Flatbands and Emergent Ferromagnetic Ordering in Fe_{3}Sn_{2} Kagome Lattices

Intrinsic anomalous Hall effect in thin films of topological kagome ferromagnet Fe3Sn2

Fe₃Sn₂, a kagome ferromagnet, is a potential quantum material with intriguing topological features. Despite substantial experimental work on the bulk single crystals, the thin film growth of Fe₃Sn₂ remains relatively unexplored. Here, we investigate the effect of two different seed layers (Ta and Pt) on the growth of Fe₃Sn₂ thin films. We demonstrate the growth of polycrystalline Fe₃Sn₂ thin films on Si/SiO₂ substrates by room temperature sputter deposition, followed by in situ annealing at 500 °C. Our structural and magnetic measurements indicate that a pure ferromagnetic phase is formed for the Pt/Fe₃Sn₂ thin films with higher saturation magnetization of M_s = 464 emu cc^-1, while a mixed-phase (consisting of ferromagnetic, Fe₃Sn₂ and antiferromagnetic, FeSn) is formed for the Ta/Fe₃Sn₂ thin films with a lower M_s of 240 emu cc^-1. The Pt/Fe₃Sn₂ thin films also exhibit an anomalous Hall coefficient, R_s ≈ 2.6 × 10^-10 Ω cm^-1 G^-1 at room temperature, which is two order of magnitude higher compared to 3d-transition metal ferromagnets. A non-zero temperature-independent anomalous Hall conductivity σintxy = (23 ± 11) Ω^-1 cm^-1 indicates an intrinsic mechanism of anomalous Hall effect originating from Berry curvature. These results are important for realizing novel topological spintronic devices on a CMOS-compatible substrate.

Observation of Topological Flat Bands in the Kagome Semiconductor Nb3Cl8

The destructive interference of wavefunctions in a kagome lattice can give rise to topological flat bands (TFBs) with a highly degenerate state of electrons. Recently, TFBs have been observed in several kagome metals, including Fe₃Sn₂, FeSn, CoSn, and YMn₆Sn₆. Nonetheless, kagome materials that are both exfoliable and semiconducting are lacking, which seriously hinders their device applications. Herein, we show that Nb₃Cl₈, which hosts a breathing kagome lattice, is gapped out because of the absence of inversion symmetry, while the TFBs survive because of the protection of the mirror reflection symmetry. By angle-resolved photoemission spectroscopy measurements and first-principles calculations, we directly observe the TFBs and a moderate band gap in Nb₃Cl₈. By mechanical exfoliation, we successfully obtain monolayer Nb₃Cl₈, which is stable under ambient conditions. In addition, our calculations show that monolayer Nb₃Cl₈ has a magnetic ground state, thus providing opportunities to study the interplay among geometry, topology, and magnetism.

A new class of bilayer kagome lattice compounds with Dirac nodal lines and pressure-induced superconductivity

Kagome lattice composed of transition-metal ions provides a great opportunity to explore the intertwining between geometry, electronic orders and band topology. The discovery of multiple competing orders that connect intimately with the underlying topological band structure in nonmagnetic kagome metals AV3Sb5 (A = K, Rb, Cs) further pushes this topic to the quantum frontier. Here we report a new class of vanadium-based compounds with kagome bilayers, namely AV6Sb6 (A = K, Rb, Cs) and V6Sb4, which, together with AV3Sb5, compose a series of kagome compounds with a generic chemical formula (Am-1Sb2m)(V3Sb)n (m = 1, 2; n = 1, 2). Theoretical calculations combined with angle-resolved photoemission measurements reveal that these compounds feature Dirac nodal lines in close vicinity to the Fermi level. Pressure-induced superconductivity in AV6Sb6 further suggests promising emergent phenomena in these materials. The establishment of a new family of layered kagome materials paves the way for designer of fascinating kagome systems with diverse topological nontrivialities and collective ground states.

