Supporting data for 'Engineering Interlayer Interactions in Graphene-based Moire Systems'

This work demonstrates the study of engineering interlayer interactions in graphene-based moiré systems. The first part investigates interlayer Coulomb drag in graphene/hBN/graphene heterostructures, demonstrating robust coupling between moiré minibands and original Dirac bands despite a significant reciprocal lattice mismatch. It reveals conventional momentum drag at high temperatures and large densities, including characteristic layer reciprocity and a power-law dependence in both regions. On the contrary, near charge neutrality at low temperatures, the drag effect exhibits abnormal density dependence and asymmetric behavior, which is controlled by the properties of the drag layer. This is likely associated with energy-dominated transport and electron-hole puddles. Remarkably, in one of the devices, multiple side peaks and nonlocal drag signatures have also been identified. The second part explores interlayer couplings and quantum Hall states in twisted graphene moiré systems through engineered heterostructures with ultrathin hBN spacers. The device with monolayer hBN demonstrates satellite Dirac points from moiré coupling, while the device with few-layer hBN shows multiple Dirac points corresponding to the independent graphene layers, highlighting the atomic-scale sensitivity of moiré effects to interlayer spacing. Both devices exhibit rich quantum Hall phenomena, such as Landau level crossings, resembling those in large-angle twisted graphene systems. Overall, this entire work not only establishes drag measurements as a sensitive probe of correlation physics in versatile moiré systems but also offers the ability to tune interlayer interactions in twisted graphene structures across arbitrary twist angles by using hBN spacers.