Two-Dimensional Kagome Lattices Made of Hetero Triangulenes Are Dirac Semimetals or Single-Band Semiconductors

Growth of Single Crystalline 2D Materials beyond Graphene on Non-metallic Substrates

The advent of 2D materials has ushered in the exploration of their synthesis, characterization and application. While plenty of 2D materials have been synthesized on various metallic substrates, interfacial interaction significantly affects their intrinsic electronic properties. Additionally, the complex transfer process presents further challenges. In this context, experimental efforts are devoted to the direct growth on technologically important semiconductor/insulator substrates. This review aims to uncover the effects of substrate on the growth of 2D materials. The focus is on non-metallic substrate used for epitaxial growth and how this highlights the necessity for phase engineering and advanced characterization at atomic scale. Special attention is paid to monoelemental 2D structures with topological properties. The conclusion is drawn through a discussion of the requirements for integrating 2D materials with current semiconductor-based technology and the unique properties of heterostructures based on 2D materials. Overall, this review describes how 2D materials can be fabricated directly on non-metallic substrates and the exploration of growth mechanism at atomic scale.

Large-scale 2D heterostructures from hydrogen-bonded organic frameworks and graphene with distinct Dirac and flat bands

The current strategies for building 2D organic-inorganic heterojunctions involve mostly wet-chemistry processes or exfoliation and transfer, leading to interface contaminations, poor crystallizing, or limited size. Here we show a bottom-up procedure to fabricate 2D large-scale heterostructure with clean interface and highly-crystalline sheets. As a prototypical example, a well-ordered hydrogen-bonded organic framework is self-assembled on the highly-oriented-pyrolytic-graphite substrate. The organic framework adopts a honeycomb lattice with faulted/unfaulted halves in a unit cell, resemble to molecular "graphene". Interestingly, the topmost layer of substrate is self-lifted by organic framework via strong interlayer coupling, to form effectively a floating organic framework/graphene heterostructure. The individual layer of heterostructure inherits its intrinsic property, exhibiting distinct Dirac bands of graphene and narrow bands of organic framework. Our results demonstrate a promising approach to fabricate 2D organic-inorganic heterostructure with large-scale uniformity and highly-crystalline via the self-lifting effect, which is generally applicable to most of van der Waals materials.

Recent progress in on-surface synthesis of nanoporous graphene materials

Nanoporous graphene (NPG) materials are generated by removing internal degree-3 vertices from graphene and introducing nanopores with specific topological structures, which have been widely explored and exploited for applications in electronic devices, membranes, and energy storage. The inherent properties of NPGs, such as the band structures, field effect mobilities and topological properties, are crucially determined by the geometric structure of nanopores. On-surface synthesis is an emerging strategy to fabricate low-dimensional carbon nanostructures with atomic precision. In this review, we introduce the progress of on-surface synthesis of atomically precise NPGs, and classify NPGs from the aspects of element types, topological structures, pore shapes, and synthesis strategies. We aim to provide a comprehensive overview of the recent advancements, promoting interdisciplinary collaboration to further advance the synthesis and applications of NPGs.

A high density nanopore 3-triangulene kagome lattice

Nanopore-containing two-dimensional materials have been explored for a wide range of applications including filtration, sensing, catalysis, energy storage and conversion. Triangulenes have recently been experimentally synthesized in a variety of sizes. In this regard, using these systems as building blocks, we theoretically examined 3-triangulene kagome crystals with inherent holes of ∼12 Å diameter and a greater density array of nanopores (≥1013 cm-2) compared to conventional 2D systems. The energetic, electronic, and transport properties of pristine and B/N-doped 3-triangulene kagome crystals were evaluated through a combination of density functional theory and non-equilibrium Green's function method. The simulated scanning tunneling microscopy images clearly capture electronic perturbation around the doped sites, which can be used to distinguish the pristine system from the doped systems. The viability of precisely controlling the band structure and transport properties by changing the type and concentration of doping atoms is demonstrated. The findings presented herein can potentially widen the applicability of these systems that combine unique electronic properties and intrinsically high-density pores, which can pave the way for the next generation of nanopore-based devices.

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.

2D Conjugated Polymer Thin Films for Organic Electronics: Opportunities and Challenges

2D conjugated polymers (2DCPs) possess extended in-plane π-conjugated lattice and out-of-plane π-π stacking, which results in enhanced electronic performance and potentially unique band structures. These properties, along with predesignability, well-defined channels, easy postmodification, and order structure attract extensive attention from material science to organic electronics. In this review, the recent advance in the interfacial synthesis and conductivity tuning strategies of 2DCP thin films, as well as their application in organic electronics is summarized. Furthermore, it is shown that, by combining topology structure design and targeted conductivity adjustment, researchers have fabricated 2DCP thin films with predesigned active groups, highly ordered structures, and enhanced conductivity. These films exhibit great potential for various thin-film organic electronics, such as organic transistors, memristors, electrochromism, chemiresistors, and photodetectors. Finally, the future research directions and perspectives of 2DCPs are discussed in terms of the interfacial synthetic design and structure engineering for the fabrication of fully conjugated 2DCP thin films, as well as the functional manipulation of conductivity to advance their applications in future organic electronics.

Tailoring photocatalytic water splitting activity of boron-thiophene polymer through pore size engineering

Taking into account the electron-rich and visible light response of thiophene, first-principles calculations have been carried out to explore the photocatalytic activity of donor-acceptor polymers incorporating thiophene and boron. Honeycomb-kagome boron-thiophene (BTP) polymers with varying numbers of thiophene units and fixed B center atoms are direct bandgap semiconductors with tunable bandgaps ranging from 2.41 to 1.88 eV and show high absorption coefficients under the ultraviolet and visible regions of the solar spectrum. Fine-tuning the band edges of the BTP polymer is efficiently achieved by adjusting the pore size through the manipulation of thiophene units between the B centers. This manipulation, achieved without excessive chemical functionalization, facilitates the generation of an appropriate quantity of photoexcited electrons and/or holes to straddle the redox potential of the water. Our study demonstrates that two units between B centers of thiophene in BTP polymers enable overall photocatalytic water splitting, whereas BTP polymers with larger pores solely promote photocatalytic hydrogen reduction. Moreover, the thermodynamics of hydrogen and oxygen reduction reactions either proceed spontaneously or need small additional external biases. Our findings provide the rationale for designing metal-free and single-material polymer photocatalysts based on thiophene, specifically for achieving efficient overall water splitting.