Observation of a Flat and Extended Surface State in a Topological Semimetal

A flat band structure in momentum space is considered key for the realization of novel phenomena. A topological flat band, also known as a drumhead state, is an ideal platform to drive new exotic topological quantum phases. Using angle-resolved photoemission spectroscopy experiments, we reveal the emergence of a highly localized surface state in a topological semimetal BaAl4 and provide its full energy and momentum space topology. We find that the observed surface state is localized in momentum, inside a square-shaped bulk Dirac nodal loop, and in energy, leading to a flat band and a peak in the density of state. These results imply this class of materials as an experimental realization of drumhead surface states and provide an important reference for future studies of the fundamental physics of correlated quantum effects in topological materials.

Flat-Band-Induced Anomalous Anisotropic Charge Transport and Orbital Magnetism in Kagome Metal CoSn

For solids, the dispersionless flat band has long been recognized as an ideal platform for achieving intriguing quantum phases. However, experimental progress in revealing flat-band physics has so far been achieved mainly in artificially engineered systems represented as magic-angle twisted bilayer graphene. Here, we demonstrate the emergence of flat-band-dominated anomalous transport and magnetic behaviors in CoSn, a paramagnetic kagome-lattice compound. By combination of angle-resolved photoemission spectroscopy measurements and first-principles calculations, we reveal the existence of a kagome-lattice-derived flat band right around the Fermi level. Strikingly, the resistivity within the kagome lattice plane is more than one order of magnitude larger than the interplane one, in sharp contrast with conventional (quasi-) two-dimensional layered materials. Moreover, the magnetic susceptibility under the out-of-plane magnetic field is found to be much smaller as compared with the in-plane case, which is revealed to be arising from the introduction of a unique orbital diamagnetism. Systematic analyses reveal that these anomalous and giant anisotropies can be reasonably attributed to the unique properties of flat-band electrons, including large effective mass and self-localization of wave functions. Our results broaden the already fascinating flat-band physics, and demonstrate the feasibility of exploring them in natural solid-state materials in addition to artificial ones.

Realizing Kagome Band Structure in Two-Dimensional Kagome Surface States of RV_{6}Sn_{6} (R=Gd, Ho)

We report angle resolved photoemission experiments on a newly discovered family of kagome metals RV_{6}Sn_{6} (R=Gd, Ho). Intrinsic bulk states and surface states of the vanadium kagome layer are differentiated from those of other atomic sublattices by the real-space resolution of the measurements with a small beam spot. Characteristic Dirac cone, saddle point, and flat bands of the kagome lattice are observed. Our results establish the two-dimensional (2D) kagome surface states as a new platform to investigate the intrinsic kagome physics.

Cascade of correlated electron states in the kagome superconductor CsV3Sb5

The kagome lattice of transition metal atoms provides an exciting platform to study electronic correlations in the presence of geometric frustration and nontrivial band topology^1-18, which continues to bear surprises. Here, using spectroscopic imaging scanning tunnelling microscopy, we discover a temperature-dependent cascade of different symmetry-broken electronic states in a new kagome superconductor, CsV₃Sb₅. We reveal, at a temperature far above the superconducting transition temperature T_c ~ 2.5 K, a tri-directional charge order with a 2a₀ period that breaks the translation symmetry of the lattice. As the system is cooled down towards T_c, we observe a prominent V-shaped spectral gap opening at the Fermi level and an additional breaking of the six-fold rotational symmetry, which persists through the superconducting transition. This rotational symmetry breaking is observed as the emergence of an additional 4a₀ unidirectional charge order and strongly anisotropic scattering in differential conductance maps. The latter can be directly attributed to the orbital-selective renormalization of the vanadium kagome bands. Our experiments reveal a complex landscape of electronic states that can coexist on a kagome lattice, and highlight intriguing parallels to high-T_c superconductors and twisted bilayer graphene.

