Dynamical Mean Field Theory of Moir\'e Bilayer Transition Metal Dichalcogenides: Phase Diagram, Resistivity, and Quantum Criticality

We present a comprehensive dynamical mean field study of the triangular lattice moir\'e Hubbard model, which is believed to represent the physics of moir\'e bilayer transition metal dichalcogenides. In these materials, important aspects of the band structure including the bandwidth and the order and location of van Hove singularities can be tuned by varying the interlayer potential. We present a magnetic and metal-insulator phase diagram and a detailed study of the dependence of the resistivity on temperature, band filling and interlayer potential. We find that transport displays Fermi liquid, strange metal and quantum critical behaviors in distinct regions of the phase diagram. Specifically, we find that the cube-root van Hove singularity ($\rho(\epsilon) \sim|\epsilon|^{-1 / 3}$) gives a strange metal behavior with a $T$-linear scattering rate and $\omega/T$ scaling. We show how magnetic order affects the resistivity. Our results elucidate the physics of the correlated states and the metal-insulator continuous transition recently observed in twisted homobilayer WSe$_2$ and heterobilayer MoTe$_2$/WSe$_2$ experiments.