2D Kagome Research Articles

Non-Noble Metal Anchored 2D Covalent Organic Framework for Ambient CO2 Fixation to High-Value Compounds.

The catalytic functionalization of CO2 into high-value compounds comprises a promising approach to mitigate its atmospheric content and sustainable generation of fine chemicals. In this respect, covalent organic frameworks (COFs) offer great potential in carbon dioxide capture and utilization. Herein, we report application of a crystalline, nanoporous 2D COF (ET-BP-COF) obtained by condensation of 4,4',4'',4'''-(ethene-1,1,2,2-tetrayl) tetraaniline (ET-NH2) and 2,2'-bipyridyl-5,5'-dialdehyde (BP-CHO) building blocks for strategic utilization of CO2. The ET-BP-COF features a unique 2D kagome (kgm) topology composed of hexagonal and triangular 1D channels decorated with bipyridine sites, which were exploited for covalent anchoring of eco-friendly, alkynophilic Cu(I) by the post-synthetic method. The Cu(I) engrafted COF was applied as a recyclable catalyst for coupling CO2 with alkynes to generate two high-value compounds, α-alkylidene cyclic carbonates (α-ACCs) and 2-oxazolidinones. Notably, Cu(I)@ET-BP-COF demonstrated excellent catalytic performance for transforming propargylic amine and CO2 to 2-oxazolidinone, an essential building block for antibiotics. Besides, an efficient transformation of propargylic alcohols to generate α-ACCs, valuable commodity chemicals, has been achieved by utilizing carbon dioxide. Further, detailed theoretical simulations disclosed the insight mechanistic path of Cu(I) catalyzed coupling of CO2 and alkynes to produce 2-oxazolidinones and α-ACCs. Significantly, the Cu(I)@COF was reusable for multiple cycles without losing framework rigidity and catalytic performance. This study showcases the potential application of ET-BP-COF for stable anchoring of eco-friendly metals as catalytic sites for effective utilization of CO2 to produce two high-value products, 2-oxazolidinones and α-ACCs, under mild atmospheric conditions.

Tunable Ambipolar Transport in a 2D Kagome Semiconductor

AbstractThe interference of electronic wavefunctions within a Kagome lattice can result in a flat band structure, where low‐energy electrons exhibit highly correlated behavior, facilitating exploration of interactions among intriguing electronic states. However, the inherent high carrier density in most known Kagome materials often hampers the manipulation of these quantum phenomena through conventional means, such as gate voltage. In this work, a unique tunability in the electrical and optoelectronic properties of exfoliated Nb3I8, a 2D semiconductor featuring a “breathing” Kagome lattice is uncovered. Characterization via temperature‐dependent ARPES confirms its semiconducting nature with a flat band structure. Experimental results from bias and gate voltage dependent transport measurements on thin film Nb3I8 transistor devices demonstrate ambipolar conductance. Notably, these findings reveal a broadband photoresponse in the device, spanning from visible to near infrared wavelengths (532 −1100 nm), with the photocurrent showing gate‐dependent characteristics that mirror the dark current's ambipolar nature. This observation marks the first instance of ambipolar transport in a Kagome semiconductor, opening up exciting new avenues for electronic and optoelectronic device development.

Atomically Thin Two-Dimensional Kagome Flat Band on the Silicon Surface.

In condensed matter physics, the Kagome lattice and its inherent flat bands have attracted considerable attention for their prediction and observation to host a variety of exotic physical phenomena. Despite extensive efforts to fabricate thin films of Kagome materials aimed at modulating flat bands through electrostatic gating or strain manipulation, progress has been limited. Here, we report the observation of a d-orbital hybridized Kagome-derived flat band in Ag/Si(111) as revealed by angle-resolved photoemission spectroscopy. Our findings indicate that silver atoms on a silicon substrate form an unconventional distorted breathing Kagome structure, where a delicate balance in the hopping parameters of the in-plane d-orbitals leads to destructive interference, resulting in double flat bands. The exact quantum destructive interference mechanism that forms the flat band is uncovered in a rigorous manner that has not been described before. These results illuminate the potential for integrating metal-semiconductor interfaces on semiconductor surfaces into Kagome physics, particularly in exploring the flat bands of ideal 2D Kagome systems.

Atomically Thin Kagome-Structured Co9Te16 Achieved through Self-Intercalation and Its Flat Band Visualization.

