Starting with twisted bilayer graphene, graphene-based moir\'e materials have recently been established as a new platform for studying strong electron correlations. In this paper, we study graphene monolayers on trilayer and demonstrate that system can host flat bands when the twist angle is close to magic-angle of 1.16$^\circ$. When monolayer ABA are not isolated, but intersected by Dirac cone...

The occurrence of superconducting and insulating phases is well-established in twisted graphene bilayers, they have also been reported other arrangements layers. We investigate three such arrangements: untwisted AB bilayer on an hBN substrate, two bilayers with respect to each other, a single ABC stacked trilayer substrate. Narrow bands different topology occur all cases, producing high density...

In a recent experiment [Lin et al., arXiv:2112.07841], the superconducting phase hosted by heterostructure of mirror-symmetric twisted trilayer graphene and WSe$_2$ was shown to exhibit significantly different critical currents in opposite directions absence external magnetic fields. We here develop microscopic theory analyze necessary conditions for this zero-field diode effect. Taking into ac...

We construct a van der Waals heterostructure consisting of three graphene layers stacked with alternating twisting angles $\pm\theta$. At the average twist angle $\theta\sim 1.56^{\circ}$, theoretically predicted magic for formation flat electron bands, narrow conduction and valence moir\'e bands appear together linearly dispersing Dirac band. Upon doping half-filled band holes, or electrons, d...