The periodic modulation of the electronic potential leads to secondary Dirac cones in the graphene spectrum 9, while the modulation of the adhesion potential is expected to produce periodic in-plane strains of the graphene lattice. This moiré pattern spatially modulates both the electronic coupling, and the vdW adhesion between the graphene and hBN lattices. Graphene on hexagonal boron nitride (hBN) is an excellent testbed for this effect, as a long-wavelength periodic interaction emerges when the two crystals are in near-rotational alignment due to their small lattice mismatch ( δ ∼1.8%) (refs 6, 7, 8). Less immediately apparent, modifying the interlayer separation through pressure can also induce a commensurate match between two crystals with slight lattice mismatch at equilibrium.
The predicted magnitude of the SOI in the graphene also depends critically on the interlayer separation in such structures. For graphene on atomically-heavy materials, such as WSe 2 or topological insulators, the strong substrate spin–orbit interaction (SOI) is predicted to strongly enhance the SOI in the graphene and possibly induce topologically non-trivial insulating states 4, 5. In bilayer graphene, for example, the electronic coupling between the two layers depends exponentially on their separation 2, controlling the effective mass of the charge carriers and the magnitude of the field-tunable band gap 3. Previous work has focused on controlling the properties of these systems through the choice and ordering of the materials in the heterostructure, as well as the rotational alignment between layers 1, but little has been done to explore the interlayer separation degree of freedom. The electronic properties of heterostructures of van der Waals (vdW) materials are expected to depend on the exact nature of the interactions between the composite layers. Our results motivate future studies tailoring the electronic properties of van der Waals heterostructures by controlling the interlayer separation of the entire device using hydrostatic pressure. We find that modifying the interlayer separation directly tunes the lattice strain and induces commensurate stacking underneath the tip. For the special case of aligned or nearly-aligned graphene on boron nitride, the graphene lattice can stretch and compress locally to compensate for the slight lattice mismatch between the two materials. Here, we demonstrate unprecedented control over interlayer interactions by locally modifying the interlayer separation between graphene and boron nitride, which we achieve by applying pressure with a scanning tunnelling microscopy tip. The interaction strength between neighbouring layers, most easily controlled through their interlayer separation, can have significant influence on the electronic properties of these composite materials. Combining atomically-thin van der Waals materials into heterostructures provides a powerful path towards the creation of designer electronic devices.
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