polarization and Nagaoka ferromagnetism, with potential control via displacement fields, using a combination of theoretical modeling and exact diagonalization.

Contribution

It introduces a detailed Hubbard model analysis of moiré quantum dot arrays, highlighting magnetic phenomena and the influence of twist angles and interactions, which is novel in this context.

Findings

Finite spin polarization observed across various filling factors.

Signatures of Nagaoka ferromagnetism near half-filling.

Magnetization can be controlled by displacement fields.

Abstract

We investigate magnetic properties of quantum dot arrays of moir\'e triangular superlattices. Starting from a reciprocal space model, we use the projection technique to obtain maximally localized Wannier functions and determine generalized Hubbard model parameters. The many-body Hamiltonian is solved using the exact diagonalization method as a function of the number of electrons in differently shaped quantum dots arrays. Finite spin polarization is observed within a wide range of filling factors for small twist angles and sufficiently strong interactions in most of the studied structures. The prospect for a magnetization controlled by applying a displacement field is presented. In the vicinity of half-filling, signatures of Nagaoka ferromagnetism in moir\'e materials are seen, which we demonstrate by comparing results with the corresponding on-site Hubbard model.