When Geim and Novoselov peeled graphene from graphite using adhesive tape, they exploited something profound: the weakness of interlayer bonding in certain crystals. That weakness isn't accidental. It emerges from the quantum mechanical nature of fluctuating electron distributions—van der Waals forces that hold layers together just loosely enough to separate, yet firmly enough to reassemble into precise heterostructures.

This seemingly mundane adhesion physics now underpins an entire field of materials engineering. We stack atomically thin sheets like nanoscale Lego, creating interfaces impossible in conventional growth. The van der Waals gap between layers becomes a design parameter, and the forces governing that gap determine what we can build and how precisely we can build it.

Understanding these forces requires moving beyond standard density functional theory into correlation physics. It demands attention to registry—how atoms in adjacent layers align—and meticulous control over interface contamination. The van der Waals interaction, often dismissed as a weak correction to stronger bonds, becomes the enabling physics for two-dimensional material assembly.

Van der Waals forces between neutral, non-polar layers arise from correlated quantum fluctuations. At any instant, the electron distribution in one layer creates a fluctuating dipole. This dipole induces a correlated response in the neighboring layer, and the time-averaged interaction is attractive. The effect is entirely quantum mechanical—classical electrostatics predicts no attraction between neutral objects.

The magnitude scales as the inverse sixth power of separation for point-like systems, but layered materials require integration over extended surfaces. The result: interaction energy per unit area that decays more slowly with distance, making interlayer cohesion significant even across the characteristic three-angstrom gaps in graphite and transition metal dichalcogenides.

Standard density functional theory fails here. Local and semi-local exchange-correlation functionals miss the long-range correlations generating dispersion. Random phase approximation calculations, coupled-cluster methods, or empirically corrected DFT-D approaches become necessary for quantitative predictions. The computational cost increases substantially, but accuracy demands it.

Interlayer binding energies typically fall in the 15-25 meV per atom range—weak compared to covalent bonds exceeding 1 eV, yet strong enough to maintain crystalline stacking at room temperature. This narrow energy window creates the essential property: layers separate under modest mechanical force but spontaneously reassemble when brought into contact.

The dispersion interaction also determines layer compressibility and shear modulus. Under pressure, the van der Waals gap contracts; under shear, layers slide with low friction. These mechanical properties—combining strong in-plane bonding with weak interlayer coupling—define the anisotropy that makes two-dimensional materials distinctive.

Takeaway

Van der Waals forces occupy a Goldilocks zone: strong enough for structural coherence, weak enough for mechanical separation—and their accurate description requires correlation physics beyond standard computational approximations.

Lateral alignment between adjacent layers profoundly modulates interlayer binding. In graphite, Bernal stacking places half the carbon atoms directly above atoms in the layer below, half above hexagon centers. This specific registry minimizes energy. Displacing one layer creates an energy landscape with periodic minima and maxima—a corrugation potential governing stacking preferences.

When two layers have slightly different lattice constants or are rotated relative to each other, this registry varies spatially. The result is a moiré pattern—a superlattice with periodicity determined by the mismatch. The corrugation potential now oscillates on this larger scale, creating regions of favorable and unfavorable stacking within each moiré unit cell.

These moiré potentials directly impact electronic structure. Electrons experience a periodic modulation superimposed on the atomic lattice. In twisted bilayer graphene near the magic angle, this modulation flattens electronic bands dramatically, enhancing correlation effects and enabling superconductivity. The van der Waals registry effect thus connects to emergent quantum phenomena.

The energy differences between stacking configurations are small—typically a few meV per atom—but their spatial variation creates measurable consequences. Atomic force microscopy reveals the moiré corrugation directly. Transport measurements show resistance variations correlating with local stacking. The weak force leaves strong signatures.

Controlling registry requires precise alignment during assembly or growth. Transfer methods using rotation stages achieve sub-degree accuracy. Thermal annealing can relax interfaces toward preferred stacking. The sensitivity to registry transforms assembly into a precision endeavor where angular errors of fractions of a degree produce qualitatively different electronic behavior.

Takeaway

Moiré physics emerges from the spatial modulation of van der Waals registry—small energy variations across the superlattice translate into profound electronic consequences that depend critically on alignment precision.

The theoretical perfection of van der Waals interfaces—atomically sharp, defect-free, contamination-free—meets the messy reality of fabrication. Transfer techniques mechanically exfoliate flakes onto polymer films, then stamp them onto target substrates or other flakes. Each step introduces potential contamination: polymer residues, atmospheric adsorbates, trapped water or hydrocarbons.

Contamination doesn't distribute uniformly. Van der Waals attraction squeezes mobile contaminants into bubbles and blisters, leaving some regions atomically clean. Interface quality varies across a single heterostructure. Device properties depend on where electrodes contact the stack, which regions channel current, where optical measurements probe.

Hot pickup techniques—transferring flakes at elevated temperature in controlled atmosphere—reduce contamination dramatically. The higher mobility allows adsorbates to diffuse away before being trapped. Annealing assembled stacks further improves interfaces, though thermal expansion mismatches and defect generation constrain temperature limits.

Epitaxial growth offers an alternative to mechanical transfer. Chemical vapor deposition can produce large-area films, and with careful control, grow one two-dimensional material directly on another. Interface quality potentially exceeds transferred structures, but controlling nucleation, domain orientation, and defect density presents distinct challenges.

The van der Waals gap itself isn't truly empty. Electron density tails from each layer overlap in the interlayer region. Density functional calculations show charge redistribution at interfaces, generating interlayer dipoles that shift band alignments. Understanding the interface requires accounting for this electronic structure, not just geometric stacking.

Takeaway

Van der Waals heterostructure quality depends as much on fabrication discipline as on fundamental physics—contamination control and transfer precision determine whether theoretical interface properties manifest in real devices.

Van der Waals forces—quantum fluctuations creating attraction between neutral surfaces—enable a fabrication paradigm impossible with conventional materials. We separate layers nature held together for geological timescales, then reassemble them with atomic precision into structures that never existed.

The physics spans scales: quantum correlations generate the force, atomic registry modulates its strength, moiré patterns impose electronic consequences, and macroscopic transfer techniques determine interface quality. Each level constrains and enables the next.

As computational methods improve and fabrication techniques mature, the design space expands. We approach a regime where van der Waals heterostructures are designed computationally, assembled robotically, and characterized with atomic resolution—transforming the weakest of interactions into a foundation for materials engineering.