Regulating the Topology of Covalent Organic Frameworks for Boosting Overall H2O2 Photogeneration

Photocatalytic oxygen reduction reactions and water oxidation reactions are extremely promising green approaches for massive H2O2 production. Nonetheless, constructing effective photocatalysts for H2O2 generation is critical and still challenging. Since the network topology has significant impacts on the electronic properties of two dimensional (2D) polymers, herein, for the first time, we regulated the H2O2 photosynthetic activity of 2D covalent organic frameworks (COFs) by topology. Through designing the linking sites of the monomers, we synthesized a pair of novel COFs with similar chemical components on the backbones but distinct topologies. Without sacrificial agents, TBD-COF with cpt topology exhibited superior H2O2 photoproduction performance (6085 and 5448 μmol g-1 h-1 in O2 and air) than TBC-COF with hcb topology through the O2-O2⋅--H2O2, O2-O2⋅--O2 1-H2O2, and H2O-H2O2 three paths. Further experimental and theoretical investigations confirmed that during the H2O2 photosynthetic process, the charge carrier separation efficiency, O2⋅- generation and conversion, and the energy barrier of the rate determination steps in the three channels, related to the formation of *OOH, *O2 1, and *OH, can be well tuned by the topology of COFs. The current study enlightens the fabrication of high-performance photocatalysts for H2O2 production by topological structure modulation.

Electronic Lieb lattice signatures embedded in two-dimensional polymers with a square lattice

Exotic band features, such as Dirac cones and flat bands, arise directly from the lattice symmetry of materials. The Lieb lattice is one of the most intriguing topologies, because it possesses both Dirac cones and flat bands which intersect at the Fermi level. However, the synthesis of Lieb lattice materials remains a challenging task. Here, we explore two-dimensional polymers (2DPs) derived from zinc-phthalocyanine (ZnPc) building blocks with a square lattice (sql) as potential electronic Lieb lattice materials. By systematically varying the linker length (ZnPc-xP), we found that some ZnPc-xP exhibit a characteristic Lieb lattice band structure. Interestingly though, fes bands are also observed in ZnPc-xP. The coexistence of fes and Lieb in sql 2DPs challenges the conventional perception of the structure-electronic structure relationship. In addition, we show that manipulation of the Fermi level, achieved by electron removal or atom substitution, effectively preserves the unique characteristics of Lieb bands. The Lieb Dirac bands of ZnPc-4P shows a non-zero Chern number. Our discoveries provide a fresh perspective on 2DPs and redefine the search for Lieb lattice materials into a well-defined chemical synthesis task.

Fingerprints of magnetoinduced charge density waves in monolayer graphene beyond half filling

A charge density wave is a condensate of fermions, whose charge density shows a long-range periodic modulation. Such charge density wave can be principally described as a macroscopic quantum state and is known to occur by various formation mechanisms. These are the lattice deforming Peierls transition, the directional, fermionic wave vector orientation prone Fermi surface nesting or the generic charge ordering, which in contrast is associated solely with the undirected effective Coulomb interaction between fermions. In two-dimensional Dirac/Weyl-like systems, the existence of charge density waves is only theoretically predicted within the ultralow energy regime at half filling. Taking graphene as host of two-dimensional fermions described by a Dirac/Weyl Hamiltonian, we tuned indirectly the effective mutual Coulomb interaction between fermions through adsorption of tetracyanoquinodimethane on top in the low coverage limit. We thereby achieved the development of a novel, low-dimensional dissipative charge density wave of Weyl-like fermions, even beyond half filling with additional magneto-induced localization and quantization. This charge density wave appears both, in the electron and the hole spectrum.

Engineering novel surface electronic states via complex supramolecular tessellations

Tailoring Shockley surface-state (SS) electrons utilizing complex interfacial supramolecular tessellations was explored by low-temperature scanning tunnelling microscopy and spectroscopy, combined with computational modelling using electron plane wave expansion (EPWE) and empirical tight-binding (TB) methods. Employing a recently introduced gas-mediated on-surface reaction protocol, three distinct types of open porous networks comprising paired organometallic species as basic tectons were selectively synthesized. In particular, these supramolecular networks feature semiregular Archimedean tilings, providing intricate quantum dots (QDs) coupling scenarios compared to hexagonal porous superlattices. Our experimental results in conjunction with modelling calculations demonstrate the possibility of realizing novel two-dimensional electronic structures such as Kagome- and Dirac-type as well as hybrid Kagome-type bands via QD coupling. Compared to constructing SS electron pathways via molecular manipulations, our studies reveal significant potential of exploiting QD coupling as a complementary and versatile route for the control of surface electronic landscapes.

