Intrinsic quantum anomalous hall effect in a two-dimensional anilato-based lattice

Structural, electronic phase transitions and thermal spin transport properties in 2D NbSe2 and NbS2: a first-principles study

How to effectively tune 2D electronic and magnetic properties is key to developing novel spintronic materials and devices. Although the strain induced metal-to-half-metal electronic phase transition (EPT) has been studied in 2H NbSe₂ and NbS₂ monolayers, the 1T phase, the Coulomb interaction and the transport properties have not been explored. Here, using first-principles calculations in junction with nonequilibrium Green's function, we present a comprehensive and comparative study on the strain tuned structural, electronic, magnetic and thermal spin transport properties for NbSe₂ and NbS₂ monolayers with and without Coulomb interaction. It is found that the Coulomb interaction makes the strain induced 2H-to-1T structural phase transition easier. Similar to the 2H phase, there is also a strain induced metal-to-half-metal EPT for the 1T phase without Coulomb interaction, and the Coulomb interaction makes the ETP easier. Remarkably, the 2H-NbSe₂ monolayer with Coulomb interaction is a bipolar spin gapless semiconductor (SGS), and novel Dirac half-metal and usually SGS can be obtained by the tensile strain. In addition, we predict the excellent spin Seebeck effect and thermal spin diode effect in the bipolar SGS of the 2H-NbSe₂ monolayer with Coulomb interaction, and expect the spin filtering effect and high magnetoresistance in the half-metals driven by the strain. We also discuss the strength of Coulomb interaction by comparing the theoretical and available experimental electronic states, indicating the indispensability of Coulomb interactions. These results suggest that 2D NbSe₂ and NbS₂ are promising candidates for phase-change spintronic materials and devices, and will stimulate extensive studies on this class of 2D systems.

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.

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.

Half-Dirac semimetals and the quantum anomalous Hall effect in Kagome Cd2N3 lattices

Half-Dirac semimetals (HDSs), which possess 100% spin-polarizations for Dirac materials, are highly desirable for exploring various topological phases of matter as low-dimensionality opens unprecedented opportunities for manipulating the quantum state of low-cost electronic nanodevices. The search for high-temperature HDSs is still a current hotspot and yet challenging experimentally. Herein based on first-principles calculations, we propose the realization of Half Dirac semimetals (HDS) in two-dimensional (2D) Kagome transition-metal nitride Cd₂N₃, which is robust against strain engineering. Monte Carlo simulations reveal that Cd₂N₃ possesses a Curie temperature reaching up to T _C = 225 K, which is much higher than that of the reported monolayers CrI₃ (T _C = 45 K) and Cr₂Ge₂Te₆ (T _C = 20 K). The band crossings in Cd₂N₃ are gapped out by the spin-orbit coupling, which brings about the quantum anomalous Hall (QAH) effect with a sizeable band gap of E _g = 4.9 meV, characterized by the nonzero Chern number (C = 1) and chiral edge states. A tight-binding model is further used to clarify the origin of HDSs and nontrivial electronic properties. The results suggest monolayer transition-metal nitrides as a promising platform to explore fascinating physical phenomena associated with novel 2D emergent HDSs and QAH insulators toward realistic spintronics devices, thus stimulating experimental interest.

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.

Metal-organic frameworks: possible new two-dimensional magnetic and topological materials

Finding new two-dimensional (2D) materials with novel quantum properties is highly desirable for technological innovations. In this work, we studied a series of metal-organic frameworks (MOFs) with different metal cores and discovered various attractive properties, such as room-temperature magnetic ordering, strong perpendicular magnetic anisotropy, huge topological band gap (>200 meV), and excellent spin-filtering performance. As many MOFs have been successfully synthesized in experiments, our results suggest realistic new 2D functional materials for the design of spintronic nanodevices.

