Anisotropic moir\'e band flattening in twisted bilayers of M-valley MXenes

Experimental studies on moir\'e materials have predominantly focused on twisted hexagonal lattice with low-energy states near the $\Gamma$- or K-points, where the electronic dispersion is typically isotropic. In contrast, we introduce a class of semiconducting transition metal carbides (MXenes) $M_2$C$T_2$ ($M$ = Ti, Zr, Hf, Sc, Y; $T$ = O, F, Cl) as a new platform for M-valley moir\'e materials, which exhibit pronounced anisotropic properties. Using Ti$_2$CO$_2$ and Zr$_2$CO$_2$ as representative examples, we perform large-scale \emph{ab initio} calculations and demonstrate that their AB-stacked twisted homobilayer hosts three threefold rotational-symmetry-related M-valleys with time-reversal symmetry. These systems show striking anisotropic band flattening in the conduction band minimum. To elucidate the underlying physics, we construct a simplified moir\'e Hamiltonian that captures the essential features of the band structure, revealing the origins of anisotropic flattening through the mechanisms of band folding and interlayer tunneling. Our findings expand the current landscape of moir\'e materials, establishing valley- and spin-degenerate, two-dimensional arrays of quasi-one-dimensional systems as promising platforms for exploring many interesting correlated electronic phases.