Coverage-Dependent Phase Stability of Pb-Intercalated Buffer-Layer Graphene on SiC(0001)

Understanding the atomic-scale structure and stability of intercalated two-dimensional (2D) metals requires precise theoretical insight. Here, we present an extensive first-principles density functional theory (DFT) investigation of Pb monolayers intercalated beneath a buffer-layer graphene on a SiC(0001) substrate. To minimize lattice-mismatch strain between graphene and SiC, we employ a slightly rotated $\sqrt{61}\times \sqrt{61}$ SiC supercell, 3.67° off the commonly used $\sqrt{3}\times \sqrt{3}$ model. This approach resolves key interfacial motifs, most notably a 10 × 10 hexagonal-like phase with alternating compressive and tensile regions, that cannot be captured with smaller or unrotated models. Systematic exploration over a Pb coverage range of 0.4 < θ ≤ 1.0 reveals a chemical potential landscape featuring diverse thermodynamically stable phases, including periodic 10 × 10 hexagonal, distorted hexagonal, elongated hexagonal, and stripe-like motifs, each associated with distinct out-of-plane corrugations in the decoupled graphene layer. At θ ≈ 0.79, multiple nearly degenerate hexagonal configurations emerge, differing only in Pb arrangements within the intercalated layer, consistent with recent scanning tunneling microscopy (STM) observations. In the intermediate coverage range 0.49 < θ < 0.71, stripe-like motifs exhibit small energy differences (< 20 meV) among themselves and lie only 5-11 meV above the hexagonal phases, explaining the coexistence of multiple patterns in experiments. These findings provide theoretical support for the observed coexistence of distinct interfacial phases and highlight the intricate, atomically precise, coverage-dependent phase stability of Pb-intercalated graphene on SiC(0001).