Unprecedented and highly stable lithium storage capacity of (001) faceted nanosheet-constructed hierarchically porous TiO2/rGO hybrid architecture for high-performance Li-ion batteries

Active crystal facets can generate special properties for various applications. Herein, we report a (001) faceted nanosheet-constructed hierarchically porous TiO₂/rGO hybrid architecture with unprecedented and highly stable lithium storage performance. Density functional theory calculations show that the (001) faceted TiO₂ nanosheets enable enhanced reaction kinetics by reinforcing their contact with the electrolyte and shortening the path length of Li⁺ diffusion and insertion-extraction. The reduced graphene oxide (rGO) nanosheets in this TiO₂/rGO hybrid largely improve charge transport, while the porous hierarchy at different length scales favors continuous electrolyte permeation and accommodates volume change. This hierarchically porous TiO₂/rGO hybrid anode material demonstrates an excellent reversible capacity of 250 mAh g^–1 at 1 C (1 C = 335 mA g^–1) at a voltage window of 1.0–3.0 V. Even after 1000 cycles at 5 C and 500 cycles at 10 C, the anode retains exceptional and stable capacities of 176 and 160 mAh g^–1, respectively. Moreover, the formed Li₂Ti₂O₄ nanodots facilitate reversed Li⁺ insertion-extraction during the cycling process. The above results indicate the best performance of TiO₂-based materials as anodes for lithium-ion batteries reported in the literature.     

Discovery of carbon-based strongest and hardest amorphous material

Carbon is one of the most fascinating elements due to its structurally diverse allotropic forms stemming from its bonding varieties (sp, sp² and sp³). Exploring new forms of carbon has been the eternal theme of scientific research. Herein, we report on amorphous (AM) carbon materials with a high fraction of sp³ bonding recovered from compression of fullerene C₆₀ under high pressure and high temperature, previously unexplored. Analysis of photoluminescence and absorption spectra demonstrates that they are semiconducting with a bandgap range of 1.5–2.2 eV, comparable to that of widely used AM silicon. Comprehensive mechanical tests demonstrate that synthesized AM-III carbon is the hardest and strongest AM material known to date, and can scratch diamond crystal and approach its strength. The produced AM carbon materials combine outstanding mechanical and electronic properties, and may potentially be used in photovoltaic applications that require ultrahigh strength and wear resistance.     

Encapsulating metal organic framework into hollow mesoporous carbon sphere as efficient oxygen bifunctional electrocatalyst

Applying metal organic frameworks (MOFs) in electrochemical systems is a currently emerging field owing to the rich metal nodes and highly specific surface area of MOFs. However, the problems for MOFs that need to be solved urgently are poor electrical conductivity and low ion transport. Here we present a facile in situ growth method for the rational synthesis of MOFs@hollow mesoporous carbon spheres (HMCS) yolk–shell-structured hybrid material for the first time. The size of the encapsulated Zeolitic Imidazolate Framework-67 (ZIF-67) is well controlled to 100 nm due to the spatial confinement effect of HMCS, and the electrical conductivity of ZIF-67 is also increased significantly. The ZIF@HMCS-25% hybrid material obtained exhibits a highly efficient oxygen reduction reaction activity with 0.823 V (vs. reversible hydrogen electrode) half-wave potential and an even higher kinetic current density (J_K = 13.8 mA cm⁻²) than commercial Pt/C. ZIF@HMCS-25% also displays excellent oxygen evolution reaction performance and the overpotential of ZIF@HMCS-25% at 10 mA cm⁻² is 407 mV. In addition, ZIF@HMCS-25% is further employed as an air electrode for a rechargeable Zn–air battery, exhibiting a high power density (120.2 mW cm⁻² at 171.4 mA cm⁻²) and long-term charge/discharge stability (80 h at 5 mA cm⁻²). This MOFs@HMCS yolk–shell design provides a versatile method for the application of MOFs as electrocatalysts directly.     

