Coverage-dependent structures and thermodynamic stability of intercalated Gd layers beneath buffer-layer graphene on SiC(0001)

• A strong coverage dependence in chemical potential, driven by Gd-Gd and Gd-substrate interactions. • A thermodynamically favored amorphous-like monolayer at θ≈ 0.4, consistent with experimental findings. • Multilayer or 3D-like Gd structures form beyond θ≈ 0.9, with intercalation affecting ZLG corrugation and interlayer spacing. • Energetic favorability of ordered/disordered phases aligns with experiments, suggesting controlled synthesis of intercalated phases. Electronic properties of two-dimensional (2D) materials are strongly influenced by their atomic arrangements, making the theoretically-aided characterization of experimentally-synthesized 2D structures crucial. Using first-principles density functional theory, we analyze nearly 200 configurations of intercalated Gd layers beneath buffer-layer graphene on SiC(0001) over a Gd coverage range of 0.01 < θ < 1.2 . By fully relaxing selectively-constructed configurations at each coverage within a large, low-strain supercell, we determine the coverage dependence of the chemical potential for intercalated Gd structures. Thermodynamically-preferred configurations below θ ≈ 0.8 form single-atom-thick monolayers, while 3D-like or multilayer structures emerge beyond θ ≈ 0.9 . Most structures are amorphous-like, including the configuration at the chemical potential minimum around θ ≈ 0.4 . In contrast, a strongly stretched Gd(0001)-like monolayer at θ = 1 / 3 and a nearly perfect Gd(0001) monolayer at θ = 1 are significantly less favorable with 0.16 eV and 0.82 eV higher chemical potentials above the minimum, respectively. Furthermore, the graphene layer decoupled by intercalated Gd near the chemical potential minimum is significantly flatter compared to its morphology above intercalated 3D structures at higher coverages and nearly isolated Gd atoms in the lowest coverage region. These findings align with our experimental results and underscore the need for further research on this unique intercalated system, which holds significant potential for diverse applications.