High-temperature and multichannel quantum anomalous Hall effect in pristine and alkali-metal-doped CrBr3 monolayers

The realization of the high-temperature and multichannel quantum anomalous Hall effect (QAHE) has been a central research area in the development of low-power-consumption electronics and quantum computing. Recently discovered two-dimensional (2D) ferromagnetic (FM) materials provide unprecedented opportunities for the exploration of the high-temperature QAHE. Based on first-principles approaches, we first reveal that a FM CrBr₃ monolayer harbors topologically nontrivial conduction bands with a high Chern number of C = 2. Then, we reveal that the interesting conduction bands can be moved downwards to the Fermi levels by electron and alkali-metal-doping; meanwhile, the QAHE characteristics can be preserved. Most strikingly, the Na-doped CrBr₃ system possesses a higher Chern number of C = -4 with a transition temperature of ∼54 K, which is attributed to the constructive coupling effect of the quadratic non-Dirac and linear Dirac band dispersions. The present study, together with recent achievements in the field of 2D FM materials, provides an experimentally achievable guide for realizing the high-temperature and multichannel QAHE based purely on 2D FM systems.

Organic topological insulators (OTI): a dream coming true?

Experimental discovery of organic topological insulators (OTI) is a dream for both topological matters and organic materials. Despite great challenges, we anticipate that the dream will become a reality by engineered studies on materials chemistry, characterization techniques and device physics of conjugated molecules.

Topological Band Engineering of Lieb Lattice in Phthalocyanine-Based Metal-Organic Frameworks

Topological properties of the Lieb lattice, i.e., the edge-centered square lattice, have been extensively studied and are, however, mostly based on theoretical models without identifying real material systems. Here, based on tight-binding and first-principles calculations, we demonstrate the Lieb-lattice features of the experimentally synthesized phthalocyanine-based metal-organic framework (MPc-MOF), which holds various intriguing topological phase transitions through band engineering. First, we show that the MPc-MOFs indeed have a peculiar Lieb band structure with 1/3 filling, which has been overlooked because of its unconventional band structure deviating from the ideal Lieb band. The intrinsic MPc-MOF presents a trivial insulating state, with its gap size determined by the on-site energy difference (ΔE) between the corner and edge-center sites. Through either chemical substitution or physical strain engineering, one can tune ΔE to close the gap and achieve a topological phase transition. Specifically, upon closing the gap, topological semimetallic/insulating states emerge from nonmagnetic MPc-MOFs, while magnetic semimetal/Chern insulator states arise from magnetic MPc-MOFs, respectively. Our discovery greatly enriches our understanding of the Lieb lattice and provides a guideline for experimental observation of the Lieb-lattice-based topological states.

π-Orbital Yin–Yang Kagome bands in anilato-based metal–organic frameworks

π-Orbital Yin–Yang Kagome bands consisting of two flat bands with opposite Chern numbers have been disclosed in anilato-based metal–organic frameworks.

Metal-Organic Frameworks in Modern Physics: Highlights and Perspectives

Owing to the synergistic combination of a hybrid organic-inorganic nature and a chemically active porous structure, metal-organic frameworks have emerged as a new class of crystalline materials. The current trend in the chemical industry is to utilize such crystals as flexible hosting elements for applications as diverse as gas and energy storage, filtration, catalysis, and sensing. From the physical point of view, metal-organic frameworks are considered molecular crystals with hierarchical structures providing the structure-related physical properties crucial for future applications of energy transfer, data processing and storage, high-energy physics, and light manipulation. Here, the perspectives of metal-organic frameworks as a new family of functional materials in modern physics are discussed: from porous metals and superconductors, topological insulators, and classical and quantum memory elements, to optical superstructures, materials for particle physics, and even molecular scale mechanical metamaterials. Based on complementary properties of crystallinity, softness, organic-inorganic nature, and complex hierarchy, a description of how such artificial materials have extended their impact on applied physics to become the mainstream in material science is offered.

The shielding effects of a C60 cage on the magnetic moments of transition metal atoms inside the corner holes of Si(111)-(7 × 7)

The strong interaction between transition metal (TM) atoms and semiconductor surface atoms may diminish the magnetic moments of the TM atoms and prevent them from being used as single atom spin-based devices. A carbon cage that can encapsulate TM atoms and isolate them from interacting with surface atoms is considered to protect the magnetic moments of the TM atoms. We have studied the magnetic moments of Fe, Co, and Ni atoms adsorbed inside the corner hole of Si(111)-(7 × 7) by using first-principles calculations based on the density functional theory. The results show that when Co and Ni atoms are directly adsorbed inside the corner hole, the magnetic moments are 1.353μB and 0, respectively. However when a C60 cage is used to encapsulate the atoms, the magnetic moments increase to 1.849μB and 0.884μB, respectively. The results show a clear protecting effect of a carbon cage. For Fe with and without C60, the magnetic moments are 2.909μB and 2.825μB, respectively. The presence of a C60 cage can also maintain their magnetic moments. Further analysis shows that the TM atoms possess magnetic moments when the conduction electrons are localized around them. All the results can be well understood in the framework of the Anderson impurity model. Our results demonstrate that a carbon cage may effectively protect the magnetic moments of TM atoms. This provides a new strategy for developing single atom spin-based devices on semiconductors.