Tunable topologically nontrivial states in newly discovered graphyne allotropes: from Dirac nodal grid to Dirac nodal loop

By means of quotient-graph associated crystal prediction method, a new graphyne allotrope with unique Dirac nodal grid state is reported in this work. It is named as 191-E24Y24-1 according to its hexagonal lattice (with P6/mmm symmetry, No. 191) containing 24 sp²-hybridized carbon atoms and 24 sp-hybridized ones. The first-principles results show that the total energy of 191-E24Y24-1 is more favorable than that of recent synthesizedβ-graphdiyne and carbon ene-yne. It is also demonstrated to be dynamically, thermally, and mechanically stable. Interestingly, the 191-E24Y24-1 harbors intrinsic semimetal features showing intriguing hexagonal Dirac nodal grid state in the reciprocal space. Such unique electronic state is stable against small external tensile strains, and it is tunable under compression strains which will transform to new triangle Dirac nodal grid state. Moreover, a new metastable graphyne allotrope named 191-E12Y36-4 with Dirac nodal loop state is also observed in the process of stretching 191-E24Y24-1 with large tensile strains. The results presented in this work reveal two novel graphyne allotropes with exotic electronic properties. These discoveries are not only physical interesting, but also provide potential material candidates for carbon-based high performance electronic nanodevices.

Constructing and Transferring Two-Dimensional Tessellation Kagome Lattices via Chemical Reactions on Cu(111) Surface

Two-dimensional (2D) tessellation of organic species acquired increased interests recently because of their potential applications in physics, biology, and chemistry. 2D tessellations have been successfully constructed on surfaces via various intermolecular interactions. However, the transformation between 2D tessellation lattices has been rarely reported. Herein, we successfully fabricated two types of Kagome lattices on Cu(111). The former phase exhibits (3,6,3,6) Kagome lattices, which are stabilized via the intermolecular hydrogen bond interactions. The latter phase is formed through direct chemical transferring from the former one maintaining almost the same Kagome lattices, except for that the unit cell rotates for 4°. Detailed scanning tunneling microscopy and density functional calculation studies reveal that the chemical transformation is achieved by the formation of the N-Cu-N metal-organic bonds via dehydrogenation reactions of the amines.

Bandgap evolution in nanographene assemblies

Recently cycloarene has been experimentally obtained in a self-assembled structure, forming graphene-like monoatomic layered systems. Here, we established bandgap engineering/prediction in cycloarene assemblies within a combination of density functional theory and tight-binding Hamiltonians. Our results show that the inter-molecule bond density rules the bandgap. The increase in such bond density increases the valence/conduction bandwidth decreasing the energy gap linearly. We derived an effective model that allows the interpretation of the arising energy gap for general particle-hole symmetric molecular arrangements based on inter-molecular bond strength.

Emergent quasiparticles in Euclidean tilings

A material's geometric structure is a fundamental part of its properties. The honeycomb geometry of graphene is responsible for its Dirac cone, while kagome and Lieb lattices host flat bands and pseudospin-1 Dirac dispersion. These features seem to be particular to a few 2D systems rather than a common occurrence. Given this correlation between structure and properties, exploring new geometries can lead to unexplored states and phenomena. Kepler is the pioneer of the mathematical tiling theory, describing ways of filling the Euclidean plane with geometric forms in his book Harmonices Mundi. In this article, we characterize 1255 lattices composed of k-uniform tiling of the Euclidean plane and unveil their intrinsic properties; this class of arranged tiles presents high-degeneracy points, exotic quasiparticles and flat bands as common features. Here, we present a guide for the experimental interpretation and prediction of new 2D systems.

Searching for kagome multi-bands and edge states in a predicted organic topological insulator

Recently, mixed honeycomb-kagome lattices featuring metal-organic networks have been theoretically proposed as topological insulator materials capable of hosting nontrivial edge states. This new family of so-called "organic topological insulators" are purely two-dimensional and combine polyaromatic-flat molecules with metal adatoms. However, their experimental validation is still pending given the generalized absence of edge states. Here, we generate one such proposed network on a Cu(111) substrate and study its morphology and electronic structure with the purpose of confirming its topological properties. The structural techniques reveal a practically flawless network that results in a kagome network multi-band observed by angle-resolved photoemission spectroscopy and scanning tunneling spectroscopy. However, at the network island borders we notice the absence of edge states. Bond-resolved imaging of the network exhibits an unexpected structural symmetry alteration that explains such disappearance. This collective lifting of the network symmetry could be more general than initially expected and provide a simple explanation for the recurrent experimental absence of edge states in predicted organic topological insulators.

