Exact Self-Similar Patterns of Atomic-Layer Boron Nitride with Koch Fractal Complexity

Wulff construction and dendritic morphology are traditional research paradigms for the morphology of two-dimensional (2D) materials. Morphology has a decisive influence on the properties of materials. Breaking through the traditional morphology and opening up a new pattern formation mechanism are expected to give birth to novel physical properties and applications in 2D materials. Here, we found a new fractal pattern formation mechanism with ideal mathematical beauty, the Koch snowflake, which previously only existed in mathematics and computers as an exact fractal with strict self-similarity. We use hexagonal boron nitride (h-BN) with 3-fold symmetry as the model system in the chemical vapor deposition (CVD) process, demonstrating the atomic-layer Koch snowflake arises from the complex coupling of lattice symmetry and the Kardar–Parisi–Zhang interaction of the edge-atomic reacting-diffusion process. By using the growth-etching method, we sculpted the Koch snowflakes, yielding a more delicate nonequilibrium structure─a Koch “leaf”. This work opens many opportunities to explore novel fractal morphologies and devices in 2D materials.