Unconventional chiral charge order in kagome superconductor KV3Sb5

Intertwining quantum order and non-trivial topology is at the frontier of condensed matter physics^1-4. A charge-density-wave-like order with orbital currents has been proposed for achieving the quantum anomalous Hall effect^5,6 in topological materials and for the hidden phase in cuprate high-temperature superconductors^7,8. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy to discover an unconventional chiral charge order in a kagome material, KV₃Sb₅, with both a topological band structure and a superconducting ground state. Through both topography and spectroscopic imaging, we observe a robust 2 × 2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2 × 2 charge modulation exhibits an intensity reversal in real space, signalling charge ordering. At the impurity-pinning-free region, the strength of intrinsic charge modulations further exhibits chiral anisotropy with unusual magnetic field response. Theoretical analysis of our experiments suggests a tantalizing unconventional chiral charge density wave in the frustrated kagome lattice, which can not only lead to a large anomalous Hall effect with orbital magnetism, but also be a precursor of unconventional superconductivity.

Dirac cone, flat band and saddle point in kagome magnet YMn6Sn6

Kagome-lattices of 3d-transition metals hosting Weyl/Dirac fermions and topological flat bands exhibit non-trivial topological characters and novel quantum phases, such as the anomalous Hall effect and fractional quantum Hall effect. With consideration of spin-orbit coupling and electron correlation, several instabilities could be induced. The typical characters of the electronic structure of a kagome lattice, i.e., the saddle point, Dirac-cone, and flat band, around the Fermi energy (EF) remain elusive in magnetic kagome materials. We present the experimental observation of the complete features in ferromagnetic kagome layers of YMn6Sn6 helically coupled along the c-axis, by using angle-resolved photoemission spectroscopy and band structure calculations. We demonstrate a Dirac dispersion near EF, which is predicted by spin-polarized theoretical calculations, carries an intrinsic Berry curvature and contributes to the anomalous Hall effect in transport measurements. In addition, a flat band and a saddle point with a high density of states near EF are observed. These multi-sets of kagome features are of orbital-selective origin and could cause multi-orbital magnetism. The Dirac fermion, flat band and saddle point in the vicinity of EF open an opportunity in manipulating the topological properties in magnetic materials.

Realistic flat-band model based on degenerate p-orbitals in two-dimensional ionic materials

Though several theoretical models have been proposed to design electronic flat-bands, the definite experimental realization in two-dimensional atomic crystal is still lacking. Here we propose a novel and realistic flat-band model based on threefold degenerate p-orbitals in two-dimensional ionic materials. Our theoretical analysis and first-principles calculations show that the proposed flat-band can be realized in 1T layered materials of alkali-metal chalogenides and metal-carbon group compounds. Some of the former are theoretically predicted to be stable as layered materials (e.g., K₂S), and some of the latter have been experimentally fabricated in previous works (e.g., Gd₂CCl₂). More interestingly, the flat-band is partially filled in the heterostructure of a K₂S monolayer and graphene layers. The spin polarized nearly flat-band can be realized in the ferromagnetic state of a Gd₂CCl₂ monolayer, which has been fabricated in experiments. Our theoretical model together with the material predictions provide a realistic platform for the study of flat-bands and related exotic quantum phases.

Field-induced topological Hall effect and double-fan spin structure with a c-axis component in the metallic kagome antiferromagnetic compound YMn6Sn6

Geometric frustration in the kagome lattice makes it a great host for the flat electronic band, nontrivial topological properties, and novel magnetism. Here, we use magnetotransport measurements to map out the field-temperature phase diagram of the centrosymmetric YMn6Sn6 with a Mn kagome lattice and show that the system exhibits the topological Hall effect (THE) with an in-plane applied magnetic field around 240 K. In addition, our neutron diffraction results demonstrate that the observed THE cannot arise from a magnetic skyrmion lattice, but instead from an in-plane field-induced double-fan spin structure with c -axis components. This paper provides a platform to understand the influence of a field-induced novel magnetic structure on magnetoelectric response in topological kagome metals.

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.