Correlating the electronic structures of metallic/semiconducting MoTe2 interface to its atomic structures

Contact interface properties are important in determining the performances of devices that are based on atomically thin two-dimensional (2D) materials, especially for those with short channels. Understanding the contact interface is therefore important to design better devices. Herein, we use scanning transmission electron microscopy, electron energy loss spectroscopy, and first-principles calculations to reveal the electronic structures within the metallic (1T^′)-semiconducting (2H) MoTe₂ coplanar phase boundary across a wide spectral range and correlate its properties to atomic structures. We find that the 2H-MoTe₂ excitonic peaks cross the phase boundary into the 1T^′ phase within a range of approximately 150 nm. The 1T^′-MoTe₂ crystal field can penetrate the boundary and extend into the 2H phase by approximately two unit-cells. The plasmonic oscillations exhibit strong angle dependence, that is a red-shift of π+σ (approximately 0.3–1.2 eV) occurs within 4 nm at 1T^′/2H-MoTe₂ boundaries with large tilt angles, but there is no shift at zero-tilted boundaries. These atomic-scale measurements reveal the structure–property relationships of the 1T^′/2H-MoTe₂ boundary, providing useful information for phase boundary engineering and device development based on 2D materials.     

Hybrid solid electrolyte enabled dendrite-free Li anodes for high-performance quasi-solid-state lithium-oxygen batteries

The dendrite growth of Li anodes severely degrades the performance of lithium-oxygen (Li-O₂) batteries. Recently, hybrid solid electrolyte (HSE) has been regarded as one of the most promising routes to tackle this problem. However, before this is realized, the HSE needs to simultaneously satisfy contradictory requirements of high modulus and even, flexible contact with Li anode, while ensuring uniform Li⁺ distribution. To tackle this complex dilemma, here, an HSE with rigid Li_1.5Al_0.5Ge_1.5(PO₄)₃ (LAGP) core@ultrathin flexible poly (vinylidene fluoride-hexafluoropropylene) (PVDF-HFP) shell interface has been developed. The introduced large amount of nanometer-sized LAGP cores can not only act as structural enhancer to achieve high Young''s modulus but can also construct Li⁺ diffusion network to homogenize Li⁺ distribution. The ultrathin flexible PVDF-HFP shell provides soft and stable contact between the rigid core and Li metal without affecting the Li⁺ distribution, meanwhile suppressing the reduction of LAGP induced by direct contact with Li metal. Thanks to these advantages, this ingenious HSE with ultra-high Young''s modulus of 25 GPa endows dendrite-free Li deposition even at a deposition capacity of 23.6 mAh. Moreover, with the successful inhibition of Li dendrites, the HSE-based quasi-solid-state Li-O₂ battery delivers a long cycling stability of 146 cycles, which is more than three times that of gel polymer electrolyte-based Li-O₂ battery. This new insight may serve as a starting point for further designing of HSE in Li-O₂ batteries, and can also be extended to various battery systems such as sodium-oxygen batteries.     

Mineralogy of the deep lower mantle in the presence of H2O

Understanding the mineralogy of the Earth''s interior is a prerequisite for unravelling the evolution and dynamics of our planet. Here, we conducted high pressure-temperature experiments mimicking the conditions of the deep lower mantle (DLM, 1800–2890 km in depth) and observed surprising mineralogical transformations in the presence of water. Ferropericlase, (Mg, Fe)O, which is the most abundant oxide mineral in Earth, reacts with H₂O to form a previously unknown (Mg, Fe)O₂H_x (x ≤ 1) phase. The (Mg, Fe)O₂H_x has a pyrite structure and it coexists with the dominant silicate phases, bridgmanite and post-perovskite. Depending on Mg content and geotherm temperatures, the transformation may occur at 1800 km for (Mg_0.6Fe_0.4)O or beyond 2300 km for (Mg_0.7Fe_0.3)O. The (Mg, Fe)O₂H_x is an oxygen excess phase that stores an excessive amount of oxygen beyond the charge balance of maximum cation valences (Mg²⁺, Fe³⁺ and H⁺). This important phase has a number of far-reaching implications including extreme redox inhomogeneity, deep-oxygen reservoirs in the DLM and an internal source for modulating oxygen in the atmosphere.     

Tracking structural evolution: operando regenerative CeOx/Bi interface structure for high-performance CO2 electroreduction

Unveiling the structural evolution and working mechanism of catalysts under realistic operating conditions is crucial for the design of efficient electrocatalysts for CO₂ electroreduction, yet remains highly challenging. Here, by virtue of operando structural measurements at multiscale levels, it is identified under CO₂ electroreduction conditions that an as-prepared CeO₂/BiOCl precatalyst gradually evolves into CeO_x/Bi interface structure with enriched Ce³⁺ species, which serves as the real catalytically active phase. The derived CeO_x/Bi interface structure compared to pure Bi counterpart delivers substantially enhanced performance with a formate Faradaic efficiency approaching 90% for 24 hours in a wide potential window. The formate Faradaic efficiency can be further increased by using isotope D₂O instead of H₂O. Density functional theory calculations suggest that the regenerative CeO_x/Bi interfacial sites can not only promote water activation to increase local ^*H species for CO₂ protonation appropriately, but also stabilize the key intermediate ^*OCHO in formate pathway.     

