Studies of Stability of Nagaoka Ferromagnetism on a Triangular Lattice

Abstract

Moire superlattices can be created by stacking two atomic layers ofdifferent materials, and its electronic properties can be manipulated using easily adjustable external factors, such as the twist angle, making them promising candidates for quantum simulators. In this study, first we briefly examine the features of the triangular moire lattice of transition metal dichalcogenides (TMDs) by treating it as a periodic system through both continuum and tight-binding models. The primary aim isto investigate the magnetic characteristics by fully incorporating correlations, which is challenging in a periodic system due to the vast size ofthe Hilbert space. Therefore, we concentrate on finite-sized triangular lattices. We examine the finite-size twisted TMDs within a moire triangular lattice and analyze their magnetic properties above half-filling. By introducing one electron into a half-filled system, the total spin of the ground state can reach its maximum, leading to the emergence of Nagaoka ferromagnetism. This form of magnetism arises from correlation effects, essentially due to constructive interference among various many body configurations. We employ exact diagonalization methods to solve the Hubbard Hamiltonian, fully accounting for these correlations. We demonstrate the emergence of Nagaoka ferromagnetism by adding one, two, and three electrons above half-filling, with the ferromagnetic characteristics varying based on the geometries of finite triangular lattices. Additionally, the interaction strength is analyzed to observe transitions in total spin and assess system stability. The Nagaoka polaron is also visualized within the finite triangular lattices.