Kagome materials have recently garnered substantial attention due to the intrinsic flat band feature and the stimulated magnetic and spin-related many-body physics. In contrast to their bulk counterparts, two-dimensional (2D) kagome materials feature more distinct kagome bands, beneficial for exploring novel quantum phenomena. Herein, we report the direct synthesis of an ultrathin kagome-structured Co-telluride (Co9Te16) via a molecular beam epitaxy (MBE) route and clarify its formation mechanism from the Co-intercalation in the 1T-CoTe2 layers. More significantly, we unveil the flat band states in the ultrathin Co9Te16 and identify the real-space localization of the flat band states by in situ scanning tunneling microscopy/spectroscopy (STM/STS) combined with first-principles calculations. A ferrimagnetic order is also predicted in kagome-Co9Te16. This work should provide a novel route for the direct synthesis of ultrathin kagome materials via a metal self-intercalation route, which should shed light on the exploration of the intriguing flat band physics in the related systems.

Synthesis and characterization of low-dimensional N-heterocyclic carbene lattices.

The covalent interaction of N-heterocyclic carbenes (NHCs) with transition metal atoms gives rise to distinctive frontier molecular orbitals (FMOs). These emergent electronic states have spurred the widespread adoption of NHC ligands in chemical catalysis and functional materials. Although formation of carbene-metal complexes in self-assembled monolayers on surfaces has been explored, design and electronic structure characterization of extended low-dimensional NHC-metal lattices remains elusive. Here we demonstrate a modular approach to engineering one-dimensional (1D) metal-organic chains and two-dimensional (2D) Kagome lattices using the FMOs of NHC-Au-NHC junctions to create low-dimensional molecular networks exhibiting intrinsic metallicity. Scanning tunneling spectroscopy and first-principles density functional theory reveal the contribution of C-Au-C π-bonding states to dispersive bands that imbue 1D- and 2D-NHC lattices with exceptionally small work functions.

The type-I, III nodal ring, type-I, III quadratic nodal point, and Dirac valley phonons in 2D kagome lattices M2C3 (M = As, Bi, Cd, Hg, P, Sb, Zn)

Topological phases in kagome systems have garnered considerable interest since the introduction of the colloidal kagome lattice. Our study employs first-principle calculations and symmetry analysis to predict the existence of ideal type-I, III nodal rings (NRs), type-I, III quadratic nodal points (QNPs), and Dirac valley phonons (DVPs) in a collection of two-dimensional (2D) kagome lattices M2C3 (M = As, Bi, Cd, Hg, P, Sb, Zn). Specifically, the Dirac valley points (DVPs) can be observed at two inequivalent valleys with Berry phases of +π and −π , connected by edge arcs along the zigzag and armchair directions. Additionally, the QNP is pinned at the Γ point, and two edge states emerge from its projections. Notably, these kagome lattices also exhibit ideal type-I and III nodal rings protected by time inversion and spatial inversion symmetries. Our work examines the various categories of nodal points and nodal ring phonons within the 2D kagome systems and presents a selection of ideal candidates for investigating topological phonons in bosonic systems.

Local gate control of Mott metal-insulator transition in a 2D metal-organic framework

Electron-electron interactions in materials lead to exotic many-body quantum phenomena, including Mott metal-insulator transitions (MITs), magnetism, quantum spin liquids, and superconductivity. These phases depend on electronic band occupation and can be controlled via the chemical potential. Flat bands in two-dimensional (2D) and layered materials with a kagome lattice enhance electronic correlations. Although theoretically predicted, correlated-electron Mott insulating phases in monolayer 2D metal-organic frameworks (MOFs) with a kagome structure have not yet been realised experimentally. Here, we synthesise a 2D kagome MOF on a 2D insulator. Scanning tunnelling microscopy (STM) and spectroscopy reveal a MOF electronic energy gap of ∼200 meV, consistent with dynamical mean-field theory predictions of a Mott insulator. Combining template-induced (via work function variations of the substrate) and STM probe-induced gating, we locally tune the electron population of the MOF kagome bands and induce Mott MITs. These findings enable technologies based on electrostatic control of many-body quantum phases in 2D MOFs.

Asymptotic, second-order homogenization of linear elastic beam networks

We propose a general approach to the higher-order homogenization of discrete elastic networks made up of linear elastic beams or springs in dimension 2 or 3. The network may be nearly (rather than exactly) periodic: its elastic and geometric properties are allowed to vary slowly in space, in addition to being periodic at the scale of the unit cell. The reference configuration may be prestressed. A homogenized strain energy depending on both the macroscopic strain ɛ and its gradient ∇ɛ is obtained by means of a two-scale expansion. The homogenized energy is asymptotically exact two orders beyond that obtained by classical homogenization. The homogenization method is implemented in a symbolic calculation language and applied to various types of networks, such as a 2D honeycomb, a 2D Kagome lattice, a 3D truss and a 1D pantograph. It is validated by comparing the predictions of the microscopic displacement to that obtained by full, discrete simulations. This second-order method remains highly accurate even when the strain gradient effects are significant, such as near the lips of a crack tip or in regions where a gradient of pre-strain is imposed.

