A New Moir\'e Platform Based on M-Point Twisting

Abstract

We introduce a new class of moir\'e systems and materials based on monolayers with triangular lattices and low-energy states at the M points of the Brillouin zone. These M-point moir\'e materials are fundamentally distinct from those derived from $\Gamma$- or K-point monolayers, featuring three time-reversal-preserving valleys related by three-fold rotational symmetry. We propose twisted bilayers of experimentally exfoliable 1T-SnSe$_2$ and 1T-ZrS$_2$ as realizations of this new class. Using extensive ab initio simulations, we develop quantitative continuum models and analytically show that the corresponding M-point moir\'e Hamiltonians exhibit emergent momentum-space non-symmorphic symmetries and a kagome plane-wave lattice in momentum space. This represents the first experimentally viable realization of a projective representation of crystalline space groups in a non-magnetic system. With interactions, these materials represent six-flavor Hubbard simulators with Mott physics, as can be seen by their flat Wilson loops. Furthermore, the presence of a non-symmorphic momentum-space in-plane mirror symmetry makes some of the M-point moir\'e Hamiltonians quasi-one-dimensional in each valley, suggesting the possibility of realizing Luttinger liquid physics. We predict the twist angles at which a series of (conduction) flat bands appear, provide a faithful continuum Hamiltonian, analyze its topology and charge density and briefly discuss several aspects of the physics of this new platform.