Regulating off-centering distortion maximizes photoluminescence in halide perovskites

Metal halide perovskites possess unique atomic and electronic configurations that endow them with high defect tolerance and enable high-performance photovoltaics and optoelectronics. Perovskite light-emitting diodes have achieved an external quantum efficiency of over 20%. Despite tremendous progress, fundamental questions remain, such as how structural distortion affects the optical properties. Addressing their relationships is considerably challenging due to the scarcity of effective diagnostic tools during structural and property tuning as well as the limited tunability achievable by conventional methods. Here, using pressure and chemical methods to regulate the metal off-centering distortion, we demonstrate the giant tunability of photoluminescence (PL) in both the intensity (>20 times) and wavelength (>180 nm/GPa) in the highly distorted halide perovskites [CH₃NH₃GeI₃, HC(NH₂)₂GeI₃, and CsGeI₃]. Using advanced in situ high-pressure probes and first-principles calculations, we quantitatively reveal a universal relationship whereby regulating the level of off-centering distortion towards 0.2 leads to the best PL performance in the halide perovskites. By applying this principle, intense PL can still be induced by substituting CH₃NH₃⁺ with Cs⁺ to control the distortion in (CH₃NH₃)_1-xCs_xGeI₃, where the chemical substitution plays a similar role as external pressure. The compression of a fully substituted sample of CsGeI₃ further tunes the distortion to the optimal value at 0.7 GPa, which maximizes the emission with a 10-fold enhancement. This work not only demonstrates a quantitative relationship between structural distortion and PL property of the halide perovskites but also illustrates the use of knowledge gained from high-pressure research to achieve the desired properties by ambient methods.     

Efficient interlayer charge release for high-performance layered thermoelectrics

Many layered superlattice materials intrinsically possess large Seebeck coefficient and low lattice thermal conductivity, but poor electrical conductivity because of the interlayer transport barrier for charges, which has become a stumbling block for achieving high thermoelectric performance. Herein, taking BiCuSeO superlattice as an example, it is demonstrated that efficient interlayer charge release can increase carrier concentration, thereby activating multiple Fermi pockets through Bi/Cu dual vacancies and Pb codoping. Experimental results reveal that the extrinsic charges, which are introduced by Pb and initially trapped in the charge-reservoir [Bi₂O₂]²⁺ sublayers, are effectively released into [Cu₂Se₂]²⁻ sublayers via the channels bridged by Bi/Cu dual vacancies. This efficient interlayer charge release endows dual-vacancy- and Pb-codoped BiCuSeO with increased carrier concentration and electrical conductivity. Moreover, with increasing carrier concentration, the Fermi level is pushed down, activating multiple converged valence bands, which helps to maintain a relatively high Seebeck coefficient and yield an enhanced power factor. As a result, a high ZT value of ∼1.4 is achieved at 823 K in codoped Bi_0.90Pb_0.06Cu_0.96SeO, which is superior to that of pristine BiCuSeO and solely doped samples. The present findings provide prospective insights into the exploration of high-performance thermoelectric materials and the underlying transport physics.     

Kinetic regulation of MXene with water-in-LiCl electrolyte for high-voltage micro-supercapacitors

MXenes are one of the key materials for micro-supercapacitors (MSCs), integrating miniaturized energy-storage components with microelectronics. However, the energy densities of MSCs are greatly hampered by MXenes’ narrow working potential window (typically ≤0.6 V) in aqueous electrolytes. Here, we report the fabrication of high-voltage MXene-MSCs through the efficient regulation of reaction kinetics in 2D Ti₃C₂T_x MXene microelectrodes using a water-in-LiCl (WIL, 20 m LiCl) salt gel electrolyte. Importantly, the intrinsic energy-storage mechanism of MXene microelectrodes in WIL, which is totally different from traditional electrolytes (1 m LiCl), was revealed through insitu and exsitu characterizations. We validated that the suppression of MXene oxidation at high anodic potential occurred due to the high content of WIL regulating anion intercalation in MXene electrodes, which effectively broadened the voltage window of MXene-MSCs. Remarkably, the symmetric planar MXene-MSCs presented a record operating voltage of 1.6 V, resulting in an exceptionally high volumetric energy density of 31.7 mWh cm⁻³. With the ultra-high ionic conductivity (69.5 mS cm⁻¹) and ultralow freezing point (−57°C) of the WIL gel electrolyte, our MSCs could be operated in a wide temperature range of −40 to 60°C, and worked for a long duration even at −40°C, demonstrative of its practicality in extreme environments.     

