A Strategy for Synthesizing 2D Atomic Layer of Coloring-Triangle Lattice via Interfacial Constraint from the Substrate

Two-dimensional (2D) flat band lattices, like Kagome and coloring-triangle (CT), offer a powerful platform for strong-correlation and topological quantum phenomena, yet their experimental realization remains challenging. We propose a strategy using substrate-constraining effects to form CT lattices through interfacial strain caused by lattice mismatch. By performing first-principles calculations on a few adsorbate–substrate systems, we show that Te forms a thermodynamically and kinetically stable CT monolayer on GaN. We establish atomic-level criteria for CT formation and quantify them into a physics-informed, descriptor-based screening workflow that rapidly prioritizes single- and binary-adsorbate candidates on 3D substrates, thereby avoiding prohibitively expensive high-throughput interface DFT calculations. Electronic-structure calculations further reveal Te p x /p y -dominated 2D metallic states together with a substrate-renormalized CT-derived kagome-like band manifold characterized by Dirac-like dispersion and flat-band features. These results provide a general paradigm for 3D substrate-guided 2D lattice engineering to integrate kagome-equivalent quantum lattices into semiconductor platforms.