Isotropic Nature of the Metallic Kagome Ferromagnet Fe3Sn2 at High Temperatures

Anisotropy and competing exchange interactions have emerged as two central ingredients needed for centrosymmetric materials to exhibit topological spin textures. Fe3Sn2 is thought to have these ingredients as well, as it has recently been discovered to host room temperature skyrmionic bubbles with an accompanying topological Hall effect. We present small-angle inelastic neutron scattering measurements that unambiguously show that Fe3Sn2 is an isotropic ferromagnet below T C ≈ 660     K to at least 480 K - the lower temperature threshold of our experimental configuration. Fe3Sn2 is known to have competing magnetic exchange interactions, correlated electron behavior, weak magnetocrystalline anisotropy, and lattice anisotropy; all of these features are thought to play a role in stabilizing skyrmions in centrosymmetric systems. Our results reveal that at elevated temperatures, there is an absence of magnetocrystalline anisotropy and that the system behaves as a typical exchange ferromagnet with a spin stiffness D T = 0   K = 271 ± 9   meV     Å 2 .

Kagome van-der-Waals Pd3P2S8 with flat band

With the advanced investigations into low-dimensional systems, it has become essential to find materials having interesting lattices that can be exfoliated down to monolayer. One particular important structure is a kagome lattice with its potentially diverse and vibrant physics. We report a van-der-Waals kagome lattice material, Pd₃P₂S_8, with several unique properties such as an intriguing flat band. The flat band is shown to arise from a possible compact-localized state of all five 4d orbitals of Pd. The diamagnetic susceptibility is precisely measured to support the calculated susceptibility obtained from the band structure. We further demonstrate that Pd₃P₂S₈ can be exfoliated down to monolayer, which ultimately will allow the possible control of the localized states in this two-dimensional kagome lattice using the electric field gating.

Localized spin-orbit polaron in magnetic Weyl semimetal Co3Sn2S2

The kagome lattice Co₃Sn₂S₂ exhibits the quintessential topological phenomena of a magnetic Weyl semimetal such as the chiral anomaly and Fermi-arc surface states. Probing its magnetic properties is crucial for understanding this correlated topological state. Here, using spin-polarized scanning tunneling microscopy/spectroscopy (STM/S) and non-contact atomic force microscopy (nc-AFM) combined with first-principle calculations, we report the discovery of localized spin-orbit polarons (SOPs) with three-fold rotation symmetry nucleated around single S-vacancies in Co₃Sn₂S_2. The SOPs carry a magnetic moment and a large diamagnetic orbital magnetization of a possible topological origin associated relating to the diamagnetic circulating current around the S-vacancy. Appreciable magneto-elastic coupling of the SOP is detected by nc-AFM and STM. Our findings suggest that the SOPs can enhance magnetism and more robust time-reversal-symmetry-breaking topological phenomena. Controlled engineering of the SOPs may pave the way toward practical applications in functional quantum devices.

Kagome lattice material Co₃Sn₂S₂ is identified as a magnetic Weyl semimetal and its magnetic properties are less studied. Here, the authors observe localized spin-orbit polarons nucleated around single S-vacancies carrying a large diamagnetic orbital magnetism in Co₃Sn₂S₂.

Target Bubbles in Fe3Sn2 Nanodisks at Zero Magnetic Field

We report a vortex-like magnetic configuration in uniaxial ferromagnet Fe₃Sn₂ nanodisks using differential phase contrast scanning transmission electron microscopy. This magnetic configuration is transferred from a conventional magnetic vortex using a zero-magnetic-field warming process and is characterized by a series of concentric cylinder domains. We termed them as "target bubbles" that are identified as three-dimensional depth-modulated magnetic objects in combination with numerical simulations. Target bubbles have room-temperature stability even at zero magnetic field and multiple stable magnetic configurations. These advantages render the target bubble an ideal bit to be an information carrier and can advance magnetic target bubbles toward functionalities in the long term by incorporating emergent degrees of freedom and purely electrically controllable magnetism.

