Local thermodynamic DOS measurement and twist-angle mapping in graphene-hBN superlattices

Abstract: Moir\'e patterns arising from twisted van der Waals stacks fundamentally reshape their electronic properties, enabling band-structure engineering that has driven rapidly growing interest in this field. In studying electronic properties, however, structural disorder present in real devices often leads to twist-angle inhomogeneity and obscures angle-dependent electronic effects when measured with bulk-averaged measurements. Probes that can access local thermodynamic response of the electronic systems with high sensitivity would be highly valuable. Here, we adopt Kelvin probe force microscopy (KPFM) to locally investigate graphene-hBN superlattices. By additionally modulating the chemical potential of the system, we obtain the inverse compressibility with high signal-to-noise ratio, enabling extraction of the local thermodynamic DOS. From this information, we determine the local twist angle along the device and find that twist-angle deviations are strongly correlated with bubble-induced strain features. Furthermore, by simultaneously tracking the offsets in the contact potential difference and in the net charge, we identify which interface within the heterostructure hosts the trapped bubbles. This capability to identify local electro-chemical environments provides a practical tool for strain-based studies and future device designs utilizing nanoscale engineering in moir\'e systems.