Two-dimensional Kagome Lattice Research Articles

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.

Emergence of Two-Dimensional F-Induced Kagome Lattice on the Cu(111) Surface

Emergence of Two-Dimensional F-Induced Kagome Lattice on the Cu(111) Surface

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.

Designer artificial chiral kagome lattice with tunable flat bands and topological boundary states

The kagome lattice is a well-known model system for the investigation of strong correlation and topological electronic phenomena due to the intrinsic flat band, magnetic frustration, etc. Introducing chirality into the kagome lattice would bring about new physics due to the unique symmetry, which is still yet to be fully explored. Here we report the investigation on a two-dimensional chiral kagome lattice utilizing tight binding band calculation and topological index analysis. It is found that the periodic chiral kagome lattice would bring about a robust zero-energy flat band. Furthermore, in the Su–Schrieffer–Heeger type dimer-/trimerized breathing chiral kagome lattice with particular edge terminations, topological corner states or metallic edge states would appear, implying new candidates for the second-order topological insulator. We also proposed the construction strategy for such lattices employing the scanning tunneling microscope atom manipulation technique.

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.

Kagome surface states and weak electronic correlation in vanadium-kagome metals

RVSn (R = Y and lanthanides) with two-dimensional vanadium-kagome surface states is an ideal platform to investigate kagome physics and manipulate the kagome features to realize novel phenomena. Utilizing the micron-scale spatially resolved angle-resolved photoemission spectroscopy and first-principles calculations, we report a systematical study of the electronic structures of RVSn (R = Gd, Tb, and Lu) on the two cleaved surfaces, i.e. the V- and RSn1-terminated (001) surfaces. The calculated bands without any renormalization match well with the main ARPES dispersive features, indicating the weak electronic correlation in this system. We observe ‘W’-like kagome surface states around the Brillouin zone corners showing R-element-dependent intensities, which is probably due to various coupling strengths between V and RSn1 layers. Our finding suggests an avenue for tuning electronic states by interlayer coupling based on two-dimensional kagome lattices.

Fragile topological phase on the triangular kagome lattice and its bulk-boundary correspondence

We predict and examine various topological states on a two-dimensional (2D) triangular kagome lattice (TKL) using the tight-binding (TB) models and theory of topological quantum chemistry (TQC). Firstly, on the basis of TQC, we diagnose band structures with fragile topology and calculate Wilson-loop spectra and Hofstadter butterfly spectra to confirm their non-trivial nature. Secondly, we examine the bulk-boundary correspondence and find that an obstructed-atomic-limit (OAL) insulator hosts fractional corner states without being accompanied by fragile topological band structures, which implies that the presence of OALs and corner states is not a sufficient condition to fragile topology. Last but not least, we predict a topological phase transition from a second-order topological phase to a first-order topological phase that can be realized in the TKL under the action of a magnetic field.

Electronic properties of two-dimensional kagome lattice based on transition metal phthalocyanine heterojunctions

Transition metal phthalocyanine molecules serve as building blocks for two-dimensional (2D) metal-organic frameworks with potential applications in optics, electronics, and spintronics. Previous theoretical studies predicted that a two-dimensional transition metal phthalocyanine framework with kagome lattice (kag-TMPc) has stable magnetically ordered properties, which are promising for spintronics and optoelectronics. However, there is a lack of studies on their heterojunctions, which can effectively tune the properties through interlayer coupling despite its weak nature. Here we use the density functional theory (DFT) to calculate the electronic properties of eight representative 2D kag-TMPc vertical heterojunctions with two different stackings (AA and AB) and interlayer distances. We find that most of the kag-MnPc-based heterojunctions can maintain the electronic properties of monolayer materials with low bandgap. The kag-MnPc/ZnPc is a ferromagnetic semiconductor with magnetic exchange energy above 40 meV, regardless of stacking sequences; the electronic properties of kag-MnPc/MnPc heterojunctions change from magnetic half-metal to magnetic semiconductor during the transition from AA stacking to AB stacking. Interestingly, the AB stacked kag-CuPc/CoPc heterojunction is a ferromagnetic semiconductor, and the spin-polarized energy band arrangement changes with the layer spacing: when the layer spacing is as long as the equilibrium distance, the spin-up and spin-down energy bands are aligned as type II; when the layer spacing increases by 0.2 Å, the spin-up energy bands are aligned as type-I energy bands, while the spin-down energy bands are aligned as type-II energy bands. This distance-dependent spin properties can realize magnetic optoelectronic “switching” and has potential applications in new magnetic field modulated electromagnetic and optoelectronic devices.