Spin-orbit quantum impurity in a topological magnet

Quantum states induced by single-atomic impurities are at the frontier of physics and material science. While such states have been reported in high-temperature superconductors and dilute magnetic semiconductors, they are unexplored in topological magnets which can feature spin-orbit tunability. Here we use spin-polarized scanning tunneling microscopy/spectroscopy (STM/S) to study the engineered quantum impurity in a topological magnet Co3Sn2S2. We find that each substituted In impurity introduces a striking localized bound state. Our systematic magnetization-polarized probe reveals that this bound state is spin-down polarized, in lock with a negative orbital magnetization. Moreover, the magnetic bound states of neighboring impurities interact to form quantized orbitals, exhibiting an intriguing spin-orbit splitting, analogous to the splitting of the topological fermion line. Our work collectively demonstrates the strong spin-orbit effect of the single-atomic impurity at the quantum level, suggesting that a nonmagnetic impurity can introduce spin-orbit coupled magnetic resonance in topological magnets.

Spin-Reorientation-Induced Band Gap in Fe_{3}Sn_{2}: Optical Signatures of Weyl Nodes

Temperature- and frequency-dependent infrared spectroscopy identifies two contributions to the electronic properties of the magnetic kagome metal Fe_{3}Sn_{2}: two-dimensional Dirac fermions and strongly correlated flat bands. The interband transitions within the linearly dispersing Dirac bands appear as a two-step feature along with a very narrow Drude component due to intraband contribution. Low-lying absorption features indicate flat bands with multiple van Hove singularities. Localized charge carriers are seen as a Drude peak shifted to finite frequencies. The spectral weight is redistributed when the spins are reoriented at low temperatures; a sharp mode appears suggesting the opening of a gap due to the spin reorientation as the sign of additional Weyl nodes in the system.

Orbital-selective Dirac fermions and extremely flat bands in frustrated kagome-lattice metal CoSn

Layered kagome-lattice 3d transition metals are emerging as an exciting platform to explore the frustrated lattice geometry and quantum topology. However, the typical kagome electronic bands, characterized by sets of the Dirac-like band capped by a phase-destructive flat band, have not been clearly observed, and their orbital physics are even less well investigated. Here, we present close-to-textbook kagome bands with orbital differentiation physics in CoSn, which can be well described by a minimal tight-binding model with single-orbital hopping in Co kagome lattice. The capping flat bands with bandwidth less than 0.2 eV run through the whole Brillouin zone, especially the bandwidth of the flat band of out-of-plane orbitals is less than 0.02 eV along Γ-M. The energy gap induced by spin-orbit interaction at the Dirac cone of out-of-plane orbitals is much smaller than that of in-plane orbitals, suggesting orbital-selective character of the Dirac fermions.

Electronic correlations and flattened band in magnetic Weyl semimetal candidate Co3Sn2S2

The interplay between electronic correlations and topological protection may offer a rich avenue for discovering emergent quantum phenomena in condensed matter. However, electronic correlations have so far been little investigated in Weyl semimetals (WSMs) by experiments. Here, we report a combined optical spectroscopy and theoretical calculation study on the strength and effect of electronic correlations in a magnet Co₃Sn₂S₂. The electronic kinetic energy estimated from our optical data is about half of that obtained from single-particle ab initio calculations in the ferromagnetic ground state, which indicates intermediate-strength electronic correlations in this system. Furthermore, comparing the energy and side-slope ratios between the interband-transition peaks at high energies in the experimental and single-particle-calculation-derived optical conductivity spectra with the bandwidth-renormalization factors obtained by many-body calculations enables us to estimate the Coulomb-interaction strength (U ∼ 4 eV) in Co₃Sn₂S₂. Besides, a sharp experimental optical conductivity peak at low energy, which is absent in the single-particle-calculation-derived spectrum but is consistent with the optical conductivity peaks obtained by many-body calculations with U ∼ 4 eV, indicates that an electronic band connecting the two Weyl cones is flattened by electronic correlations and emerges near the Fermi energy in Co₃Sn₂S₂. Our work paves the way for exploring flat-band-generated quantum phenomena in WSMs.