Intrinsic ferromagnetism and topological properties in two-dimensional rhenium halides

The realization of robust intrinsic ferromagnetism in two-dimensional (2D) materials in conjunction with the intriguing quantum anomalous Hall (QAH) effect has provided a fertile ground for novel physics and for the next-generation spintronic and topological devices. On the basis of density functional theory (DFT), we predict that layered 5d transition-metal heavier halides (TMHs), such as ReX3 (X = Br, I), show intrinsic ferromagnetism with high spin polarization and high Curie temperatures. The outstanding dynamic and thermodynamic stability ensures their experimental feasibility. The strong spin-orbit coupling (SOC) of Re makes the electronic structure of the ReI3 monolayer topologically nontrivial with a large Chern number (C = -4). DFT+U calculations reveal that the 2D system undergoes a nontrivial to trivial transition with increasing on-site Hubbard Coulomb interaction U through the emergence of a Dirac cone. This transition is corroborated by the emergence of chiral edge states and the anomalous Hall conductivity. These findings not only demonstrate room-temperature ferromagnetism in atomically thin 5d TMHs, but also pave the way for the potential realization of the QAH effect with high Chern numbers in pristine 2D layers.

Two-dimensional honeycomb-kagome Ta2S3: a promising single-spin Dirac fermion and quantum anomalous hall insulator with half-metallic edge states

Recent experimental success in the realization of two-dimensional (2D) magnetism has invigorated the search for new 2D magnetic materials with a large magnetocrystalline anisotropy, high Curie temperature, and high carrier mobility. Using first-principles calculations, here we predict a novel class of single-spin Dirac fermion states in a 2D Ta2S3 monolayer, characterized by a band structure with a large gap in one spin channel and a Dirac cone in the other with carrier mobility comparable to that of graphene. Ta2S3 is dynamically and thermodynamically stable under ambient conditions, and possesses a large out-of-plane magnetic anisotropy energy and a high Curie temperature (TC = 445 K) predicted from the spin-wave theory. When the spin and orbital degrees of freedom are allowed to couple, the Ta2S3 monolayer becomes a Chern insulator with a fully spin-polarized half-metallic edge state. An effective four-band tight-binding model is constructed to clarify the origin of a semi-Dirac cone in a spin-up channel and nontrivial band topology, which can be well maintained on a semiconducting substrate. The combination of these unique single-spin Dirac fermion and quantum anomalous Hall states renders the 2D Ta2S3 lattice a promising platform for applications in topologically high fidelity data storage and energy-efficient spintronic devices.

Dichotomy between frustrated local spins and conjugated electrons in a two-dimensional metal-organic framework

Dichotomy between local spins and conjugated electrons spawns various exotic physical phenomena, however, it has mostly been reported in three-dimensional (3D) inorganic systems. We show, for the first time, that a rare 2D metal-organic framework exhibits intriguing dichotomy behavior, which can be directly identified through scanning tunneling microscopy/spectroscopy (STM/STS). In a newly synthesized Cu-hexaiminobenzene [Cu3(HAB)2], on the one hand, the Cu2+ ions form an ideal S - 1/2 antiferromagnetic (AFM) kagome lattice; on the other hand, the conjugated-electrons from the organic ligands produce a frustrated πx,y model on a honeycomb lattice, giving rise to completely dispersionless energy bands around the Fermi level that favour the ferromagnetic (FM) state. Remarkably, the frustrated local spins and conjugated electrons interact through a strong FM Hund's coupling, giving rise to a wide range of intriguing quantum phases. Furthermore, we propose that this dichotomy can be directly characterized through STM/STS measurements due to its special 2D nature, which provides a unique exciting platform to investigate the dichotomy of frustrated spins and electrons in a single lattice.