Rational Molecular Design of Redox-Active Carbonyl-Bridged Heterotriangulenes for High-Performance Lithium-Ion Batteries

Carbonyl aromatic compounds are promising cathode candidates for lithium-ion batteries (LIBs) because of their low weight and absence of cobalt and other metals, but they face constraints of limited redox-potential and low stability compared to traditional inorganic cathode materials. Herein, by means of first-principles calculations, a significant improvement of the electrochemical performance for carbonyl-bridged heterotriangulenes (CBHTs) is reported by introducing pyridinic N in their skeletons. Different center atoms (B, N, and P) and different types of functionalization with nitrogen effectively regulate the redox activity, conductivity, and solubility of CBHTs by influencing their electron affinity, energy levels of frontier orbitals and molecular polarity. By incorporating pyridinic N adjacent to the carbonyl groups, the electrochemical performance of N-functionalized CBHTs is significantly improved. Foremost, the estimated energy density reaches 1524 Wh kg-1 for carbonyl-bridged tri (3,5-pyrimidyl) borane, 50% higher than in the inorganic reference material LiCoO2 , rendering N-functionalized CBHTs promising organic cathode materials for LIBs. The investigation reveals the underlying structure-performance relationship of conjugated carbonyl compounds and sheds new lights for the rational design of redox-active organic molecules for high-performance lithium ion batteries (LIBs).

Electronic Band Engineering of Two-Dimensional Kagomé Polymers

Two-dimensional conjugated polymers (2DCPs) are an emerging class of materials that exhibit properties similar to graphene yet do not have the limitation of zero bandgap. On-surface synthesis provides exceptional control on the polymerization reaction, allowing tailoring properties by choosing suitable monomers. Heteroatom-substituted triangulene 2DCPs constitute a playing ground for such a design and are predicted to exhibit graphene-like band structures with high charge mobility and characteristic Dirac cones in conduction or valence states. However, measuring these properties experimentally is challenging and requires long-range-ordered polymers, preferably with an epitaxial relationship with the substrate. Here, we investigate the electronic properties of a mesoscale-ordered carbonyl-bridged triphenylamine 2DCP (P2TANGO) and demonstrate the presence of a Dirac cone by combining angle-resolved photoemission spectroscopy (ARPES) with density functional theory (DFT) calculations. Moreover, we measure the absolute energy position of the Dirac cone with respect to the vacuum level. We show that the bridging functionality of the triangulene (ether vs carbonyl) does not significantly perturb the band structure but strongly affects the positioning of the bands with respect to the Au(111) states and allows control of the ionization energy of the polymer. Our results provide proof of the controllable electronic properties of 2DCPs and bring us closer to their use in practical applications.

Two-Dimensional Conjugated Polymers: a New Choice For Organic Thin-Film Transistors

Organic thin-film transistors (OTFTs) as a vital component among transistors have shown great potential in smart sensing, flexible displays, and bionics due to their flexibility, biocompatibility and customizable chemical structures. Even though linear conjugated polymer semiconductors are common for constructing channel materials of OTFTs, advanced materials with high charge carrier mobility, tunable band structure, robust stability, and clear structure-property relationship are indispensable for propelling the evolution of OTFTs. Two-dimensional conjugated polymers (2DCPs), featured with conjugated lattice, tailorable skeletons, and functional porous structures, match aforementioned criteria closely. In this review, we firstly introduce the synthesis of 2DCP thin films, focusing on their characteristics compatible with the channels of OTFTs. Subsequently, the physics and operating mechanisms of OTFTs and the applications of 2DCPs in OTFTs are summarized in detail. Finally, the outlook and perspective in the field of OTFTs using 2DCPs are provided as well.

2D Covalent Organic Frameworks with Kagome Lattice: Synthesis and Applications

2D covalent organic frameworks with Kagome (kgm) topology are a promising class of crystalline frameworks that possess both triangular and hexagonal pores. These dual-pore structures enable kgm COFs to exhibit unique advantages in selective separation, mass transfer, and targeted drug release. However, the synthesis of 2D kgm COFs has been hindered by the reliance on empirical methods. This review systematically summarizes the conventional macrocycle-to-framework strategy, typical [4+2] co-polymerization synthetic strategy, and bifunctional molecules self-condensation approach for constructing 2D kgm COFs. Factors influencing the formation of kgm lattice are surveyed, such as monomer type, solvent polarity, substrate concentration, etc., and highlight the representative examples on targeted synthesis. Additionally, applications of 2D kgm COFs and relationships between structure and performances are summarized. Finally, key fundamental perspectives are proposed to accelerate the further development of this intriguing material.

Magnetic Coupling Control in Triangulene Dimers

Metal-free magnetism remains an enigmatic field, offering prospects for unconventional magnetic and electronic devices. In the pursuit of such magnetism, triangulenes, endowed with inherent spin polarization, are promising candidates to serve as monomers to construct extended structures. However, controlling and enhancing the magnetic interactions between the monomers persist as a significant challenge in molecular spintronics, as so far only weak antiferromagnetic coupling through the linkage has been realized, hindering their room temperature utilization. Herein, we investigate 24 triangulene dimers using first-principles calculations and demonstrate their tunable magnetic coupling (J), achieving unprecedented strong J values of up to -144 meV in a non-Kekulé dimer. We further establish a positive correlation between bandgap, electronic coupling, and antiferromagnetic interaction, thereby providing molecular-level insights into enhancing magnetic interactions. By twisting the molecular fragments, we demonstrate an effective and feasible approach to control both the sign and strength of J by tuning the balance between potential and kinetic exchanges. We discover that J can be substantially boosted at planar configurations up to -198 meV. We realize ferromagnetic coupling in nitrogen-doped triangulene dimers at both planar and largely twisted configurations, representing the first example of ferromagnetic triangulene dimers that cannot be predicted by the Ovchinnikov rule. This work thus provides a practical strategy for augmenting magnetic coupling and open up new avenues for metal-free ferromagnetism.