Tunable topological Dirac surface states and van Hove singularities in kagome metal GdV6Sn6.

Transition-metal-based kagome materials at van Hove filling are a rich frontier for the investigation of novel topological electronic states and correlated phenomena. To date, in the idealized two-dimensional kagome lattice, topologically Dirac surface states (TDSSs) have not been unambiguously observed, and the manipulation of TDSSs and van Hove singularities (VHSs) remains largely unexplored. Here, we reveal TDSSs originating from a ℤ2 bulk topology and identify multiple VHSs near the Fermi level (EF) in magnetic kagome material GdV6Sn6. Using in situ surface potassium deposition, we successfully realize manipulation of the TDSSs and VHSs. The Dirac point of the TDSSs can be tuned from above to below EF, which reverses the chirality of the spin texture at the Fermi surface. These results establish GdV6Sn6 as a fascinating platform for studying the nontrivial topology, magnetism, and correlation effects native to kagome lattices. They also suggest potential application of spintronic devices based on kagome materials.

Discovery of charge density wave in a kagome lattice antiferromagnet.

A hallmark of strongly correlated quantum materials is the rich phase diagram resulting from competing and intertwined phases with nearly degenerate ground-state energies1,2. A well-known example is the copper oxides, in which a charge density wave (CDW) is ordered well above and strongly coupled to the magnetic order to form spin-charge-separated stripes that compete with superconductivity1,2. Recently, such rich phase diagrams have also been shown in correlated topological materials. In 2D kagome lattice metals consisting of corner-sharing triangles, the geometry of the lattice can produce flat bands with localized electrons3,4, non-trivial topology5-7, chiral magnetic order8,9, superconductivity and CDW order10-15. Although CDW has been found in weakly electron-correlated non-magnetic AV3Sb5 (A = K, Rb, Cs)10-15, it has not yet been observed in correlated magnetic-ordered kagome lattice metals4,16-21. Here we report the discovery of CDW in the antiferromagnetic (AFM) ordered phase of kagome lattice FeGe (refs. 16-19). The CDW in FeGe occurs at wavevectors identical to that of AV3Sb5 (refs. 10-15), enhances the AFM ordered moment and induces an emergent anomalous Hall effect22,23. Our findings suggest that CDW in FeGe arises from the combination of electron-correlations-driven AFM order and van Hove singularities (vHSs)-driven instability possibly associated with a chiral flux phase24-28, in stark contrast to strongly correlated copper oxides1,2 and nickelates29-31, in which the CDW precedes or accompanies the magnetic order.

Corner- and sublattice-sensitive Majorana zero modes on the kagome lattice

In a first-order topological phase with sublattice degrees of freedom, a change in the boundary sublattice termination has no effect on the existence of gapless boundary states in dimensions higher than one. However, such a change may strongly affect the physical properties of those boundary states. Motivated by this observation, we perform a systematic study of the impact of sublattice terminations on the boundary physics on the two-dimensional kagome lattice. We find that the energies of the Dirac points of helical edge states in two-dimensional first-order topological kagome insulators sensitively depend on the terminating sublattices at the edge. Remarkably, this property admits the realization of a time-reversal invariant second-order topological superconducting phase with highly controllable Majorana Kramers pairs at the corners and sublattice domain walls by putting the topological kagome insulator in proximity to a $d$-wave superconductor. Moreover, substituting the $d$-wave superconductor with a conventional $s$-wave superconductor, we find that highly controllable Majorana zero modes can also be realized at the corners and sublattice domain walls if an in-plane Zeeman field is additionally applied. Our study reveals promising platforms to implement highly controllable Majorana zero modes.