Large-scale multiferroic complex oxide epitaxy with magnetically switched polarization enabled by solution processing

Complex oxides with tunable structures have many fascinating properties, though high-quality complex oxide epitaxy with precisely controlled composition is still out of reach. Here we have successfully developed solution-based single-crystalline epitaxy for multiferroic (1-x)BiTi_(1-y)/2Fe_yMg_(1-y)/2O₃–(x)CaTiO₃ (BTFM–CTO) solid solution in large area, confirming its ferroelectricity at the atomic scale with strong spontaneous polarization. Careful compositional tuning leads to a bulk magnetization of 0.07 ± 0.035 μ_B/Fe at room temperature, enabling magnetically induced polarization switching exhibiting a large magnetoelectric coefficient of 2.7–3.0 × 10⁻⁷ s/m. This work demonstrates the great potential of solution processing in large-scale complex oxide epitaxy and establishes novel room-temperature magnetoelectric coupling in epitaxial BTFM–CTO film, making it possible to explore a much wider space of composition, phase, and structure that can be easily scaled up for industrial applications.     

Approaching 18% efficiency of ternary organic photovoltaics with wide bandgap polymer donor and well compatible Y6 : Y6-1O as acceptor

A series of ternary organic photovoltaics (OPVs) are fabricated with one wide bandgap polymer D18-Cl as donor, and well compatible Y6 and Y6-1O as acceptor. The open-circuit-voltage (V_OC) of ternary OPVs is monotonously increased along with the incorporation of Y6-1O, indicating that the alloy state should be formed between Y6 and Y6-1O due to their excellent compatibility. The energy loss can be minimized by incorporating Y6-1O, leading to the V_OC improvement of ternary OPVs. By finely adjusting the Y6-1O content, a power conversion efficiency of 17.91% is achieved in the optimal ternary OPVs with 30 wt% Y6-1O in acceptors, resulting from synchronously improved short-circuit-current density (J_SC) of 25.87 mA cm⁻², fill factor (FF) of 76.92% and V_OC of 0.900 V in comparison with those of D18-Cl : Y6 binary OPVs. The J_SC and FF improvement of ternary OPVs should be ascribed to comprehensively optimal photon harvesting, exciton dissociation and charge transport in ternary active layers. The more efficient charge separation and transport process in ternary active layers can be confirmed by the magneto-photocurrent and impedance spectroscopy experimental results, respectively. This work provides new insight into constructing highly efficient ternary OPVs with well compatible Y6 and its derivative as acceptor.     

Superconductivity in chromium nitrides Pr3Cr10-xN11 with strong electron correlations

Exploration of superconductivity in Cr-based compounds has attracted considerable interest because only a few Cr-based superconductors (CrAs, A₂Cr₃As₃ and ACr₃As₃ (A = K, Rb, Cs, Na)) have been discovered so far and they show an unconventional pairing mechanism. We report the discovery of bulk superconductivity at 5.25 K in chromium nitride in Pr₃Cr_10-xN₁₁ with a cubic lattice structure. A relatively large upper critical field of H_c2(0) ∼ 12.6 T is determined, which is larger than the estimated Pauli-paramagnetic pair-breaking magnetic field. The material has a large electronic specific-heat coefficient of 170 mJ K⁻² mol⁻¹—about 10 times larger than that estimated by the electronic structure calculation, which suggests that correlations between 3d electrons are very strong in Pr₃Cr_10-xN₁₁, and thus quantum fluctuations might be involved. Electronic structure calculations show that the density of states at the Fermi energy are contributed predominantly by Cr 3d electrons, implying that the superconductivity results mainly from the condensation of Cr 3d electrons. Pr₃Cr_10-xN₁₁ represents a rare example of possible unconventional superconductivity emerging in a 3D system with strong electron correlations. Nevertheless, clarification of the specific pairing symmetry needs more investigation.     