Room Temperature On-Surface Synthesis of a Vinylene-Linked Single Layer Covalent Organic Framework

Conjugated single-layered two-dimensional covalent organic frameworks are flat and extended polymer networks with a unique combination of material properties, giving rise to potential applications in sensing, optoelectronics, and photonics. Despite their great potential, thus far only a few reactions to access such extended conjugated 2D polymers have been reported. Here, the on-surface polymerization of the first vinylene-linked single layered two-dimensional covalent organic framework using reversible Knoevenagel polycondensation under solvothermal conditions is described. Self-assembly of the two monomer building blocks at the solid-liquid interface led to the formation of extended covalent networks at room temperature without the need of additional catalysts or reagents. The described approach grants access to extended conjugated 2D polymers under unprecedentedly mild conditions and paves the way to new hybrid material systems.

Exceptionally high charge mobility in phthalocyanine-based poly(benzimidazobenzophenanthroline)-ladder-type two-dimensional conjugated polymers

Two-dimensional conjugated polymers (2DCPs), composed of multiple strands of linear conjugated polymers with extended in-plane π-conjugation, are emerging crystalline semiconducting polymers for organic (opto)electronics. They are represented by two-dimensional π-conjugated covalent organic frameworks, which typically suffer from poor π-conjugation and thus low charge carrier mobilities. Here we overcome this limitation by demonstrating two semiconducting phthalocyanine-based poly(benzimidazobenzophenanthroline)-ladder-type 2DCPs (2DCP-MPc, with M = Cu or Ni), which are constructed from octaaminophthalocyaninato metal(II) and naphthalenetetracarboxylic dianhydride by polycondensation under solvothermal conditions. The 2DCP-MPcs exhibit optical bandgaps of ~1.3 eV with highly delocalized π-electrons. Density functional theory calculations unveil strongly dispersive energy bands with small electron-hole reduced effective masses of ~0.15m0 for the layer-stacked 2DCP-MPcs. Terahertz spectroscopy reveals the band transport of Drude-type free carriers in 2DCP-MPcs with exceptionally high sum mobility of electrons and holes of ~970 cm2 V-1 s-1 at room temperature, surpassing that of the reported linear conjugated polymers and 2DCPs. This work highlights the critical role of effective conjugation in enhancing the charge transport properties of 2DCPs and the great potential of high-mobility 2DCPs for future (opto)electronics.

Predicting Magnetic Coupling and Spin-Polarization Energy in Triangulene Analogues

Triangulene and its analogue metal-free magnetic systems have garnered increasing attention since their discovery. Predicting the magnetic coupling and spin-polarization energy with quantitative accuracy is beyond the predictive power of today's density functional theory (DFT) due to their intrinsic multireference character. Herein, we create a benchmark dataset of 25 magnetic systems with nonlocal spin densities, including the triangulene monomer, dimer, and their analogues. We calculate the magnetic coupling (J) and spin-polarization energy (ΔE_spin) of these systems using complete active space self-consistent field (CASSCF) and coupled-cluster methods as high-quality reference values. This reference data is then used to benchmark 22 DFT functionals commonly used in material science. Our results show that, while some functionals consistently correctly predict the qualitative character of the ground state, achieving quantitative accuracy with small relative errors is currently not feasible. PBE0, M06-2X, and MN15 are predicting the correct electronic ground state for all systems investigated here and also have the lowest mean absolute error for predicting both ΔE_spin (0.34, 0.32, and 0.31 eV) and J (11.74, 12.66, and 10.64 meV). They may therefore also serve as starting points for higher-level methods such as the GW or the random phase approximation. As other functionals fail for the prediction of the ground state, they cannot be recommended for metal-free magnetic systems.

Synthesis, Hole Doping, and Electrical Properties of a Semiconducting Azatriangulene-Based Covalent Organic Framework

Two-dimensional covalent organic frameworks (2D COFs) containing heterotriangulenes have been theoretically identified as semiconductors with tunable, Dirac-cone-like band structures, which are expected to afford high charge-carrier mobilities ideal for next-generation flexible electronics. However, few bulk syntheses of these materials have been reported, and existing synthetic methods provide limited control of network purity and morphology. Here, we report transimination reactions between benzophenone-imine-protected azatriangulenes (OTPA) and benzodithiophene dialdehydes (BDT), which afforded a new semiconducting COF network, OTPA-BDT. The COFs were prepared as both polycrystalline powders and thin films with controlled crystallite orientation. The azatriangulene nodes are readily oxidized to stable radical cations upon exposure to an appropriate p-type dopant, tris(4-bromophenyl)ammoniumyl hexachloroantimonate, after which the network's crystallinity and orientation are maintained. Oriented, hole-doped OTPA-BDT COF films exhibit electrical conductivities of up to 1.2 × 10^-1 S cm^-1, which are among the highest reported for imine-linked 2D COFs to date.

Tailoring On-Surface Molecular Reactions and Assembly through Hydrogen-Modified Synthesis: From Triarylamine Monomer to 2D Covalent Organic Framework

Relative to conventional wet-chemical synthesis techniques, on-surface synthesis of organic networks in ultrahigh vacuum has few control parameters. The molecular deposition rate and substrate temperature are typically the only synthesis variables to be adjusted dynamically. Here we demonstrate that reducing conditions in the vacuum environment can be created and controlled without dedicated sources─relying only on backfilled hydrogen gas and ion gauge filaments─and can dramatically influence the Ullmann-like on-surface reaction used for synthesizing two-dimensional covalent organic frameworks (2D COFs). Using tribromo dimethylmethylene-bridged triphenylamine ((Br₃)DTPA) as monomer precursors, we find that atomic hydrogen (H^•) blocks aryl-aryl bond formation to such an extent that we suspect this reaction may be a factor in limiting the ultimate size of 2D COFs created through on-surface synthesis. Conversely, we show that control of the relative monomer and hydrogen fluxes can be used to produce large self-assembled islands of monomers, dimers, or macrocycle hexamers, which are of interest in their own right. On-surface synthesis of oligomers, from a single precursor, circumvents potential challenges with their protracted wet-chemical synthesis and with multiple deposition sources. Using scanning tunneling microscopy and spectroscopy (STM/STS), we show that changes in the electronic states through this oligomer sequence provide an insightful view of the 2D COF (synthesized in the absence of atomic hydrogen) as the end point in an evolution of electronic structures from the monomer.

