Gradient Electronic Landscapes in van der Waals Heterostructures.

Two-dimensional (2D) materials, such as graphene and hexagonal boron nitride (hBN), provide a versatile platform for quantum electronics. Experiments generally require encapsulation of graphene within hBN flakes, forming a protective van der Waals (vdW) heterostructure that preserves the delicate properties of the embedded crystal. To produce functional devices, heterostructures are typically shaped by electron beam lithography and etching, which have 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 to produce smooth topographic landscapes in vdW heterostructures by patterning the thickness of the top hBN flake with nanometer precision. We electrically gate a sinusoidal topography to impose a periodic electric-field gradient on the graphene layer to spatially modulate charge-carrier density. We observe signatures of the landscape in transport measurements─resistance-peak spreading and commensurability oscillations─establishing this approach for tailoring mathematically precise potentials in quantum electronics.