Moiré materials based on M-point twisting

When two monolayer materials are stacked with a relative twist, an effective moiré translation symmetry emerges, leading to fundamentally different properties in the resulting heterostructure. As such, moiré materials have recently provided highly tunable platforms for exploring strongly correlated systems^1,2. However, previous studies have focused almost exclusively on monolayers with triangular lattices and low-energy states near the Γ (refs. ^3,4) or K (refs. ^5-9) points of the Brillouin zone (BZ). Here we introduce a new class of moiré systems based on monolayers with triangular lattices but low-energy states at the M points of the BZ. These M-point moiré materials feature three time-reversal-preserving valleys related by threefold rotational symmetry. We propose twisted bilayers of exfoliable 1T-SnSe₂ and 1T-ZrS₂ as realizations of this new class. Using extensive ab initio simulations, we identify twist angles that yield flat conduction bands, provide accurate continuum models, analyse their topology and charge density and explore the platform's rich physics. Notably, the M-point moiré Hamiltonians exhibit emergent momentum-space non-symmorphic symmetries and a kagome plane-wave lattice structure. This represents, to our knowledge, the first experimentally viable realization of projective representations of crystalline space groups in a non-magnetic system. With interactions, these systems act as six-flavour Hubbard simulators with Mott physics. Moreover, the presence of a momentum-space non-symmorphic in-plane mirror symmetry renders some of the M-point moiré Hamiltonians quasi-one-dimensional in each valley, suggesting the possibility of realizing Luttinger-liquid physics.