Topological flat bands in a kagome lattice multiorbital system

Flat bands and dispersive Dirac bands are known to coexist in the electronic bands in a two-dimensional kagome lattice. Including the relativistic spin-orbit coupling, such systems often exhibit nontrivial band topology, allowing for gapless edge modes between flat bands at several locations in the band structure, and dispersive bands or at the Dirac band crossing. Here, we theoretically demonstrate that a multiorbital system on a kagome lattice is a versatile platform to explore the interplay between nontrivial band topology and electronic interaction. Specifically, here we report that the multiorbital kagome model with the atomic spin–orbit coupling naturally supports topological bands characterized by nonzero Chern numbers {{{{{{{mathcal{C}}}}}}}}, including a flat band with | {{{{{{{mathcal{C}}}}}}}}| =1. When such a flat band is 1/3 filled, the non-local repulsive interactions induce a fractional Chern insulating state. We also discuss the possible realization of our findings in real kagome materials.

Facile Synthesis of Conductive Metal-Organic Frameworks Nanotubes for Ultrahigh-Performance Flexible NO Sensors.

Cu-benzenehexathiol (Cu-BHT) has attracted significant attention due to its record high electrical conductivity and crystal defects Cu2c . However, the nonporous structure and small specific surface area of Cu-BHT with two-dimensional kagome lattice invariably limit its practical application in sensing and catalysis. In this work, Cu-BHT nanotubes (Cu-BHT-NTs) are designed and prepared via a facile homogeneous reaction to solve these problems. Compared with the traditional nanorod-like structure, the Cu-BHT-NTs not only have a higher specific surface area but also possess a higher proportion of crystal defects (66.6%). The successfully configured DPPTT/Cu-BHT-NTs heterostructure organic field-effect transistor (OFET)-based sensor exhibits excellent sensitivity as high as 13610%, a minimum detection limits down to 5ppb, and exceptional selectivity to nitric oxide (NO) toxic gases. Theoretical analysis systematically shows that Cu2c sites in the Cu-BHT-NTs increase the number of electrons transferred from the heterostructure to NO molecules, confirming that the high sensitivity and selectivity result from the high binding between Cu-BHT-NTs and NO molecules. Furthermore, a fully flexible device based on the heterojunction OFET sensor is prepared to ensure the convenience of wearing and carrying gas sensors, opening up a new avenue for the next generation of wearable intelligent electronics.

Twisting and Rippling of a Two-Dimensional Kagome Lattice: Silica on Au(111)

Twisting and Rippling of a Two-Dimensional Kagome Lattice: Silica on Au(111)

Synthesis of the Two-Dimensional Robust Kagome Lattice on Au(111) via the Introduction of Fe Atoms

Synthesis of the Two-Dimensional Robust Kagome Lattice on Au(111) via the Introduction of Fe Atoms

Controlling the magnetic properties of two-dimensional carbon-based Kagome polymers

With the help of first principles calculations, we have explored a promising route to control the magnetic properties of two-dimensional organic polymers based on all-carbon triangulene monomers. Similar to small triangulene nanostructures, the Kagome-organized triangulene polymer exhibits an antiferromagnetic ground state, but behaves as a Mott-insulator with relatively poor carrier mobilities. The doping of triangulenes with boron or nitrogen atoms contributes to switch the ground state of the polymer into a stable ferromagnetic phase, well separated in energy from the antiferromagnetic phase. The existence of a stable ferromagnetic phase is a direct consequence of electron confinement within B/N-rich triangulenes, where the D3h symmetry of the monomers in the Kagome pattern plays a major role on the resulting electronic structure properties. In addition, the two-dimensional Kagome lattice arrangement of B-rich triangulene polymer leads to highly dispersed spin-polarized semiconducting bands and high carrier mobilities that largely exceed known values for pure silicon. In contrast, the ferromagnetic phase of N-rich polymer shows half-metallic behaviour with lower mobilities than B-rich cases. Our results suggest that triangulene-based polymers could be used in diverse sectors from spin-based logic devices to quantum storage applications.