Topological flat bands in frustrated kagome lattice CoSn

Electronic flat bands in momentum space, arising from strong localization of electrons in real space, are an ideal stage to realize strongly-correlated phenomena. Theoretically, the flat bands can naturally arise in certain geometrically frustrated lattices, often with nontrivial topology if combined with spin-orbit coupling. Here, we report the observation of topological flat bands in frustrated kagome metal CoSn, using angle-resolved photoemission spectroscopy and band structure calculations. Throughout the entire Brillouin zone, the bandwidth of the flat band is suppressed by an order of magnitude compared to the Dirac bands originating from the same orbitals. The frustration-driven nature of the flat band is directly confirmed by the chiral d-orbital texture of the corresponding real-space Wannier functions. Spin-orbit coupling opens a large gap of 80 meV at the quadratic touching point between the Dirac and flat bands, endowing a nonzero Z2 invariant to the flat band. These findings demonstrate that kagome-derived flat bands are a promising platform for novel emergent phases of matter at the confluence of strong correlation and topology.

Quantum distance and anomalous Landau levels of flat bands

Semiclassical quantization of electronic states under a magnetic field, as proposed by Onsager, describes not only the Landau level spectrum but also the geometric responses of metals under a magnetic field^1-5. Even in graphene with relativistic energy dispersion, Onsager's rule correctly describes the π Berry phase, as well as the unusual Landau level spectrum of Dirac particles^6,7. However, it is unclear whether this semiclassical idea is valid in dispersionless flat-band systems, in which an infinite number of degenerate semiclassical orbits are allowed. Here we show that the semiclassical quantization rule breaks down for a class of dispersionless flat bands called 'singular flat bands'⁸. The singular flat band has a band crossing with another dispersive band that is enforced by the band-flatness condition, and shows anomalous magnetic responses. The Landau levels of a singular flat band develop in the empty region in which no electronic states exist in the absence of a magnetic field, and exhibit an unusual 1/n dependence on the Landau level index n, which results in diverging orbital magnetic susceptibility. The total energy spread of the Landau levels of a singular flat band is determined by the quantum geometry of the relevant Bloch states, which is characterized by their Hilbert-Schmidt quantum distance. We show that there is a universal and simple relationship between the total Landau level spread of a flat band and the maximum Hilbert-Schmidt quantum distance, which can be verified in various candidate materials. The results indicate that the anomalous Landau level spectrum of flat bands is promising for the direct measurement of the quantum geometry of wavefunctions in condensed matter.

Many-Body Resonance in a Correlated Topological Kagome Antiferromagnet

We use scanning tunneling microscopy to elucidate the atomically resolved electronic structure in the strongly correlated kagome Weyl antiferromagnet Mn_{3}Sn. In stark contrast to its broad single-particle electronic structure, we observe a pronounced resonance with a Fano line shape at the Fermi level resembling the many-body Kondo resonance. We find that this resonance does not arise from the step edges or atomic impurities but the intrinsic kagome lattice. Moreover, the resonance is robust against the perturbation of a vector magnetic field, but broadens substantially with increasing temperature, signaling strongly interacting physics. We show that this resonance can be understood as the result of geometrical frustration and strong correlation based on the kagome lattice Hubbard model. Our results point to the emergent many-body resonance behavior in a topological kagome magnet.

