3D microwave imaging of a van der Waals heterostructure
Van der Waals (vdW) heterostructures offer a tunable platform for the realization of emergent phenomena in layered electron systems. While scanning probe microscopy techniques have proven useful for the characterization of surface states and 2D crystals, the subsurface imaging of quantum phenomena in multi-layer systems presents a significant challenge. In 3D heterostructures, states that occupy different planes can simultaneously contribute to the signal detected by the microscope probe, which complicates image analysis and interpretation. Here we present a quantum imaging technique that offers a glimpse into the third dimension by resolving states out of plane: it extracts the charge density landscape of individual atomic planes inside a vdW heterostructure, layer by layer. As a proof-of-concept, we perform layer-resolved imaging of quantum Hall states and charge disorder in double-layer graphene using milliKelvin microwave impedance microscopy. Here the discrete energy spectrum of the top layer enables transmission of microwaves through gapped states, thus opening direct access to quantum phases in the subsurface layer. Resolving how charge is distributed out-of-plane offers a direct probe of interlayer screening, revealing signatures of negative quantum capacitance driven by many-body correlations. At the same time, we extract key features of the band structure and thermodynamics, including gap sizes. Notably, by imaging the charge distribution on different atomic planes beneath the surface, we shed light on the roles of surface impurities and screening on the stability of fractional quantum Hall states. We also show that the uppermost graphene layer can serve as a top gate: This unlocks access to a wide range of phenomena that require displacement field control, from fractional Chern insulators in Moir\'e superlattices to correlated states in multilayer graphene.