Correlated Physics in M-Point Twisted Moiré Systems

We investigate the interacting physics of a new class of M-twist moiré systems, deriving the corresponding interacting Wannier model. Depending on the stacking configuration, the Wannier centers form either a triangular or kagome lattice. Using Hartree-Fock simulations, we explore the phase diagram, identifying an antiferromagnetic valley-polarized state at filling factors 1 and 2. However, we find the spin order in the Hartree-Fock simulation is unstable due to the quasi-one-dimensional nature of the valleys, leading to fluctuations that destabilize long-range spin order. Our results underscore the intricate interplay of symmetry, topology, and interactions in these novel moiré materials, providing a promising platform for studying quantum magnetism and correlated electronic phases.