Michael C. Tringides

Nucleation is a fundamental process in nature controlling phase transitions and pattern formation. Classical nucleation is based on the gradual aggregation of diffusing atoms after a critical cluster size is reached. Contrary to these expectations, we have observed in real time the formation of perfect Pb(111) islands with more than 10 ⁵ atoms emerging out of the compressed wetting layer within a few seconds during growth of Pb on Ge(111) below room temperature. Pb deposited on Ge(111) in a temperature range between -30°C and 10°C exhibited explosive nucleation of height-selected islands upon reaching a critical coverage of 1.33±0.07ML with respect to Ge(111). Island nucleation was fueled by the 2% compression of the Pb wetting layer at the critical coverage. The island areas grew linearly with time, exhibiting collective diffusion, where thousands of atoms follow correlated, non-random walk diffusion. The total growth rate was higher with increasing temperature. Density functional theory simulations of the chemical potential and binding sites of the Pb/Ge(111) system give insight into the role of the compression of the wetting layer and the strain within the growing Pb layers, which explain this nonclassical behavior of the system.

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 rotated61×61 SiC supercell, 3.67° off the commonly used 3×3model. 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).

The intercalation of rare-earth metals into the galleries of epitaxial graphene layer(s) grown on SiC(0001) substrate offers a unique synthesis approach to form functional two-dimensional (2D) heterostructures with properties controlled by atomically defined graphene-metal interfaces. The most stable position for the intercalated atoms is found beneath the buffer layer, where they form bonds with the silicon-terminated SiC substrate. Here, we systematically studied the thermally assisted intercalation of gadolinium (Gd) under epitaxial bilayer graphene (BLG) as a function of coverage and annealing temperatures. We identified kinetic conditions to form a non-equilibrium phase, where the intercalants populate the gallery between the top BLG layers. The more energetically favorable structure is also observed, in which Gd atoms diffuse beneath the buffer layer, forming a quasi-ordered “triangular” phase at the SiC interface. Scanning tunneling microscopy and spectroscopy reveal the coexistence of Gd atoms at different subsurface locations in adjacent regions. Density functional theory is employed to model Gd intercalation at various sites and to assess their stability, in agreement with experimental observations. Nano-infrared imaging unambiguously identifies the Gd-intercalated regions at the mesoscale. The successful synthesis of metastable phases in BLG highlights the importance of fine-tuning the kinetic parameters for the precise synthesis of 2D metal-graphene heterostructures.

Recently realized high-mobility semiconducting epitaxial graphene on silicon carbide (SiC) [Zhao, J. Nature 2024, 625 (7993), 60-65, 10.1038/s41586-023-06811-0] provided an important step toward integration of the graphene-based system into active components in postsilicon micro- and nanoelectronics. However, the exact atomic-scale structure and complex bonding configurations of the first epitaxial graphene carbon layer (C_buffer) remain an open problem. Our recent report [Kolmer, M. Communications Physics 2024, 7 (1), 16, 10.1038/s42005-023-01515-3] has shed new light on understanding this interface, where the external transverse electric field-dependent dynamic switching behavior of the C_buffer-SiC bonds was observed. Here, using scanning tunneling microscopy and spectroscopy (STM and STS), we present direct evidence of silicon (Si) vacancies at the interface and provide their distribution at the topmost reconstructed SiC(0001) layer. Bias voltage and epitaxial graphene thickness-dependent characterization of the collective C_buffer-SiC interface showed that "Si" vacancy sites beneath C_buffer are stable under STM electric fields. Moreover, the vacancies introduce localized electronic states below the Fermi level, thereby enhancing the charge-transfer phenomenon across the interface.

Stacking and twisting 2D van der Waals (vdW) layers have become versatile platforms to tune the electron correlation. These platforms rely on exfoliating vdW materials down to a single vdW layer and a few vdW layers. We calculate the intrinsic layer-dependent surface and exfoliation energies of typical vdW materials such as graphite, h-BN, black P, MX₂ (M = Mo or W; X = S, Se, or Te), MX (M = Ga or In; X = S, Se, or Te), Bi₂Te₃, and MnBi₂Te₄ using density functional theory. For exchange-correlation functionals with explicit vdW interaction, a single vdW layer always has the smallest surface energy, giving a surface energy reduction when compared to that of thicker vdW layers. However, the magnitude of this surface energy reduction quickly decreases with an increase in the number of atomic layers inside the single vdW layer for different vdW materials. Such atomic-layer dependence in surface energy reduction helps explain the different effectiveness of exfoliation for different vdW materials down to a single vdW layer.

Intercalation of metal atoms at the SiC(0001)-graphene (Gr) interface can provide confined 2D metal layers with interesting properties. The intercalated Pb monolayer (ML) has shown the coexistence of the Gr(10x10)-moire and a stripe phase, which still lacks understanding. Using density functional theory calculation and thermal annealing with ab initio molecular dynamics, we have studied the formation energy of SiC(0001)/Pb/Gr for different coverages of intercalated Pb. Near the coverage of a Pb(111)-like ML mimicking the (10x10)-moire, we find a slightly more stable stripe structure, where one half of the structure has compressive strain with Pb occupying the Si-top sites and the other half has tensile strain with Pb off the Si-top sites. This stripe structure along the Gr zigzag direction has a periodicity of 2.3 nm across the [1-210] direction agreeing with the previous observations using scanning tunneling microscopy. Analysis with electron density difference and density of states show the tensile region has a more metallic character than the compressive region, while both are dominated by the charge transfer from the Pb ML to SiC(0001). The small energy difference between the stripe and Pb(111)-like structures means the two phases are almost degenerate and can coexist, which explains the experimental observations.

The electronic properties of two-dimensional (2D) material systems strongly depend on their atomic arrangement, so validating the structure of an experimentally fabricated 2D system is an important task for researchers. First-principles density-functional theory (DFT) is used to analyze about 100 configurations of Pb intercalated under buffer-layer graphene on SiC(0001). These configurations are constructed by using seven different types of supercells corresponding to varying strain. By comparing the chemical potentials of the intercalated Pb structures, we find that the thermodynamically most preferred intercalated Pb configurations appear under the low-strained buffer-layer graphene. We also find that plentiful structures with the lowest chemical potentials are amorphous-like Pb monolayers. These are almost energetically degenerate with various Pb(111)-like monolayers having slightly higher chemical potentials. Our DFT results also indicate that intercalated plumbene-like monolayers under the high-strained buffer-layer graphene generally have higher chemical potentials. However, intercalated plumbene-like monolayers under a low-strained buffer-layer graphene do also exist with significantly lower chemical potentials relative to the structures under the high-strained buffer-layer graphene, despite some distortions in their structures. These results are consistent with previously available experimental results and suggest further studies on this unique system to promote the synthesis of phases with the anticipated properties, which are attractive for applications.