Emergent Kagome Electrides.

In a two-dimensional (2D) Kagome lattice, the ideal Kagome bands including Dirac cones, van Hove singularities, and a flat band are highly expected, because they can provide a promising platform to investigate novel physical phenomena. However, in the reported Kagome materials, the complex 3D and multiorder electron hoppings result in the disappearance of the ideal Kagome bands in these systems. Here, we propose an alternative way to achieve the ideal Kagome bands in non-Kagome materials by confining excess electrons in the system to the crystal interstitial sites to form a 2D Kagome lattice, coined as a Kagome electride. Then, we predict two novel stable 2D Kagome electrides in hexagonal materials Li5Si and Li5Sn, whose band structures are similar to the ideal Kagome bands, including topological Dirac cones with beautiful Fermi arcs in their surface states, van Hove singularities, and a flat band. In addition, Li5Si is revealed to be a low-temperature superconductor at ambient pressure, and its superconducting transition temperature Tc can be increased from 1.1 K at 0 GPa to 7.2 K at 100 GPa. The high Tc is unveiled to be the consequence of strong electron-phonon coupling originated from the sp-hybridized phonon-coupled bands and phonon softening caused by strong Fermi nesting. Due to the strong Fermi nesting, the charge density wave phase transition occurs at 110 GPa with the lattice reconstructed from hexagonal to orthorhombic, accompanied with the increase of Tc to 10.5 K. Our findings pave an alternative way to fabricate more real materials with Kagome bands in electrides.

Topological properties and optical conductivities tuned by spin-orbit coupling and strain in kagome lattices

The spin–orbit coupling (SOC) effect is the dominant origin of the topological properties in a topological insulator which can be induced and enhanced through various methods. Here we theoretically study the effects of varying SOC on the topological properties of two-dimensional kagome lattice based on the tight-binding approximation. We find that the system can undergo a transition between two non-trivial topological states by tuning the SOC strength. In addition, the topological phase transition can be achieved with a weaker SOC under a uniform tensile strain, which suggests that strain engineering can be used to regulate topological states. Besides, the characteristics of optical spin Hall conductivity are also studied, which supplies an experimental determination to reveal the different topological states. Furthermore, we propose an external mechanical strain modulated spin-switch device, which can generate opposite spin currents under stretch and compressed strain. Our results indicate that with the combination of SOC and strain, kagome lattice materials have potential applications on tunable spintronics and optoelectronic devices.

Corner modes of the breathing kagome lattice: Origin and robustness

We study the non-trivial phase of the two-dimensional breathing kagome lattice, displaying both edge and corner modes. The corner localized modes of a two-dimensional flake were initially identified as a signature of a higher-order topological phase but later shown to be trivial for perturbations that were thought to protect them. Using various theoretical and simulation techniques, we confirm that it does not display higher-order topology the corner modes are of trivial nature. Nevertheless, they might be protected. First, we show a set of perturbations within a tight-binding model that can move the corner modes away from zero energy, also repeat some perturbations that were used to show that the modes are trivial. In addition, we analyze the protection of the corner modes in more detail and find that only perturbations respecting the sublattice or generalized chiral and crystalline symmetries, and the lattice connectivity, pin the corner modes to zero energy robustly. A destructive interference model corroborates the results. Finally, we analyze a muffin-tin model for the bulk breathing kagome lattice. Using topological and symmetry markers, such as Wilson loops and Topological Quantum Chemistry, we identify the two breathing phases as adiabatically disconnected different obstructed atomic limits.