Emergent Spin Frustration in Neutral Mixed-Valence 2D Conjugated Polymers: A Potential Quantum Materials Platform

Two-dimensional conjugated polymers (2DCPs)─organic 2D materials composed of arrays of carbon sp² centers connected by π-conjugated linkers─are attracting increasing attention due to their potential applications in device technologies. This interest stems from the ability of 2DCPs to host a range of correlated electronic and magnetic states (e.g., Mott insulators). Substitution of all carbon sp² centers in 2DCPs by nitrogen or boron results in diamagnetic insulating states. Partial substitution of C sp² centers by B or N atoms has not yet been considered for extended 2DCPs but has been extensively studied in the analogous neutral mixed-valence molecular systems. Here, we employ accurate first-principles calculations to predict the electronic and magnetic properties of a new class of hexagonally connected neutral mixed-valence 2DCPs in which every other C sp² nodal center is substituted by either a N or B atom. We show that these neutral mixed-valence 2DCPs significantly energetically favor a state with emergent superexchange-mediated antiferromagnetic (AFM) interactions between C-based spin-¹/₂ centers on a triangular sublattice. These AFM interactions are surprisingly strong and comparable to those in the parent compounds of cuprate superconductors. The rigid and covalently linked symmetric triangular AFM lattice in these materials thus provides a highly promising and robust basis for 2D spin frustration. As such, extended mixed-valence 2DCPs are a highly attractive platform for the future bottom-up realization of a new class of all-organic quantum materials, which could host exotic correlated electronic states (e.g., unusual magnetic ordering, quantum spin liquids).

Organic Higher-Order Topological Insulators: Heterotriangulene-Based Covalent Organic Frameworks

The ability to design and control the chemical characteristics of covalent organic frameworks (COFs) offers a new avenue for the development of functional materials, especially with respect to topological properties. Based on density functional theory calculations, by varying the core units through the choice of bridging groups [O, C═O, CH₂, or C(CH₃)₂] and the linker units [acetylene, diacetylene, or benzene], we have designed heterotriangulene-based COFs that are predicted to be two-dimensional higher-order topological insulators (TIs). The higher-order TI characteristics of these COFs are identified via their topological invariants and the presence of in-gap topological corner modes and gapped edge states. The frontier molecular orbital energies of the building moieties play an important role in determining the size of the higher-order TI gap, which we find to be highly dependent on linker units. We also examined the deposition of the COFs on a boron nitride substrate to assess the feasibility of experimental observation of a higher-order TI phase in the organic layer. This work thus provides new insights into heterotriangulene-based COFs and guidance for the exploration of purely organic topological materials.

Intrinsic Second-Order Topological Insulator in Two-Dimensional Covalent Organic Frameworks

As an intriguing topological phase, higher-order topological insulators have attracted tremendous attention, but the candidate materials are limited in artificial and inorganic systems. In this work, we propose a universal approach to search for two-dimensional (2D) second-order topological insulators (SOTIs) in covalent organic frameworks (COFs) with C₃ symmetric cores. The underlying mechanism is illustrated through tight-binding calculations in a star lattice, showing the 2D SOTI in an overlooked energy window between two Kagome-bands with four types of nontrivial band structures. The emergence of the unique topological edge and corner states can be understood from the Su-Schrieffer-Heeger model. Furthermore, using the frontier orbital of the monomer building block as an indicator, the 2D SOTI is directly confirmed in three realistic COFs by first-principles calculations. Our results not only extend the concept of organic topological insulators from first-order to second-order but also demonstrate the universal existence of intrinsic higher-order topology in 2D COFs.

Sumanene Monolayer of Pure Carbon: A Two-Dimensional Kagome-Analogy Lattice with Desirable Band Gap, Ultrahigh Carrier Mobility, and Strong Exciton Binding Energy

The design and synthesis of novel two-dimensional (2D) materials that possess robust structural stability and unusual physical properties may open up enormous opportunities for device and engineering applications. Herein, a 2D sumanene lattice that can be regarded as a derivative of the conventional Kagome lattice is proposed. The tight-binding analysis demonstrates sumanene lattice contains two sets of Dirac cones and two sets of flat bands near the Fermi surface, distinctively different from the Kagome lattice. Using first-principles calculations, two possible routines for the realization of stable 2D sumanene monolayers (named α phase and β phase) are theoretically suggested, and an α-sumanene monolayer can be experimentally synthesized with chemical vapor deposition using C₂₁ H₁₂ as a precursor. Small binding energies on Au(111) surface (e.g., -37.86 eV Å^-2 for α phase) signify the possibility of their peel-off after growing on the noble metal substrate. Importantly, the GW plus Bethe-Salpeter equation calculations demonstrate both monolayers have moderate band gaps (1.94 eV for α) and ultrahigh carrier mobilities (3.4 × 10⁴ cm²  V^-1  s^-1 for α). In particular, the α-sumanene monolayer possesses a strong exciton binding energy of 0.73 eV, suggesting potential applications in optics.

Spin engineering of triangulenes and application for nano nonlinear optical materials design

The recently synthesized triangulenes with non-bonding edge states could have broad potential applications in magnetics, spintronics and electro-optics if they have appropriate electronic structure modulation. In the present work, strategies based on molecular orbital theory through heteroatom doping are proposed to redistribute, reduce or eliminate the spin of triangulenes for novel functional materials design, and the role of B, N, NBN, and BNB in such intended electronic structure manipulation is scrutinized. π-Extended triangulenes with tunable electronic properties could be potential nonlinear optical (NLO) materials with appropriate inhibition of their polyradical nature. The elimination of spin is achieved by B, N, NBN, and BNB doping with the intended geometric arrangement for enhanced polarity. Intended doping of BNB results in an optimal structure with large static first hyperpolarizability (〈β₀〉) as well as strong Hyper-Rayleigh scattering (HRS) β_HRS(-2ω; ω, ω) (ω = 1064.0 nm), TG7-BNB-ba with a large 〈β₀〉 (18.85 × 10^-30 esu per heavy atom) and β_HRS (1.15 × 10^-28 esu per heavy atom) much larger than that of a synthesized triangular molecule (1.12 × 10^-30 esu of 〈β₀〉 per heavy atom and 5.04 × 10^-30 esu of β_HRS per heavy atom). The strong second order NLO responses in the near-infrared and visible regions, particularly the strong sum frequency generation, make these B or (and) N doped triangulenes promising candidates for the fabrication of novel carbon-based optoelectronic devices and micro-NLO devices.

