Artificial relativistic molecules

The creation of artificial atomic clusters or lattices on solid surfaces offers the potential to tailor electronic, magnetic, and topological properties for both fundamental research and technological applications. Previous studies have explored quantum confinement, topological edge modes, superlattice Dirac bands, flat bands, atomic-scale spin interactions, and topological defects in atomic-scale chains and clusters. Two primary approaches—direct atom-by-atom manipulation and self-assembly—have been employed. However, limitations exist, particularly in fabricating energetically and kinetically unfavorable structures. Template-guided self-assembly offers a potential solution, utilizing templates to create unusual growth environments. Step edges and one-dimensional surface superstructures have been used as templates on various surfaces, resulting in anisotropic clusters. Two-dimensional superstructures, such as moiré structures and metal-organic frameworks, have also been suggested, but the formation of artificial molecules has not been previously reported. This research utilizes a novel template-guided atomic self-assembly technique, leveraging the strong relativistic effects in lead (Pb) atoms to create long-ranged interatomic bonds, thereby producing artificial molecules with relativistic Dirac electronic orbitals. The honeycomb charge-order superstructure of the van der Waals crystal IrTe2 serves as the template, hosting Pb clusters ranging from dimers to heptamers, including benzene-like hexagonal rings. Atomically resolved spectroscopy and electronic structure calculations provide evidence of molecular orbital formation through direct orbital overlap between neighboring Pb adatoms. The study demonstrates the role of spin-orbit coupling (SOC) in enhancing interatomic interaction and creating relativistic molecules at unusually large interatomic distances. This work highlights the unique stabilization of nanoscale assemblies via relativistic effects and the potential of novel superstructures on van der Waals crystals for fabricating otherwise unfavored molecules with unprecedented properties.

The existing literature extensively documents the pursuit of tailored electronic, magnetic, and topological properties in artificially created atomic structures. Early work focused on the quantum confinement effects observed in self-assembled chains and clusters of gold and copper atoms on different substrates, revealing the emergence of one-dimensional band structures. Studies on atomic chains also explored the potential for topological edge modes and superlattice Dirac bands, depending on the arrangement and interaction of the atoms. The creation of artificial atomic lattices, often using techniques like atom-by-atom manipulation, opened avenues to investigate flat bands and atomic-scale spin interactions. Further studies examined the influence of topological defects in these structures and their impact on the overall properties. However, challenges remained in assembling energetically unfavorable structures. The use of templates, like step edges and one-dimensional superstructures on metal and silicon surfaces, demonstrated the ability to induce anisotropic cluster growth. The proposal to utilize two-dimensional superstructures, including moiré patterns in hexagonal boron nitride and metal-organic frameworks, as templates represents a significant advancement in this field, although the formation of artificial molecules with these techniques remained elusive before the present study.

The experimental setup involved depositing Pb atoms on the surface of a cleaved IrTe2 van der Waals crystal. The IrTe2 crystal, known to exhibit a honeycomb charge-order superstructure below 180 K, provided the template for the self-assembly of Pb atoms. Scanning tunneling microscopy (STM) was used to image the Pb clusters formed on the IrTe2 surface with atomic resolution. Scanning tunneling spectroscopy (STS) measurements were performed to characterize the electronic energy levels of the Pb clusters. Density functional theory (DFT) calculations, incorporating spin-orbit coupling (SOC), were used to simulate the atomic structure, electronic structure, and stability of the Pb clusters on the IrTe2 surface. The DFT calculations employed the Vienna ab initio simulation package (VASP) with the generalized gradient approximation (GGA) and projector augmented-wave (PAW) method. A (5 × 5) and (7 × 7) supercell of the IrTe2 surface was modeled, with a vacuum spacing of approximately 23.6 Å to simulate the surface environment. A plane-wave basis set with a cutoff of 211 eV and a 15 × 15 × 1 k-point mesh were used for Brillouin-zone integrations. Structural relaxation was performed until residual forces were below 0.02 eV/Å. The calculated lattice constant of IrTe2 was 3.839 Å. The Fermi level was adjusted to account for discrepancies between theoretical and experimental results, likely due to factors such as the charge-ordered structure, doping effects, and limitations in DFT band-energy calculations. The experimental STM measurements were conducted with a commercial ultrahigh vacuum cryogenic STM at 4.3 K, utilizing PtIr tips. Differential conductance (dI/dV) measurements were obtained using lock-in detection with a 1.17 kHz modulation. The combination of experimental STM/STS and theoretical DFT calculations enabled a comprehensive investigation of the structure and electronic properties of the artificial Pb molecules formed on the IrTe2 template.

