Locally mapping the phase diagram of alternating twist multilayer graphene: an STM and a non-contact AFM study, Part 2

The rich phase diagrams of moire lattices in multilayer twisted graphene systems hosts superconducting and correlated insulating phases that sensitively depend on the charge density and displacement field. In this work we study the correlated insulating states of integer fillings of quad-layer twisted graphene with a backgate by non-contact AFM and STM at ultra-low temperatures. In STM experiment, the local density and the displacement field are coupled parameters preventing the analysis of the whole phase diagram. Additionally, a difference in the work function of the tip and the sample creates a local density profile due to tip gating that might affect the spectroscopic data. Complementing STM measurements, tip gating can be tuned in non-contact AFM addressing this challenge. Capacitance and dissipation spectroscopies studied with non-contact AFM display distinct signals across phase transitions in quad-layer twisted graphene heterostructures. We demonstrate that the phase diagram can be mapped out independently controlling the displacement field and the density.