Two-dimensional heterotriangulene-based manganese organic frameworks: bipolar magnetic and half semiconductors with perpendicular magnetocrystalline anisotropy

Two-dimensional (2D) organic intrinsic magnetic semiconductors have potential applications in low-dimensional organic spintronic devices due to their remarkable physical properties. However, 2D metal-organic frameworks with magnetic and semiconducting properties are rare. In this work, the electronic and magnetic properties of 2D heterotriangulene-based manganese organic frameworks including triphenylamine (TPA) and triphenylborane (TPB) organic ligands with methylene (M), carbonyl (C) or oxygen (O) coordination groups were studied by first-principles calculations. XTPA-Mn (X = M and O) is a bipolar magnetic semiconductor with a large spin-flip band gap. CTPA-Mn and XTPB-Mn (X = M, C and O) are half semiconductors with perpendicular magnetocrystalline anisotropy. The electronic properties of materials ranging from half semiconductors to bipolar magnetic semiconductors appear in CTPA-Mn and XTPB-Mn (X = M and C) at biaxial strains. XTPA-Mn and XTPB-Mn with a frustrated antiferromagnetic configuration are semiconductors with good ductility and stability. These results enrich the diversity of 2D organic intrinsic magnetic semiconductors, which have potential applications in spintronic devices.

Charge Transport in Organic Semiconductors: The Perspective from Nonadiabatic Molecular Dynamics

Organic semiconductors (OSs) are an exciting class of materials that have enabled disruptive technologies in this century including large-area electronics, flexible displays, and inexpensive solar cells. All of these technologies rely on the motion of electrical charges within the material and the diffusivity of these charges critically determines their performance. In this respect, it is remarkable that the nature of the charge transport in these materials has puzzled the community for so many years, even for apparently simple systems such as molecular single crystals: some experiments would better fit an interpretation in terms of a localized particle picture, akin to molecular or biological electron transfer, while others are in better agreement with a wave-like interpretation, more akin to band transport in metals.

Exciting recent progress in the theory and simulation of charge carrier transport in OSs has now led to a unified understanding of these disparate findings, and this Account will review one of these tools developed in our laboratory in some detail: direct charge carrier propagation by quantum-classical nonadiabatic molecular dynamics. One finds that even in defect-free crystals the charge carrier can either localize on a single molecule or substantially delocalize over a large number of molecules depending on the relative strength of electronic couplings between the molecules, reorganization, or charge trapping energy of the molecule and thermal fluctuations of electronic couplings and site energies, also known as electron–phonon couplings.

Our simulations predict that in molecular OSs exhibiting some of the highest measured charge mobilities to date, the charge carrier forms “flickering” polarons, objects that are delocalized over 10–20 molecules on average and that constantly change their shape and extension under the influence of thermal disorder. The flickering polarons propagate through the OS by short (≈10 fs long) bursts of the wave function that lead to an expansion of the polaron to about twice its size, resulting in spatial displacement, carrier diffusion, charge mobility, and electrical conductivity. Arguably best termed “transient delocalization”, this mechanistic scenario is very similar to the one assumed in transient localization theory and supports its assertions. We also review recent applications of our methodology to charge transport in disordered and nanocrystalline samples, which allows us to understand the influence of defects and grain boundaries on the charge propagation.

Unfortunately, the energetically favorable packing structures of typical OSs, whether molecular or polymeric, places fundamental constraints on charge mobilities/electronic conductivity compared to inorganic semiconductors, which limits their range of applications. In this Account, we review the design rules that could pave the way for new very high-mobility OS materials and we argue that 2D covalent organic frameworks are one of the most promising candidates to satisfy them.

We conclude that our nonadiabatic dynamics method is a powerful approach for predicting charge carrier transport in crystalline and disordered materials. We close with a brief outlook on extensions of the method to exciton transport, dissociation, and recombination. This will bring us a step closer to an understanding of the birth, survival, and annihiliation of charges at interfaces of optoelectronic devices.

Engineering of flat bands and Dirac bands in two-dimensional covalent organic frameworks (COFs): relationships among molecular orbital symmetry, lattice symmetry, and electronic-structure characteristics

Two-dimensional covalent organic frameworks (2D-COFs), also referred to as 2D polymer networks, display unusual electronic-structure characteristics, which can significantly enrich and broaden the fields of electronics and spintronics. In this Focus article, our objective is to lay the groundwork for the conceptual description of the fundamental relationships among the COF electronic structures, the symmetries of their 2D lattices, and the frontier molecular orbitals (MOs) of their core and linker components. We focus on monolayers of hexagonal COFs and use tight-binding model analyses to highlight the critical role of the frontier-MO symmetry, in addition to lattice symmetry, in determining the nature of the electronic bands near the Fermi level. We rationalize the intriguing feature that, when the core unit has degenerate highest occupied MOs [or lowest unoccupied MOs], the COF highest valence band [or lowest conduction band] is flat but degenerate with a dispersive band at a high-symmetry point of the Brillouin zone; the consequences of having such band characteristics are briefly described. Multi-layer and bulk 2D COFs are found to maintain the salient features of the monolayer electronic structures albeit with a reduced bandgap due to the interlayer coupling. This Focus article is thus meant to provide an effective framework for the engineering of flat and Dirac bands in 2D polymer networks.

Graphene-based nano-devices: high spin Seebeck and pure spin photogalvanic effects

We investigate the magnetic, thermoelectric transport, and photogalvanic effect (PGE) properties of two nano-devices based on sawtooth edged graphene nanoribbons (SGNRs). It is found that a robust spin-semiconducting property exists in SGNRs. When SGNRs are arranged in a configuration, a large spin Seebeck coefficient is obtained, indicating a high Seebeck effect under a temperature difference. In addition, we also propose a new spatial inversion symmetry nano-device, which is constructed by two head to head semi-infinite SGNRs in a configuration. The results show that spin-up and spin-down currents are generated by the PGE with opposite flowing directions and the same magnitude. As a result, only a finite pure spin current arises without an accompanying charge current. More importantly, the pure spin current is robustly induced by photons and is independent of the photon energy, polarization angle and the model of polarization (linear or elliptical polarization), which is attributed to the symmetry of the spatial inversion and anti-symmetry of the spin density inversion. The results presented here provide a useful insight into the real application of both spin caloritronics and photoelectric carbon-based nano-devices.