Ultrahigh-yield on-surface synthesis and assembly of circumcoronene into a chiral electronic Kagome-honeycomb lattice

On-surface synthesis has revealed remarkable potential in the fabrication of atomically precise nanographenes. However, surface-assisted synthesis often involves multiple-step cascade reactions with competing pathways, leading to a limited yield of target nanographene products. Here, we devise a strategy for the ultrahigh-yield synthesis of circumcoronene molecules on Cu(111) via surface-assisted intramolecular dehydrogenation of the rationally designed precursor, followed by methyl radical-radical coupling and aromatization. An elegant electrostatic interaction between circumcoronenes and metallic surface drives their self-organization into an extended superlattice, as revealed by bond-resolved scanning probe microscopy measurements. Density functional theory and tight-binding calculations reveal that unique hexagonal zigzag topology of circumcoronenes, along with their periodic electrostatic landscape, confines two-dimensional electron gas in Cu(111) into a chiral electronic Kagome-honeycomb lattice with two emergent electronic flat bands. Our findings open up a new route for the high-yield fabrication of elusive nanographenes with zigzag topologies and their superlattices with possible nontrivial electronic properties.

Creating supramolecular semiregular Archimedean tilings via gas-mediated deprotonation of a terminal alkyne derivative

Combining surface-confined reactions with supramolecular self-assembly allows the chemical transformation of simple molecular precursors into higher-level tectons to generate complex tessellations with unique structural and functional properties.

Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices

Topological flat bands, such as the band in twisted bilayer graphene, are becoming a promising platform to study topics such as correlation physics, superconductivity, and transport. In this Letter, we introduce a generic approach to construct two-dimensional (2D) topological quasiflat bands from line graphs and split graphs of bipartite lattices. A line graph or split graph of a bipartite lattice exhibits a set of flat bands and a set of dispersive bands. The flat band connects to the dispersive bands through a degenerate state at some momentum. We find that, with spin-orbit coupling (SOC), the flat band becomes quasiflat and gapped from the dispersive bands. By studying a series of specific line graphs and split graphs of bipartite lattices, we find that (i) if the flat band (without SOC) has inversion or C_{2} symmetry and is nondegenerate, then the resulting quasiflat band must be topologically nontrivial, and (ii) if the flat band (without SOC) is degenerate, then there exists a SOC potential such that the resulting quasiflat band is topologically nontrivial. This generic mechanism serves as a paradigm for finding topological quasiflat bands in 2D crystalline materials and metamaterials.

Flatband in a three-dimensional tungsten nitride compound

Herein, the flatband of a W₁N₂ crystal is theoretically investigated. It is revealed that the flatband can be well-described by a tight-binding model of the N₁₂ skeleton, where the dispersion of the flatband is governed by both the ppσ bonding strength (V_ppσ) and the ppπ bonding strength (V_ppπ) between the nearest-neighbor N atoms. It is also found that the proper strength of the ppπ bonding between neighboring N atoms plays a prime role in the formation of the flatband. In addition, when the compound is doped with holes, the electrons at the flatband are fully polarized, showing a ferromagnetic character. This behavior has a weak correlation with the on-site Coulomb interaction U. Moreover, several three-dimensional compounds possessing flatbands in the whole k space are predicted.

Engineering Metal-spxy Dirac Bands on the Oxidized SiC Surface

The ability to construct 2D systems, beyond materials' natural formation, enriches the search and control capability of new phenomena, for instance, the synthesis of topological lattices of vacancies on metal surfaces through scanning tunneling microscopy. In the present study, we demonstrate that metal atoms encaged in a silicate adlayer on silicon carbide is an interesting platform for lattice design, providing a ground to experimentally construct tight-binding models on an insulating substrate. Based on the density functional theory, we have characterized the energetic and electronic properties of 2D metal lattices embedded in the silica adlayer. We show that the characteristic band structures of those lattices are ruled by surface states induced by the metal-s orbitals coupled by the host-p_xy states, giving rise to sp_xy Dirac bands neatly lying within the energy gap of the semiconductor substrate.

Topological two-dimensional polymers

There are more than 200 two-dimensional (2D) networks with different topologies. The structural topology of a 2D network defines its electronic structure. Including the electronic topological properties, it gives rise to Dirac cones, topological flat bands and topological insulators. In this Tutorial Review, we show how electronic properties of 2D networks can be calculated by means of a tight-binding approach, and how these properties change when 2nd-neighbour interactions and spin-orbit coupling are included. We explain how to determine whether or not the resulting electronic features have topological signatures by calculation of Chern numbers, Z2 invariants, and by the nanoribbon approach. This tutorial gives suggestions how such topological properties could be realized in explicit atomistic chemical 2D systems made of molecular frameworks, in particular in 2D polymers, where the edges and vertices of a given 2D net are substituted by properly selected molecular building blocks and stitched together in such a way that long-range π-conjugation is retained.