Computation insights of kagome structure for probing electronic and thermodynamic properties by applying external factors such as strain, spin-orbital coupling, and external magnetic field

In this study, we explored the electronic properties of a two-dimensional (2D) kagome lattice in the presence of an external magnetic field, spin-orbit coupling (SOC), and strain. Our focus was on investigating the energy-dependent behavior of the electronic heat capacity and paramagnetic spin susceptibility in response to changing factors. Employing the Green's function approach, we successfully determined the energy dependence of the electronic heat capacity and paramagnetic susceptibility using the tight-binding model. Notably, at low energies, the electronic heat capacity almost reaches the Schottky anomaly peak, while the paramagnetic susceptibility sharply decreases. Furthermore, we conducted a detailed investigation of the energy-dependent paramagnetic susceptibility and electronic heat capacity of a kagome lattice monolayer, considering the influences of SOC and magnetic field factors. Our investigation of the density of states (DOS) in the presence of SOC suggests that semimetal-to-insulator phase transitions occur. Additionally, throughout our study, we observed variations in the DOS spectrum, indicating the influence of both compressive and tensile strains. We found that these alterations, along with the splitting of levels under different conditions, led to changes in the material's electrical properties.

Chiral breathing-valley locking in two-dimensional kagome lattice Ta3I8

The exploration of valley-related physics is essential to the development and refinement of valleytronics. Here, a paradigm called chiral breathing-valley locking (CBVL) is proposed, in which two chiral “breathing” phases are completely locked to their valley indexes. Utilizing first-principles calculations, a two-dimensional (2D) kagome lattice with large spontaneous valley polarization (VP), namely, monolayer Ta3I8, is proposed to realize CBVL. There are two breathing phases with chiral symmetry in Ta3I8, and they can change to each other under some conditions. The valley indexes change between “−K” and “K” along the breathing of the two chiral symmetric phases, so CBVL can be obtained. Remarkably, the VP is up to 199.7 meV, so CBVL can cause the obvious switching of the anomalous valley Hall effect (AVHE). Additionally, a 2D Janus Kagome structure TaI4X4 is constructed to confirm experimentally the feasibility of electric field modulation on the CBVL. The built-in electric field and the breathing mode can mutually influence each other in TaI4X4, which provides a synergistic regulation of the AVHE. Our findings broaden the horizon for exploring AVHE materials and provide a platform for future valleytronic applications.

Prediction of a two-dimensional high Curie temperature Weyl nodal line kagome semimetal.

Kagome lattices may have numerous exotic physical properties, such as stable ferromagnetism and topological states. Herein, combining the particle swarm structure search method with first-principles calculations, we identify a two-dimensional (2D) kagome Mo2Se3 crystal structure with space group P6/mmm. The results show that 2D kagome Mo2Se3 is a 100% spin-polarized topological nodal line semimetal and exhibits excellent ambient stability. The band crossing points form two nodal loops around the high-symmetry points Γ and K. On the other hand, Mo2Se3 shows intrinsic ferromagnetism with a large magnetic moment of 3.05 μB per Mo atom and magnetic anisotropy energy (MAE) of 4.78 meV. Monte Carlo simulations estimate that Mo2Se3 possesses a high Curie temperature of about 673 K. In addition, its ferromagnetic ground state can be well preserved under external strain, and the MAE can be improved by increasing the strain. More importantly, the position of each nodal line can be adjusted to the Fermi level through hole doping. This multifunctional 2D magnetic material that combines spin and topology has great potential in the field of nanoscale spintronic devices.