Designing Two-Dimensional Versatile Room-Temperature Ferromagnets via Assembling Large-Scale Magnetic Quantum Dots

Two-dimensional (2D) ferromagnets possess astonishing potential in new-concept spintronics. However, most of the reported intrinsic 2D ferromagnets show a low Curie temperature far below room temperature. Here, we propose a series of 2D magnetic covalent and metal organic frameworks (COFs/MOFs) by assembling triangular zigzag graphene quantum dots (TZGDs) with various linkages, involving small-sized TZGDs, nonmetal atoms, magnetic metal atoms, and molecules. Upon first-principles calculations, we demonstrate 2D magnetic semiconductors with an enhanced Curie temperature of up to 472 K can be realized through the strong p(d)-p direct exchange interaction between TZGDs and linkages. Particularly, the TZGD size hardly affects the Curie temperature, whereas linkages can modulate the Curie temperature significantly. The TZGD size and linkages can regulate the electronic and magnetic properties of TZGD-based 2D ferromagnets. Our results confirm the possibility of designing 2D ferromagnets based on TZGDs and motivate the research of 2D ferromagnets on magnetic quantum dots and molecular magnets.

Two-Dimensional Metal-Organic Framework on Superconducting NbSe2

The combination of two-dimensional (2D) materials into vertical heterostructures has emerged as a promising path to designer quantum materials with exotic properties. Here, we extend this concept from inorganic 2D materials to 2D metal-organic frameworks (MOFs) that offer additional flexibility in realizing designer heterostructures. We successfully fabricate a monolayer 2D Cu-dicyanoanthracene MOF on a 2D van der Waals NbSe₂ superconducting substrate. The structural and electronic properties of two different phases of the 2D MOF are characterized by low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS), complemented by density-functional theory (DFT) calculations. These experiments allow us to follow the formation of the kagome band structure from Star of David-shaped building blocks. This work extends the synthesis and electronic tunability of 2D MOFs beyond the electronically less relevant metal and semiconducting surfaces to superconducting substrates, which are needed for the development of emerging quantum materials such as topological superconductors.

Acetylene-Mediated Electron Transport in Nanostructured Graphene and Hexagonal Boron Nitride

The discovery of graphene has catalyzed the search for other 2D carbon allotropes, such as graphynes, graphdiynes, and 2D π-conjugated polymers, which have been theoretically predicted or experimentally synthesized during the past decade. These materials exhibit a conductive nature bound to their π-conjugated sp² electronic system. Some cases include sp-hybridized moieties in their nanostructure, such as acetylenes in graphynes; however, these act merely as electronic couplers between the conducting π-orbitals of sp² centers. Herein, via first-principles calculations and quantum transport simulations, we demonstrate the existence of an acetylene-meditated transport mechanism entirely hosted by sp-hybridized orbitals. For that we propose a series of nanostructured 2D materials featuring linear arrangements of closely packed acetylene units which function as sp-nanowires. Because of the very distinct nature of this unique transport mechanism, it appears to be highly complementary with π-conjugation, thus potentially becoming a key tool for future carbon nanoelectronics.

Topology-Mediated Enhanced Polaron Coherence in Covalent Organic Frameworks

We employ the Holstein model for polarons to investigate the relationship among defects, topology, Coulomb trapping, and polaron delocalization in covalent organic frameworks (COFs). We find that intrasheet topological connectivity and π-column density can override disorder-induced deep traps and significantly enhance polaron migration by several orders of magnitude in good agreement with recent experimental observations. The combination of percolation networks and micropores makes trigonal COFs ideally suited for charge transport followed by kagome/tetragonal and hexagonal structures. By comparing the polaron spectral signatures and coherence numbers of large three-dimensional frameworks having a maximum of 180 coupled chromophores, we show that controlling nanoscale defects and the location of the counteranion is critical for the design of new COF-based materials yielding higher mobilities. Our analysis establishes design strategies for enhanced conductivity in COFs that can be readily generalized to other classes of conductive materials such as metal-organic frameworks and perovskites.

Rational Design of Two-Dimensional Binary Polymers from Heterotriangulenes for Photocatalytic Water Splitting

On the basis of first-principles calculations, we report the design of three two-dimensional (2D) binary honeycomb-kagome polymers composed of B- and N-centered heterotriangulenes with a periodically alternate arrangement as in hexagonal boron nitride. The 2D binary polymers with donor-acceptor characteristics are semiconductors with a direct band gap of 1.98-2.28 eV. The enhanced in-plane electron conjugation contributes to high charge carrier mobilities for both electrons and holes, about 6.70 and 0.24 × 10³ cm² V^-1 s^-1, respectively, for the 2D binary polymer with carbonyl bridges (2D CTPAB). With appropriate band edge alignment to match the water redox potentials and pronounced light adsorption for the ultraviolet and visible range of spectra, 2D CTPAB is predicted to be an effective photocatalyst/photoelectrocatalyst to promote overall water splitting.

Multiscale Modeling Strategy of 2D Covalent Organic Frameworks Confined at an Air-Water Interface

Two-dimensional covalent organic frameworks (2D COFs) have attracted attention as versatile active materials in many applications. Recent advances have demonstrated the synthesis of monolayer 2D COF via an air-water interface. However, the interfacial 2D polymerization mechanism has been elusive. In this work, we have used a multiscale modeling strategy to study dimethylmethylene-bridged triphenylamine building blocks confined at the air-water interface to form a 2D COF via Schiff-base reaction. A synergy between the computational investigations and experiments allowed the synthesis of a 2D-COF with one of the linkers considered. Our simulations complement the experimental characterization and show the preference of the building blocks to be at the interface with a favorable orientation for the polymerization. The air-water interface is shown to be a key factor to stabilize a flat conformation when a dimer molecule is considered. The structural and electronic properties of the monolayer COFs based on the two monomers are calculated and show a semiconducting nature with direct bandgaps. Our strategy provides a first step toward the in silico polymerization of 2D COFs at air-water interfaces capturing the initial steps of the synthesis up to the prediction of electronic properties of the 2D material.

Host guest chemistry and supramolecular doping in triphenylamine-based covalent frameworks on Au(111)

The post-synthetic modification of covalent organic frameworks (COFs) via host-guest chemistry is an important method to tailor their electronic properties for applications. Due to the limited structural control in the assembly of two-dimensional surface-supported COFs, supramolecular networks are traditionally used at present for host-guest experiments on surfaces, which lack structural and thermal stability, however. Here, we present a combined scanning tunneling microscopy and density functional theory study to understand the host-guest interaction in triphenylamine-based covalently-linked macrocycles and networks on Au(111). These triphenylamine-based structures feature carbonyl and hydrogen functionalized pores that create preferred adsorption sites for trimesic acid (TMA) and halogen atoms. The binding of the TMA through optimized hydrogen-bond interactions is corroborated by selective adsorption positions within the pores. Band structure calculations reveal that the strong intermolecular charge transfer through the TMA bonding reduces the band gap in the triphenylamine COFs, demonstrating the concept of supramolecular doping by host-guest interactions in surface-supported COFs. Halogen atoms selectively adsorb between two carbonyl groups at Au hollow sites. The mainly dispersive interaction of the halogens with the triphenylamine COF leads to a small downshift of the bands. Most of the halogens change their adsorption position selectively upon annealing near the desorption temperature. In conclusion, we demonstrate evidence for supramolecular doping via post-synthetic modification and to track chemical reactions in confined space.