The STM images revealed the formation of Pb clusters of various sizes and configurations, ranging from monomers to heptamers, confined within the honeycomb unit cells of the IrTe2 charge-order superstructure. Two characteristic Pb-Pb distances were observed, corresponding to √3a0 and 2a0 (a0 being the IrTe2 lattice constant). The 2a0-spaced dimers were more frequently observed than the √3a0-spaced dimers. Interestingly, benzene-like hexagonal ring clusters were also identified among other configurations. STS measurements revealed the electronic energy levels of the Pb clusters. For a monomer, three main spectral features were observed, corresponding to the relativistic splitting of the 6p valence electrons of Pb due to spin-orbit coupling. In Pb dimers, a clear energy splitting between bonding and antibonding states was observed for the 6p1/2 state, with the magnitude of splitting depending on the Pb-Pb distance. DFT calculations, including SOC, successfully reproduced these experimental observations, demonstrating the formation of relativistic molecular orbitals at unusually large Pb-Pb distances (around 7 Å). The calculations demonstrated that the interaction between Pb atoms is primarily due to SOC and that the 2a0 distance imposed by the substrate is optimal for the formation of Pb dimers. The DFT analysis showed that the 2a0 distance optimizes the balance between ionic repulsion and the energy gain from orbital overlap of adatom-substrate hybridized states. Two key SOC effects were identified: reduced donation of p electrons to the substrate, reducing ionic repulsion, and enhanced orbital overlap of Pb-Te hybridized states. The benzene-like ring-shaped hexamers and pentamers also exhibited interesting molecular orbital formations, confirmed both experimentally through dI/dV maps and theoretically through DFT calculations. The calculations showed a broken AB sublattice symmetry for the lowest-energy state of the hexamer, a Kekulé-like distortion for the second state, and a mirror-symmetry-broken two-fold symmetric bonding feature for the third state. While the DFT underestimated the molecular bonding interaction, the calculations were able to reproduce the spatial characteristics of the molecular orbitals, showing the significance of relativistic effects and the interaction with the substrate. The pentamer displayed edge states at its truncated ends, indicative of circularly delocalized electron systems.

The findings of this study directly demonstrate the creation of artificial relativistic molecules using a template-guided self-assembly approach. The successful formation of these molecules, particularly at unusually large interatomic distances, highlights the crucial role of spin-orbit coupling in both the condensation of Pb atoms and the formation of molecular orbitals. The observation of relativistic Dirac molecular orbitals in the experimental data and the corroboration through DFT calculations establishes a new regime of relativistic chemistry. The unusual bonding and spin structures of these orbitals, combined with the intrinsic electronic properties of the IrTe2 substrate (such as charge ordering and superconductivity), open exciting possibilities for exploring novel quantum phenomena in these artificial molecular systems. The use of a two-dimensional superstructure as a template offers a versatile approach to constructing and controlling artificial molecules. The choice of Pb atoms, with their strong relativistic effects and appropriate interaction strength with the substrate, proved crucial for this success. The research opens avenues for exploring other 2D superstructures as templates, creating a wide range of artificial molecules with tailored properties. The versatility of this technique, combined with atom-by-atom manipulation to control interatomic distances, suggests a broad range of possibilities for future research.

This research successfully fabricated various artificial Pb molecules using a novel honeycomb template based on the charge-ordered superstructure of IrTe2. The formation of molecular orbitals was clearly observed in Pb clusters, ranging from dimers to unusual benzene-ring-type molecules. Spin-orbit coupling played a crucial role in both the condensation of Pb atoms and the formation of molecular orbitals, resulting in unprecedented relativistic Dirac molecules. The unusual bonding and spin structure of these orbitals, combined with the substrate's unique electronic properties, could lead to the development of new quantum systems. Future research should explore different 2D superstructures as templates, expanding the potential of this template-guided self-assembly approach for creating artificial molecules with diverse properties.

While the DFT calculations successfully reproduced many of the experimental observations, there were some discrepancies, particularly in the energy level estimations for the benzene-like hexamer. This difference is likely due to limitations in the model, particularly in fully accounting for the substrate's charge-ordered correlated state and the influence of doping effects from the Pb adsorbates. Future theoretical studies could benefit from improved models that address these complexities. The exact reasons for the selective occupation of honeycomb sites by Pb atoms are not fully understood and warrant further investigation. Furthermore, the study primarily focused on Pb molecules. Exploring other heavy atoms or combinations thereof could reveal additional unique properties and phenomena.