Anomalous Nernst effect in honeycomb and kagome magnet LaCo5 at room temperature

Magnetic order-induced time reversal symmetry breaking in the kagome lattice is predicted to generate Weyl semimetal and Chern insulating phases. The two-dimensional (2D) honeycomb lattices with spin orbit coupling (SOC) and ferromagnetism are also known to host the Chern insulating phase. Here, we study the transport properties of the ferromagnetic topological material LaCo5 crystals with TC = 840 K, which is the highest among the reported magnetic topological materials up to now. It is composed of 2D Co2 kagome layers that are separated by La–Co1 layers, in which the Co1 atoms exhibit a honeycomb structure. Both the 2D kagome and honeycomb layers exhibit out-of-plane magnetization. The large intrinsic anomalous Hall effect and anomalous Nernst effect of about 4.6 μVK−1 are observed in the ab plane with the B//c configuration at room temperature, which can be attributed to non-zero Berry curvature according to the first-principles calculations. Our results enrich the magnetic topological materials with honeycomb and kagome lattices, providing a good platform for the further study of the QAHE. The excellent thermoelectric performance, high TC, nontoxicity, and low cost also make LaCo5 a promising candidate for the applications of thermoelectric generators and heat flow sensors at high temperatures.

On Degree-Based Topological Indices of Kagome Graphene, and Carbon Kagome Nanotubes and Nanotori

Approaches based on graph descriptors have been used in cheminformatics and bioinformatics for molecular property prediction. In this article, we apply partition technique and simple counting schemes to describe the structure of a two-dimensional (2D) kagome graphene and then derive the closed form of various degree-based topological indices (graph descriptor) of 2D kagome graphene, and its tubular and toroidal forms.

On-Surface Synthesis of Novel Kagome Lattices Coordinated via Four-Fold N-Ag Bonding.

The Kagome lattice structures based on metal-organic coordination have garnered widespread interest because of their topologically Dirac/flat bands and other exotic electronic structures. However, the experimental fabrication of large-area two-dimensional (2D) Kagome lattice structures of metal-organic frameworks (MOFs) via on-surface synthesis remains limited. Herein, we successfully construct two kinds of large-scale 2D Kagome-type lattices stabilized by 4-fold N-Ag coordination on the Ag(111) surface. With the aid of scanning tunneling microscopy (STM) and synchrotron radiation photoemission spectroscopy (SRPES), we clearly elucidate the reaction pathway and mechanism of fabrication of the two Kagome lattices. This work provides a novel platform for investigating related intriguing physical properties.

Optically induced reconfigurable Kagome photonic lattice assisted by a liquid crystal spatial light modulator

A 2D Kagome photonic lattice possesses special band structures involving a flat band that allows the localization state and Dirac cones that show linear dispersion. Here, we report the construction of an instantaneously reconfigurable electromagnetically induced Kagome lattice in a Λ-type 85Rb atomic configuration theoretically and experimentally under the condition of electromagnetically induced transparency, which is excited by a weak Gaussian probe field and a strong coupling field with a Kagome intensity profile. The incident Gaussian probe field is discretely diffracted into a Kagome profile inside the atomic vapor cell with a spatially modulated susceptibility, which is induced by the structured coupling field generated by a liquid crystal spatial light modulator. We also explored the dynamical evolution of the probe field inside the Kagome photonic lattice by manipulating systematic parameters. This current work provides an alternative way to design instantaneously reconfigurable Kagome photonic lattices with a simplified experimental configuration. The instantaneous tunability may help to promote the discovery of underlying beam dynamics and the design of tunable devices relying on the properties of Kagome photonic structures.

A two-dimensional kagome magnet with tunable topological phases

Kagome magnets have garnered a lot of investigation due to their plentiful topological states and promising, strong correlated phenomena. However, there have been few reports of two-dimensional (2D) van der Waals kagome magnets. Here, we suggest a stable 2D van der Waals kagome material, V3Br8, which exhibits a ferromagnetic ground state with a Curie temperature of 89 K. Near the Fermi level, there is only a set of three kagome bands from one spin species, which possesses Van Hove singularities at the M point and a Weyl point at the K point. It is interesting that its ground state is gapless at the K point and maintains a 2D Weyl half semimetal state even in the presence of spin-orbit coupling, while when the magnetization rotates from the in-plane direction of the ground state to the out-of-plane direction, the spin-orbit coupling will open an energy gap at the K point, resulting in a topological phase transition to a quantum anomalous Hall effect state. We further demonstrate that the tensile strain can optimize the band structure and raise the Curie temperature to above 100 K. In addition, a Li atom intercalated V3Br8 (V3Br8Li) is revealed to be a stable structure that can successfully tune the Fermi level to the Weyl point while maintaining the ferromagnetic ground state. Moreover, V3Br8Li displays an out-of-plane magnetism, producing the quantum anomalous Hall effect . Our findings provide a solid foundation for future research into topological states and singular effects in 2D kagome magnets.