Quantum-limit Chern topological magnetism in TbMn6Sn6

The quantum-level interplay between geometry, topology and correlation is at the forefront of fundamental physics^1-15. Kagome magnets are predicted to support intrinsic Chern quantum phases owing to their unusual lattice geometry and breaking of time-reversal symmetry^14,15. However, quantum materials hosting ideal spin-orbit-coupled kagome lattices with strong out-of-plane magnetization are lacking^16-21. Here, using scanning tunnelling microscopy, we identify a new topological kagome magnet, TbMn₆Sn₆, that is close to satisfying these criteria. We visualize its effectively defect-free, purely manganese-based ferromagnetic kagome lattice with atomic resolution. Remarkably, its electronic state shows distinct Landau quantization on application of a magnetic field, and the quantized Landau fan structure features spin-polarized Dirac dispersion with a large Chern gap. We further demonstrate the bulk-boundary correspondence between the Chern gap and the topological edge state, as well as the Berry curvature field correspondence of Chern gapped Dirac fermions. Our results point to the realization of a quantum-limit Chern phase in TbMn₆Sn₆, and may enable the observation of topological quantum phenomena in the RMn₆Sn₆ (where R is a rare earth element) family with a variety of magnetic structures. Our visualization of the magnetic bulk-boundary-Berry correspondence covering real space and momentum space demonstrates a proof-of-principle method for revealing topological magnets.

Interplay of Magnetism and Topological Superconductivity in Bilayer Kagome Metals

The binary intermetallic materials, M_{3}Sn_{2} (M=3d transition metal) present a new class of strongly correlated systems that naturally allows for the interplay of magnetism and metallicity. Using first principles calculations we confirm that bulk Fe_{3}Sn_{2} is a ferromagnetic metal, and show that M=Ni and Cu are paramagnetic metals with nontrivial band structures. Focusing on Fe_{3}Sn_{2} to understand the effect of enhanced correlations in an experimentally relevant atomistically thin single kagome bilayer, our ab initio results show that dimensional confinement naturally exposes the flatness of band structure associated with the bilayer kagome geometry in a resultant ferromagnetic Chern metal. We use a multistage minimal modeling of the magnetic bands progressively closer to the Fermi energy. This effectively captures the physics of the Chern metal with a nonzero anomalous Hall response over a material relevant parameter regime along with a possible superconducting instability of the spin-polarized band resulting in a topological superconductor.

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.

Direct Observation of Flatband Loop States Arising from Nontrivial Real-Space Topology

Topological properties of lattices are typically revealed in momentum space using concepts such as the Chern number. Here, we study unconventional loop states, namely, the noncontractible loop states (NLSs) and robust boundary modes, mediated by nontrivial topology in real space. While such states play a key role in understanding fundamental physics of flatband systems, their experimental observation has been hampered because of the challenge in realizing desired boundary conditions. Using a laser-writing technique, we optically establish photonic kagome lattices with both an open boundary by properly truncating the lattice, and a periodic boundary by shaping the lattice into a Corbino geometry. We thereby demonstrate the robust boundary modes winding around the entire edge of the open lattice and, more directly, the NLSs winding in a closed loop akin to that in a torus. We prove that the NLSs due to real-space topology persist in ideal Corbino-shaped kagome lattices of arbitrary size. Our results could be of great importance for our understanding of the singular flatbands and the intriguing physics phenomenon applicable for strongly interacting systems.

Dirac fermions and flat bands in the ideal kagome metal FeSn

A kagome lattice of 3d transition metal ions is a versatile platform for correlated topological phases hosting symmetry-protected electronic excitations and magnetic ground states. However, the paradigmatic states of the idealized two-dimensional kagome lattice-Dirac fermions and flat bands-have not been simultaneously observed. Here, we use angle-resolved photoemission spectroscopy and de Haas-van Alphen quantum oscillations to reveal coexisting surface and bulk Dirac fermions as well as flat bands in the antiferromagnetic kagome metal FeSn, which has spatially decoupled kagome planes. Our band structure calculations and matrix element simulations demonstrate that the bulk Dirac bands arise from in-plane localized Fe-3d orbitals, and evidence that the coexisting Dirac surface state realizes a rare example of fully spin-polarized two-dimensional Dirac fermions due to spin-layer locking in FeSn. The prospect to harness these prototypical excitations in a kagome lattice is a frontier of great promise at the confluence of topology, magnetism and strongly correlated physics.

