Kagome Topology in Two-Dimensional Noble-Metal Monolayers

Two-dimensional (2D) metallic lattices with kagome topology provide a unique platform for exploring the interplay between geometric frustration, reduced coordination, and lattice stability in elemental systems. Motivated by the recent experimental realization of atomically thin gold layers and kagome goldene, we present a first-principles investigation of free-standing kagome monolayers of Cu, Ag, and Au. Using density functional theory combined with lattice dynamics and ab initio molecular dynamics, we systematically assess their structural, mechanical, dynamical, and thermal stability. All kagome monolayers satisfy the 2D Born criteria and exhibit relatively low in-plane stiffness compared to graphene and hexagonal goldene, reflecting the porous nature of the kagome lattice and its metallic bonding. Among the three systems, the Au-based lattice displays the highest in-plane Young’s modulus. Phonon calculations reveal that the unstrained kagome phase is dynamically unstable for all metals. However, a moderate biaxial tensile strain of 5% stabilizes the Ag and Au monolayers, while Cu retains residual unstable modes. Finite-temperature simulations further show that Cu rapidly reconstructs toward a trigonal lattice, Ag remains metastable at low temperature but collapses at room temperature, and Au exhibits competing kagome and trigonal motifs at 300 K, indicating near-degeneracy between these phases. These results establish that strain engineering and atomic size are key determinants of the stability of metallic kagome monolayers and provide guidance for future substrate-supported realizations.

💡 Research Summary

This paper presents a comprehensive first‑principles investigation of free‑standing kagome monolayers composed of the noble metals copper (Cu), silver (Ag), and gold (Au). Using density functional theory (DFT) with the PBE exchange‑correlation functional, the authors optimized the atomic structures, calculated elastic constants, performed phonon analyses via density‑functional perturbation theory, and carried out ab initio molecular dynamics (AIMD) simulations at 50 K and 300 K.

Structural optimization shows that all three metals adopt a hexagonal P6/mmm symmetry with three atoms per primitive cell and a coordination number of four, characteristic of the kagome lattice. The equilibrium lattice constants follow the expected size trend: Cu (a = 4.74 Å) < Au (a = 5.30 Å) < Ag (a = 5.45 Å). The anomalously smaller Au lattice constant relative to Ag is attributed to relativistic contraction of the 6s orbital and enhanced 5d–6s hybridization, which strengthen Au–Au bonds.

Mechanical analysis reveals that the in‑plane elastic constants satisfy the 2D Born stability criteria (C₁₁ > 0 and C₁₁ > |C₁₂|) for all three systems. The calculated 2D Young’s moduli are 31.6 N m⁻¹ (Cu), 27.8 N m⁻¹ (Ag), and 55.4 N m⁻¹ (Au). Although Au exhibits the highest stiffness among the three, all values are roughly an order of magnitude lower than that of graphene (≈340 N m⁻¹) because metallic bonding is less directional and the kagome framework is intrinsically porous, allowing rotational and shear deformations. Compared with the dense triangular “goldene” phase, the kagome goldene’s modulus is reduced by a factor of two to three, underscoring the dominant role of lattice topology in mechanical response.

Phonon dispersion calculations demonstrate that the unstrained kagome monolayers are dynamically unstable: each exhibits imaginary frequencies (negative values) across the Brillouin zone, especially in the low‑frequency region associated with soft shear modes. To probe strain‑induced stabilization, a modest 5 % biaxial tensile strain was applied. Under this strain, Ag and Au display fully positive phonon spectra, indicating that gentle tensile strain can lift the soft modes and render the structures dynamically stable. Cu, however, retains residual imaginary branches even after strain, suggesting that its smaller atomic radius and weaker relativistic bonding cannot accommodate the open kagome geometry sufficiently.

Thermal stability was examined through AIMD simulations on a 4 × 4 × 1 supercell in the NVT ensemble. Cu collapses rapidly into a trigonal lattice at both 50 K and 300 K, with the transition occurring within ~3.5 ps, reflecting a low energy barrier and high susceptibility to thermal fluctuations. Ag remains in the kagome configuration at 50 K but undergoes a similar collapse at 300 K, indicating that thermal energy at room temperature is enough to overcome its reconstruction barrier. Au shows a more nuanced behavior: at 300 K the kagome lattice does not fully transform, but significant distortions develop, and snapshots reveal coexistence of kagome‑like and trigonal‑like motifs. This suggests that the kagome and trigonal phases of gold are nearly degenerate, producing a shallow energy landscape where both structures can be locally stabilized.

The authors discuss the implications of these findings for experimental realization. Since free‑standing kagome monolayers are intrinsically unstable, substrate‑induced constraints, external tensile strain (e.g., via lattice‑mismatched substrates), or chemical passivation could be employed to stabilize them. The fact that a modest 5 % strain suffices for Ag and Au implies that appropriate substrate engineering is a viable route. Cu, however, appears fundamentally unsuitable for a pure kagome monolayer and may require alloying or alternative elements with larger atomic radii.

In summary, the paper establishes that atomic size and relativistic effects are key determinants of the stability of 2D noble‑metal kagome lattices. Mechanical stability is confirmed by Born criteria, but dynamical stability requires strain engineering for Ag and Au, while Cu remains unstable. Thermal simulations reveal that Au sits at the borderline between kagome and trigonal phases, offering a promising platform for strain‑tunable electronic phenomena such as flat bands and Dirac nodes. These insights provide a solid theoretical foundation for future substrate‑supported growth and device applications of metallic kagome monolayers.