Magnetic phase diagram of the breathing-kagome antiferromagnet Nd3BWO9

The newly discovered Nd${}_{3}$BWO${}_{9}$ is a rare instance of a disorder-free magnet with an exchange topology interpolating between 2D kagome and 1D spin tubes. In this study, an array of measurements reveals its exotic phase diagram. The complex frustration mechanism results in several ordered phases, including two different, typically two-dimensional 1/3- magnetization plateaux. Meanwhile, one-dimensional tube correlations are unequivocally identified by signatures in both thermodynamic and microscopic probes.

Spontaneous magnetization of Kagome lattice in Ising model

The spontaneous magnetization of the Kagome lattice in the Ising model is thoroughly investigated. The proof of the fallacy of spontaneous magnetization obtained earlier and repeatedly migrating from publication to publication is given. An exact expression is presented in the standard Onsager form for spontaneous magnetization in the anisotropic case (depending on arbitrary values and the signs of exchange interactions in all three directions on the Kagome lattice). The frustration properties of the Ising model on 2D Kagome lattice comprehensively studied including the conditions for frustration appearance. The properties of 3D Kagome materials (sometimes contradictory) are explained on the basis of obtained rigorous theoretical results.

Crystal Structures and Physicochemical Properties of Be2N and Mg2N as Electride Materials

Electrides are a special family of materials with exotic physical properties and various crystal structures in different dimensions. Among them, alkaline-earth metal nitrides (${\mathrm{AE}}_{2}\mathrm{N}$) have attracted enormous attention, since the synthesis of ${\mathrm{Ca}}_{2}\mathrm{N}$ as a two-dimensional (2D) electride. However, apart from ${\mathrm{Ca}}_{2}\mathrm{N}$, the physicochemical properties of other ${\mathrm{AE}}_{2}\mathrm{N}$ are not well understood, and in some cases, their crystal structures remain unknown. To overcome these issues, here, we conduct systematic investigations into the crystal structures, electronic structures, and optical properties of two typical ${\mathrm{AE}}_{2}\mathrm{N}$, i.e., ${\mathrm{Mg}}_{2}\mathrm{N}$ and ${\mathrm{Be}}_{2}\mathrm{N}$, based on first-principles calculations. By symmetry analysis, we derive a crystal structure with $R\overline{3}m$ symmetry for ${\mathrm{Be}}_{2}\mathrm{N}$, which is energetically more stable than all the other structures proposed previously. Our calculations show that $R\overline{3}m$ ${\mathrm{Be}}_{2}\mathrm{N}$ is a 2D electride with the anionic electrons located in the interstitial space, forming a 2D Kagome lattice. Moreover, distinct from traditional 2D electrides, it exhibits anomalous physicochemical properties, such as having a small interstitial space, a high work function, and a large cleavage energy, mainly due to the relatively strong bonding effect between anionic electrons and cationic framework. For ${\mathrm{Mg}}_{2}\mathrm{N}$, on the other hand, we find that the most stable structure has R3m symmetry, which shows a total energy of 0.005 eV per formula unit lower than the previously predicted Cmcm structure. Moreover, different from $R\overline{3}m$ ${\mathrm{Be}}_{2}\mathrm{N}$, R3m ${\mathrm{Mg}}_{2}\mathrm{N}$ is identified as a zero-dimensional (0D) electride with a semiconducting band structure, since its anionic electrons are confined in separated 0D cavities and cannot interact with each other. These studies thus provide a deeper understanding of the crystal structures and physicochemical properties of ${\mathrm{Be}}_{2}\mathrm{N}$ and ${\mathrm{Mg}}_{2}\mathrm{N}$ as potential electride materials.

Targeted Synthesis of Isomeric Naphthalene‐Based 2D Kagome Covalent Organic Frameworks

AbstractTargeted synthesis of kagome (kgm) topologic 2D covalent organic frameworks remains challenging, presumably due to the severe dependence on building units and synthetic conditions. Herein, two isomeric “two‐in‐one” monomers with different lengths of substituted arms based on naphthalene core (p‐Naph andm‐Naph) are elaborately designed and utilized for the defined synthesis of isomerickgmNaph‐COFs. The two isomeric frameworks exhibit splendid crystallinity and showcase the same chemical composition and topologic structure with, however, different pore channels. Interestingly, C60is able to uniformly be encapsulated into the triangle channels ofm‐Naph‐COF via in situ incorporation method, while not the isomericp‐Naph‐COF, likely due to the different pore structures of the two isomeric COFs. The resulting stable C60@m‐Naph‐COF composite exhibits much higher photoconductivity than them‐Naph‐COF owing to charge transfer between the conjugated skeletons and C60guests.