Gradient Electronic Landscapes in van der Waals Heterostructures

Abstract: Two-dimensional (2D) materials such as graphene and hexagonal boron nitride (hBN) provide a versatile platform for quantum electronics. Experiments generally require encapsulating graphene within hBN flakes, forming a protective van der Waals (vdW) heterostructure that preserves delicate properties of the embedded crystal. To produce functional devices, heterostructures are typically shaped by electron beam lithography and etching, which has driven progress in 2D materials research. However, patterns are primarily restricted to in-plane geometries such as boxes, holes, and stripes, limiting opportunities for advanced architectures. Here, we use thermal scanning-probe lithography (tSPL) to produce smooth topographic landscapes in vdW heterostructures, controlling the thickness degree of freedom with nanometer precision. We electrically gate a sinusoidal topography to impose an electric-field gradient on the graphene layer to spatially modulate charge-carrier doping. We observe signatures of the landscape in transport measurements-resistance-peak spreading and commensurability oscillations-establishing tSPL for tailoring high-quality quantum electronics.