Quasiparticle electronic structure of two-dimensional heterotriangulene-based covalent organic frameworks adsorbed on Au(111)

The modular nature and unique electronic properties of two-dimensional (2D) covalent organic frameworks (COFs) make them an attractive option for applications in catalysis, optoelectronics, and spintronics. The fabrications of such devices often involve interfaces formed between COFs and substrates. In this work, we employ the first-principlesGWapproach to accurately determine the quasiparticle electronic structure of three 2D carbonyl bridged heterotriangulene-based COFs featuring honeycomb-kagome lattice, with their properties ranging from a semi-metal to a wide-gap semiconductor. Moreover, we study the adsorption of these COFs on Au(111) surface and characterize the quasiparticle electronic structure at the heterogeneous COF/Au(111) interfaces. To reduce the computational cost, we apply the recently developed dielectric embeddingGWapproach and show that our results agree with existing experimental measurement on the interfacial energy level alignment. Our calculations illustrate how the many-body dielectric screening at the interface modulates the energies and shapes of the Dirac bands, the effective masses of semiconducting COFs, as well as the Fermi velocity of the semi-metallic COF.

Understanding Topological Insulators in Real Space

A real space understanding of the Su–Schrieffer–Heeger model of polyacetylene is introduced thanks to delocalization indices defined within the quantum theory of atoms in molecules. This approach enables to go beyond the analysis of electron localization usually enabled by topological insulator indices—such as IPR—enabling to differentiate between trivial and topological insulator phases. The approach is based on analyzing the electron delocalization between second neighbors, thus highlighting the relevance of the sublattices induced by chiral symmetry. Moreover, the second neighbor delocalization index, δi,i+2, also enables to identify the presence of chirality and when it is broken by doping or by eliminating atom pairs (as in the case of odd number of atoms chains). Hints to identify bulk behavior thanks to δ1,3 are also provided. Overall, we present a very simple, orbital invariant visualization tool that should help the analysis of chirality (independently of the crystallinity of the system) as well as spreading the concepts of topological behavior thanks to its relationship with well-known chemical concepts.

2D Honeycomb-Kagome Polymer Tandem as Effective Metal-Free Photocatalysts for Water Splitting

On the basis of first-principles calculations, the potential of applying 2D honeycomb-kagome polymers made of heteroatom-centered triangulene derivatives to photocatalyze water splitting is explored. The designed 2D polymers possess indirect bandgaps in the range of 1.80-2.84 eV and show pronounced light absorption in the ultraviolet and visible region of the solar spectrum. With suitable band edge alignment, the examined N- and B-center polymers can generate sufficient photon-excited electrons and holes to activate the hydrogen and oxygen evolution reactions, respectively. The combination of lattice-inherent band features (flat bands) with chemical functionalization (potential shift due to heteroatoms) makes it possible to construct tandem cells with suppressed electron/hole recombination for effective overall water splitting. In addition, there is a potential difference between the half-electrodes that can be utlized to power​ auxiliary components in self-sufficient photocatalyzers.

Two dimensional honeycomb-kagome Be3Pb2: a mechanically flexible topological insulator with high intrinsic carrier mobilities

We theoretically predict a stable 2D nanosheet consisting of Pb and Be atoms sited at the honeycomb and kagome sites, respectively, forming a mixed honeycomb-kagome phase of Be3Pb2. Without the spin-orbit interaction, its band structure resembles that of honeycomb-structured graphene, namely, the valence and conduction bands touch at isolated points, whose energies linearly depend on the momentum. The presence of spin-orbit coupling (SOC), however, would result in a small bandgap opening, ∼116 meV. So, the SOC induces an electronic phase transition from a semimetal to a semiconductor. A coarse estimation based on the deformation potential method gives rise to very high carrier mobilities which are at least comparable to those of black phosphorene. Most interestingly, the 2D Be3Pb2 shows a non-trivial topology in the electronic structure accompanying the SOC induced band gap opening. Hence, 2D Be3Pb2 would be a versatile candidate for many applications, e.g., nanoelectronic devices.

Exotic Topological Bands and Quantum States in Metal-Organic and Covalent-Organic Frameworks

ConspectusMetal-organic and covalent-organic frameworks (MOFs/COFs) have been extensively studied for fundamental interests and their promising applications, taking advantage of their unique structural properties, i.e., high porosity and large surface-to-volume ratio. However, their electronic and magnetic properties have been somewhat overlooked because of their relatively poor performance as conductive and/or magnetic materials. Recent experimental breakthroughs in synthesizing two-dimensional (2D) π-conjugated MOFs/COFs with high conductivity and robust magnetism through doping have generated renewed and increasing interest in their electronic properties. Meanwhile, comprehensive theoretical studies of the underlying physical principles have led to discovery of many exotic quantum states, such as topological insulating states, which were only observed in inorganic systems. Especially, the diversity and high tunability of MOFs/COFs have provided a playground to explore novel quantum physics and quantum chemistry as well as promising applications.The band theory has empowered us to understand the most fundamental electronic properties of inorganic crystalline materials, which can also be used to better understand MOFs/COFs. The first obvious difference between the two is that instead of atomic orbitals residing at lattice sites of inorganic crystals, molecular orbitals of organic ligands are predominant in MOFs/COFs. The second key difference is that usually all atomic orbitals in an inorganic crystal are subject to one common group of lattice symmetry, while atomic orbitals of metal ion and molecular orbitals of different organic ligands in MOFs/COFs belong to different subgroups of lattice symmetries. Both these differences will impact the band structure of MOFs/COFs, in particular making it more complex. Consequently, which subset of bands are of most importance depends strongly on the location of Fermi level, i.e., electron counting and charge doping. Furthermore, there are usually two types of characteristic electrons coupled in MOFs, i.e., strongly correlated localized d and f electrons and diffusive s and p electrons, which interplay with lattice, orbital, and spin degrees of freedom, leading to more exotic topological and magnetic band structures.In this Account, we present an up-to-date review of recent theoretical developments to better understand the exotic band structures of MOFs/COFs. Starting from three fundamental 2D lattice models, i.e., honeycomb, Kagome, and Lieb lattices, exotic Dirac and flat bands as well as the intriguing topological quantum states they host, e.g., quantum spin Hall and quantum anomalous Hall states, are outlined. In addition to the single-lattice models, we further elaborate on combined lattice model Hamiltonians, which give rise to overlapping bands hosting novel quantum states, such as nodal-line Dirac semimetal and unconventional superconducting states. Also, first-principles predictions of candidate MOFs/COFs that host these exotic bands and hence quantum phases are reviewed, which greatly extends the pool of materials beyond inorganic crystals for hosting exotic band structures.