Hierarchical structural complexity in atomically precise nanocluster frameworks

The supramolecular chemistry of nanoclusters is a flourishing area of nano-research; however, the controllable assembly of cluster nano-building blocks in different arrays remains challenging. In this work, we report the hierarchical structural complexity of atomically precise nanoclusters in micrometric linear chains (1D array), grid networks (2D array) and superstructures (3D array). In the crystal lattice, the Ag₂₉(SSR)₁₂(PPh₃)₄ nanoclusters can be viewed as unassembled cluster dots (Ag₂₉–0D). In the presence of Cs⁺ cations, the Ag₂₉(SSR)₁₂ nano-building blocks are selectively assembled into distinct arrays with different oxygen-carrying solvent molecules―Cs@Ag₂₉(SSR)₁₂(DMF)_x as 1D linear chains (Ag₂₉–1D), Cs@Ag₂₉(SSR)₁₂(NMP)_x as 2D grid networks (Ag₂₉–2D), and Cs@Ag₂₉(SSR)₁₂(TMS)_x as 3D superstructures (Ag₂₉–3D). Such self-assemblies of these Ag₂₉(SSR)₁₂ units have not only been observed in their crystalline state, but also in their amorphous state. Due to the diverse surface structures and crystalline packing modes, these Ag₂₉-based assemblies manifest distinguishable optical absorptions and emissions in both solutions and crystallized films. Furthermore, the surface areas of the nanocluster crystals are evaluated, the maximum value of which occurs when the cluster nano-building blocks are assembled into 2D arrays (i.e. Ag₂₉–2D). Overall, this work presents an exciting example of the hierarchical assembly of atomically precise nanoclusters by simply controlling the adsorbed molecules on the cluster surface.     

Practical high-performance lead-free piezoelectrics: structural flexibility beyond utilizing multiphase coexistence

Due to growing concern for the environment and human health, searching for high-performance lead-free piezoceramics has been a hot topic of scientific and industrial research. Despite the significant progress achieved toward enhancing piezoelectricity, further efforts should be devoted to the synergistic improvement of piezoelectricity and its thermal stability. This study provides new insight into these topics. A new KNN-based lead-free ceramic material is presented, which features a large piezoelectric coefficient (d₃₃) exceeding 500 pC/N and a high Curie temperature (T_c) of  ∼200°C. The superior piezoelectric response strongly relies on the increased composition-induced structural flexibility due to lattice softening and decreased unit cell distortion. In contrast to piezoelectricity anomalies induced via polymorphic transition, this piezoelectricity enhancement is effective within a broad temperature range rather than a specific small range. In particular, a hierarchical domain architecture composed of nano-sized domains along the submicron domains was detected in this material system, which further contributes to the high piezoelectricity.     

Exposed facet-controlled N2 electroreduction on distinct Pt3Fe nanostructures of nanocubes,nanorods and nanowires

Understanding the correlation between exposed surfaces and performances of controlled nanocatalysts can aid effective strategies to enhance electrocatalysis, but this is as yet unexplored for the nitrogen reduction reaction (NRR). Here, we first report controlled synthesis of well-defined Pt₃Fe nanocrystals with tunable morphologies (nanocube, nanorod and nanowire) as ideal model electrocatalysts for investigating the NRR on different exposed facets. The detailed electrocatalytic studies reveal that the Pt₃Fe nanocrystals exhibit shape-dependent NRR electrocatalysis. The optimized Pt₃Fe nanowires bounded with high-index facets exhibit excellent selectivity (no N₂H₄ is detected), high activity with NH₃ yield of 18.3 μg h⁻¹ mg⁻¹_cat (0.52 μg h⁻¹ cm⁻²_ECSA; ECSA: electrochemical active surface area) and Faraday efficiency of 7.3% at −0.05 V versus reversible hydrogen electrode, outperforming the {200} facet-enclosed Pt₃Fe nanocubes and {111} facet-enclosed Pt₃Fe nanorods. They also show good stability with negligible activity change after five cycles. Density functional theory calculations reveal that, with high-indexed facet engineering, the Fe-3d band is an efficient d-d coupling correlation center for boosting the Pt 5d-electronic exchange and transfer activities towards the NRR.     

Graphdiyne-based metal atomic catalysts for synthesizing ammonia

Development of novel catalysts for nitrogen reduction at ambient pressures and temperatures with ultrahigh ammonia (NH₃) yield and selectivity is challenging. In this work, an atomic catalyst with separated Pd atoms on graphdiyne (Pd-GDY) was synthesized, which shows fascinating electrocatalytic properties for nitrogen reduction. The catalyst has the highest average NH₃ yield of 4.45 ± 0.30 mg_NH3 mg_Pd⁻¹ h⁻¹, almost tens of orders larger than for previously reported catalysts, and 100% reaction selectivity in neutral media. Pd-GDY exhibits almost no decreases in NH₃ yield and Faradaic efficiency. Density functional theory calculations show that the reaction pathway prefers to perform at the (Pd, C1, C2) active area because of the strongly coupled (Pd, C1, C2), which elevates the selectivity via enhanced electron transfer. By adjusting the p–d coupling accurately, reduction of self-activated nitrogen is promoted by anchoring atom selection, and side effects are minimized.     