Magnetic-Field Control of Topological Electronic Response near Room Temperature in Correlated Kagome Magnets

Strongly correlated kagome magnets are promising candidates for achieving controllable topological devices owing to the rich interplay between inherent Dirac fermions and correlation-driven magnetism. Here we report tunable local magnetism and its intriguing control of topological electronic response near room temperature in the kagome magnet Fe_{3}Sn_{2} using small angle neutron scattering, muon spin rotation, and magnetoresistivity measurement techniques. The average bulk spin direction and magnetic domain texture can be tuned effectively by small magnetic fields. Magnetoresistivity, in response, exhibits a measurable degree of anisotropic weak localization behavior, which allows the direct control of Dirac fermions with strong electron correlations. Our work points to a novel platform for manipulating emergent phenomena in strongly correlated topological materials relevant to future applications.

de Haas-van Alphen effect of correlated Dirac states in kagome metal Fe3Sn2

Primarily considered a medium of geometric frustration, there has been a growing recognition of the kagome network as a harbor of lattice-borne topological electronic phases. In this study we report the observation of magnetoquantum de Haas-van Alphen oscillations of the ferromagnetic kagome lattice metal Fe3Sn2. We observe a pair of quasi-two-dimensional Fermi surfaces arising from bulk massive Dirac states and show that these band areas and effective masses are systematically modulated by the rotation of the ferromagnetic moment. Combined with measurements of Berry curvature induced Hall conductivity, our observations suggest that the ferromagnetic Dirac fermions in Fe3Sn2 are subject to intrinsic spin-orbit coupling in the d electron sector which is likely of Kane-Mele type. Our results provide insights for spintronic manipulation of magnetic topological electronic states and pathways to realizing further highly correlated topological materials from the lattice perspective.

Half-Excitonic Insulator: A Single-Spin Bose-Einstein Condensate

First-principles calculations reveal an unusual electronic state (dubbed as half excitonic insulator) in monolayer 1T-MX_{2} (M=Co, Ni and X=Cl, Br). Its one spin channel has a many-body ground state due to excitonic instability, while the other is characterized by a conventional band insulator gap. This disparity arises from a competition between the band gap and exciton binding energy, which exhibits a spin dependence due to different orbital occupations. Such a state can be identified by optical absorption measurements and angle-resolved photoemission spectroscopy. Our theory not only provides new insights for the study of exciton condensation in magnetic materials but also suggests that strongly correlated materials could be fertile candidates for excitonic insulators.

High-Magnetic-Field Tunneling Spectra of ABC-Stacked Trilayer Graphene on Graphite

ABC-stacked trilayer graphene (TLG) was predicted to exhibit novel many-body phenomena due to the existence of almost dispersionless flat bands near the charge neutrality point. Here, using high-magnetic-field scanning tunneling microscopy, we present Landau Level (LL) spectroscopy measurements of high-quality ABC-stacked TLG on graphite. We observe an approximately linear magnetic-field scaling of valley splitting and spin splitting in the ABC-stacked TLG. Our experiment indicates that the spin splitting decreases dramatically with increasing the LL index. When the lowest LL is partially filled, we find an obvious enhancement of the spin splitting, attributing to strong many-body effects. Moreover, we observe linear energy scaling of the inverse lifetime of quasiparticles, providing an additional evidence for the strong electron-electron interactions in the ABC-stacked TLG. These results imply that interesting broken-symmetry states and novel electron correlated effects could emerge in the ABC-stacked TLG in the presence of high magnetic fields.

Topological flat band, Dirac fermions and quantum spin Hall phase in 2D Archimedean lattices

We've constructed a guide to the electronic properties and topological phases of Archimedean lattices. Within these lattices, a rich electronic structure emerges forming type-I and II Dirac fermions, topological flat bands and high-degeneracy points.