Hexagonal Zr3X (X = Al, Ga, In) Metals: High Dynamic Stability, Nodal Loop, and Perfect Nodal Surface States

In recent years, topological semimetals/metals, including nodal point, nodal line, and nodal surface semimetals/metals, have been studied extensively because of their potential applications in spintronics and quantum computers. In this study, we predict a family of materials, Zr₃X (X = Al, Ga, In), hosting the nodal loop and nodal surface states in the absence of spin–orbit coupling. Remarkably, the energy variation of the nodal loop and nodal surface states in Zr₃X are very small, and these topological signatures lie very close to the Fermi level. When the effect of spin–orbit coupling is considered, the nodal loop and nodal surface states exhibit small energy gaps (<25 and 35 meV, respectively) that are suitable observables that reflect the spin-orbit coupling response of these topological signatures and can be detected in experiments. Moreover, these compounds are dynamically stable, and they consequently form potential material platforms to study nodal loop and nodal surface semimetals.

Realization of Opened and Closed Nodal Lines and Four- and Three-fold Degenerate Nodal Points in XPt (X = Sc, Y, La) Intermetallic Compound: A Computational Modeling Study

Realizing rich topological elements in topological materials has attracted increasing attention in the fields of chemistry, physics, and materials science. Topological semimetals/metals are classified into three main types: nodal-point, nodal-line, and nodal-surface types with zero-, one-, and two-dimensional topological elements, respectively. This study reports that XPt (X = Sc, Y, La) intermetallic compounds are topological metals with opened and closed nodal lines, and triply degenerate nodal points (TNPs) when the spin-orbit coupling (SOC) is ignored. Based on the calculated phonon dispersions, one can find that ScPt and YPt are dynamically stable whereas LaPt is not. When SOC is added, the one-dimensional nodal line and zero-dimensional TNPs disappear. Interestingly, a new zero-dimensional topological element, that is, Dirac points with 4-fold degenerate isolated band crossings with linear band dispersion appear. The proposed materials can be considered a good platform to realize zero- and one-dimensional topological elements in a single compound and to study the relationship between zero- and one-dimensional topological elements.

Isolated flat bands and physics of mixed dimensions in a 2D covalent organic framework

We demonstrate that it is possible to rationally incorporate both an isolated flat band and the physics of zero dimensions (0D), one dimension (1D), and two dimensions (2D) in a single 2D material. Such unique electronic properties are present in a recently synthesized 2D covalent organic framework (COF), where "I"-shaped building blocks and "T"-shaped connectors result in quasi-1D chains that are linked by quasi-0D bridge units arranged in a stable 2D lattice. The lowest unoccupied conduction band is an isolated flat band, and electron-doping gives rise to novel quantum phenomena, such as magnetism and Mott insulating phases. The highest occupied valence band arises from wave functions in the quasi-1D chains. Examples of mixed dimensional physics are illustrated in this system. The strong electron-hole asymmetry in this material results in a large Seebeck coefficient, while the quasi-1D nature of the chains leads to linear dichroism, in conjunction with strongly bound 2D excitons. We elucidate strategies to design and optimize 2D COFs to host both isolated flat bands and quantum-confined 1D subsystems. The properties of the 2D COF discussed here provide a taste of the intriguing possibilities in this open research field.

Non-Collinear Orbital-induced Planar Quantum Anomalous Hall Effect

Based on the 2D star lattice with noncollinear orbital, we present an intriguing six-band tight-binding model for planar quantum anomalous Hall effect (PQAHE) with in-plane magnetization. Depending on the orientation of the noncollinear orbital, the characterized Dirac-, Kagome-, and Four-band are all realizable. Moreover, including the intrinsic spin-orbital coupling, a topological phase diagram versus angle of both in-plane magnetization and noncollinear orbital is mapped out, showing a tunable PQAHE with Chern number of either +1 or -1. Most remarkably, using first-principles calculations, this exact model of PQAHE is identified in an experimentally synthesized 2D metal-organic framework (MOF) of Pr₂(C₆O₄Cl₂)₃. These notable results not only demonstrate the significance of noncollinear orbital for designing PQAHE but also provide a MOF platform for its realization, greatly enriching the fundamental topological physics and extending the candidate topological materials.

Unique topological nodal line states and associated exceptional thermoelectric power factor platform in Nb3GeTe6 monolayer and bulk

To date, ideal topological nodal line semimetal (TNLS) candidates in high dynamically stable and high thermally stable two-dimensional (2D) materials are still extremely scarce. Herein, by performing first-principles calculations, on the one hand, we found that three-dimensional Nb₃GeTe₆ bulk possesses a single closed TNL in the k_x = 0 plane and a fourfold TNL in the S-R direction without considering spin-orbit coupling (SOC). Under the SOC effect, a new topological signature, i.e., hourglass-like Dirac nodal line, occurs in Nb₃GeTe₆ bulk. On the other hand, we found that the 2D Nb₃GeTe₆ monolayer features a doubly degenerate TNL along surface X-S paths. Importantly, this monolayer enjoys the following advantages: (i) it has high thermal stability at room temperature and above; (ii) its TNL is nearly flat in energy and is very close to the Fermi level (E_F), which provides a fantastic maximum value platform of the thermoelectric power factor around the E_F; and (iii) no extraneous bands are close to the TNL, near the Fermi level. Moreover, we explore the entanglement between the topological states and thermolectric properties for the 2D Nb₃GeTe₆ monolayer. Our work not only reports the discovery of a novel TNL material, but also builds the link between the TNL and thermoelectric properties.