Efficient potential-tuning strategy through p-type doping for designing cathodes with ultrahigh energy density

Designing new cathodes with high capacity and moderate potential is the key to breaking the energy density ceiling imposed by current intercalation chemistry on rechargeable batteries. The carbonaceous materials provide high capacities but their low potentials limit their application to anodes. Here, we show that Fermi level tuning by p-type doping can be an effective way of dramatically raising electrode potential. We demonstrate that Li(Na)BCF₂/Li(Na)B₂C₂F₂ exhibit such change in Fermi level, enabling them to accommodate Li⁺(Na⁺) with capacities of 290–400 (250–320) mAh g⁻¹ at potentials of 3.4–3.7 (2.7–2.9) V, delivering ultrahigh energy densities of 1000–1500 Wh kg⁻¹. This work presents a new strategy in tuning electrode potential through electronic band structure engineering.     

Anisotropic alignments of hierarchical Li2SiO3/TiO2 @nano-C anode//LiMnPO4@nano-C cathode architectures for full-cell lithium-ion battery

We report on low-cost fabrication and high-energy density of full-cell lithium-ion battery (LIB) models. Super-hierarchical electrode architectures of Li₂SiO₃/TiO₂@nano-carbon anode (LSO.TO@nano-C) and high-voltage olivine LiMnPO₄@nano-carbon cathode (LMPO@nano-C) are designed for half- and full-system LIB-CR2032 coin cell models. On the basis of primary architecture-power-driven LIB geometrics, the structure keys including three-dimensional (3D) modeling superhierarchy, multiscale micro/nano architectures and anisotropic surface heterogeneity affect the buildup design of anode/cathode LIB electrodes. Such hierarchical electrode surface topologies enable continuous in-/out-flow rates and fast transport pathways of Li⁺-ions during charge/discharge cycles. The stacked layer configurations of pouch LIB-types lead to excellent charge/discharge rate, and energy density of 237.6 Wh kg⁻¹. As the most promising LIB-configurations, the high specific energy density of hierarchical pouch battery systems may improve energy storage for long-driving range of electric vehicles. Indeed, the anisotropic alignments of hierarchical electrode architectures in the large-scale LIBs provide proof of excellent capacity storage and outstanding durability and cyclability. The full-system LIB-CR2032 coin cell models maintain high specific capacity of ∼89.8% within a long-term life period of 2000 cycles, and average Coulombic efficiency of 99.8% at 1C rate for future configuration of LIB manufacturing and commercialization challenges.     

Electronic structures and topological properties in nickelates Lnn+1NinO2n+2

After the significant discovery of the hole-doped nickelate compound Nd_0.8Sr_0.2NiO₂, analyses of the electronic structure, orbital components, Fermi surfaces and band topology could be helpful to understand the mechanism of its superconductivity. Based on first-principle calculations, we find that Ni states contribute the largest Fermi surface. The states form an electron pocket at Γ, while 5d_xy states form a relatively bigger electron pocket at A. These Fermi surfaces and symmetry characteristics can be reproduced by our two-band model, which consists of two elementary band representations: B_1g@1a ⊕ A_1g@1b. We find that there is a band inversion near A, giving rise to a pair of Dirac points along M-A below the Fermi level upon including spin-orbit coupling. Furthermore, we perform density functional theory based Gutzwiller (DFT+Gutzwiller) calculations to treat the strong correlation effect of Ni 3d orbitals. In particular, the bandwidth of has been renormalized largely. After the renormalization of the correlated bands, the Ni 3d_xy states and the Dirac points become very close to the Fermi level. Thus, a hole pocket at A could be introduced by hole doping, which may be related to the observed sign change of the Hall coefficient. By introducing an additional Ni 3d_xy orbital, the hole-pocket band and the band inversion can be captured in our modified model. Besides, the nontrivial band topology in the ferromagnetic two-layer compound La₃Ni₂O₆ is discussed and the band inversion is associated with Ni and La 5d_xy orbitals.