Moiré patterns — the interference fringes formed when two periodic lattices are overlaid at a slight angle — have become the primary language for describing bilayer 2D materials. The moiré lattice, characterized by its Bravais vectors, encodes the twist angle and lattice mismatch. Engineering moiré materials means controlling these parameters.
The moiré lattice is an incomplete description (arXiv:2603.21446). When two layers are deformed relative to each other (heterodeformation), strain accumulates along networks of domain walls — strain solitons. Different heterodeformations can produce identical moiré Bravais lattices while generating completely different soliton networks. The lattice sees the periodicity; it misses the internal structure.
The soliton network captures what the lattice cannot: topology, connectivity, and the full multilattice geometry of the interface. The researchers establish a one-to-one mapping between heterodeformations and soliton network geometry, parameterized by line vector–Burgers vector pairs borrowed from dislocation theory. The network is a faithful map; the lattice is a lossy compression.
This enables inverse design. Specify the desired soliton network — its connectivity, its domain wall types, its symmetry — and the framework constructs the heterodeformation that produces it. This goes beyond twist-angle engineering, which can only access a subset of possible configurations. Arbitrary heterodeformations access the full space.
The structural insight: the defect network is more informative than the lattice it interrupts. The moiré pattern captures what repeats; the soliton network captures what connects. When two representations disagree about what's the same (identical lattice, different networks), the one that distinguishes more states is the better map. The bulk is ambiguous; the boundaries are specific.