Layer-resolved microwave imaging of a van der Waals heterostructure

Van der Waals (vdW) heterostructures offer a tunable platform for the realization of emergent phenomena in double-layer electron systems, such as excitonic superfluidity. While scanning probe microscopy techniques have proven useful for the characterization of surface states and two-dimensional crystals, the subsurface imaging of quantum phenomena in multi-layer systems presents a significant challenge. In 3D heterostructures, states that occupy different planes simultaneously contribute to the signal detected by the 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 correlations. Notably, by imaging thecharge distribution on different atomic planes, 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 layer can serve as a top gate, which can screen surface disorder and enable microscopy with displacement field control: This unlocks access to a wide range of phenomena that can only be observed in top-gated devices, from fractional Chern insulators in Moire superlattices to correlated states in multilayer graphene.