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Flat bands and nontrivial topological physics are two important topics of condensed matter physics. With a unique stacking configuration analogous to the Su-Schrieffer-Heeger (SSH) model, rhombohedral graphite (RG) is a potential candidate for realizing both flat bands and nontrivial topological physics. Here we report experimental evidence of topological flat bands (TFBs) on the surface of bulk RG, which are topologically protected by bulk helical Dirac nodal lines via the bulk-boundary correspondence. Moreover, upon {\it in situ} electron doping, the surface TFBs show a splitting with exotic doping evolution, with an order-of-magnitude increase in the bandwidth of the lower split band, and pinning of the upper band near the Fermi level. These experimental observations together with Hartree-Fock calculations suggest that correlation effects are important in this system. Our results demonstrate RG as a new platform for investigating the rich interplay between nontrivial band topology, correlation effects, and interaction-driven symmetry-broken states., Comment: 15 pages, 5 figures

The recently discovered nonlinear Hall (NLH) effect arises either without external magnetic field (type-I) or with an in-plane magnetic field (type-II). In this work we propose a new type of geometrical nonlinear Hall effect with an out-of-plane magnetic field (type-III) induced by the combination of Lorentz force and anomalous electronic velocity. The type-III NLH effect is proportional to the more refined structures of Bloch wave functions, i.e., the dipole moment of square of Berry curvature, thus becoming prominent near the band crossings or anticrossings. Our effective model analysis and first-principles calculations show that gate-tuned MnBi$_2$Te$_4$ thin film under uniaxial strain is an ideal platform to observe this effect. Especially, giant unidirectional magnetoresistance can occur in this material, based on which an efficient electrical transistor device prototype can be built. Finally a symmetry analysis indicates that type-III NLH effect has unique symmetry properties stemming from Berry curvature square dipole, which is different from other previously reported NLH effects and can exist in a wider class of magnetic crystals. Our study offers new paradigms for nonlinear electronics.

Nonlinear optical (NLO) effects in materials with band crossings have attracted significant research interests due to the divergent band geometric quantities around these crossings. Most current research has focused on band crossings between the valence and conduction bands. However, such crossings are absent in insulators, which are more relevant for NLO applications. In this work, we demonstrate that NLO effects can be significantly enhanced by band crossings within the valence or conduction bands, which we designate as "deep band crossings" (DBCs). As an example, in two dimensions, we show that shift conductivity can be substantially enhanced or even divergent due to a mirror-protected "deep Dirac nodal point". In three dimensions, we propose GeTe as an ideal material where shift conductivity is enhanced by "deep Dirac nodal lines". The ubiquity of this enhancement is further confirmed by high-throughput calculations. Other types of DBCs and NLO effects are also discussed. By manipulating band crossings between arbitrary bands, our work offers a simple, practical, and universal way to greatly enhance NLO effects.

We propose that flat bands and van Hove singularities near the magic angle can be stabilized against angle disorder in the twisted Kane-Mele model. With continuum model and maximally localized Wannier function approaches, we identify a quadratic dispersion relationship between the bandwidth, interaction parameters versus the twist angle, in contrast to twisted bilayer graphene (TBG). Introducing Kane-Mele spin-orbit coupling to TBG greatly reduces the fractional Chern insulator indicator and enhances the stability of fractional Chern states near the magic angle, as confirmed by exact diagonalization calculations. Moreover, in twisted bilayer Pt$_2$HgSe$_3$ with intrinsic Kane-Mele spin-orbit coupling, we identify a topological flat band at a large twist angle around 4 degrees., Comment: 5+6 pages, 4+2 figures, the label in Fig. 3 has been corrected

Recent discoveries of zero-field fractional Chern insulators in moir\'e materials have attracted intensive research interests. However, most current theoretical and experimental attempts focus on systems with low Chern number bands, in analogy to the Landau levels. Here we propose candidate material systems for realizing fractional Chern insulators with higher Chern numbers. The material setup involves $\Gamma$-valley twisted homobilayer transition metal dichalcogenides in proximity to a skyrmion lattice. The skyrmion exchange potential induces a flat band with a high Chern number $C = -2$. Using the momentum-space projected exact diagonalization method, we perform a comprehensive study at various filling factors, confirming the generalized Jain series. Our research provides theoretical guidance on realizing unconventional fractional Chern insulators beyond the Landau level picture., Comment: 6 pages, 4 figures

The interplay of chiralities in light and quantum matter provides an opportunity to design and manipulate chirality-dependent properties in quantum materials. Herein we report the chirality-dependent Floquet engineering on topological fermions with the high Chern number in chiral crystal CoSi via circularly polarized light (CPL) pumping. Intense light pumping does not compromise the gapless nature of topological fermions in CoSi, but displaces the crossing points in momentum space along the direction of light propagation. The Floquet chirality index is proposed to signify the interplay between the chiralities of topological fermion, crystal, and incident light, which determines the amplitudes and directions of light-induced momentum shifts. Regarding the time-reversal symmetry breaking induced by the CPL pumping, momentum shifts of topological fermions result in the birth of transient anomalous Hall signals in non-magnetic CoSi within an ultrafast time scale, which Mid-infrared (IR) pumping and terahertz (THz) Kerr or Faraday probe spectroscopy could experimentally detect. Our findings provide insights into exploring novel applications in optoelectronic devices by leveraging the degree of freedom of chirality in the non-equilibrium regime.

Deep learning electronic structures from ab initio calculations holds great potential to revolutionize computational materials studies. While existing methods proved success in deep-learning density functional theory (DFT) Hamiltonian matrices, they are limited to DFT programs using localized atomic-like bases and heavily depend on the form of the bases. Here, we propose the DeepH-r method for deep-learning DFT Hamiltonians in real space, facilitating the prediction of DFT Hamiltonian in a basis-independent manner. An equivariant neural network architecture for modeling the real-space DFT potential is developed, targeting a more fundamental quantity in DFT. The real-space potential exhibits simplified principles of equivariance and enhanced nearsightedness, further boosting the performance of deep learning. When applied to evaluate the Hamiltonian matrix, this method significantly improved in accuracy, as exemplified in multiple case studies. Given the abundance of data in the real-space potential, this work may pave a novel pathway for establishing a ``large materials model" with increased accuracy.

Two-dimensional (2D) moir\'e materials have emerged as a highly tunable platform for investigating novel quantum states of matter arising from strong electronic correlations and nontrivial band topology. Recently, topological flat bands formed in 2D semiconducting moir\'e superlattices have attracted great interests. In particular, a series of topological quantum phases, including the long-sought fractional quantum anomalous Hall (FQAH) effect, have recently been experimentally observed in twisted bilayer MoTe2 (tMoTe2). However, the microscopic information of tMoTe2 moir\'e superlattice and its electronic structure is still lacking. Here, we present scanning tunneling microscopy and spectroscopy (STM/STS) studies of the tMoTe2 moir\'e superlattice, with twist angles ranging from about 2.3{\deg} to 2.8{\deg}. We developed a contact-STM mode to apply pressure on tMoTe2 and observed a phase transition from band insulator to metal of tMoTe2 under pressure at the charge neutrality point. STM imaging reveals a pronounced in-plane lattice reconstruction with periodic strain redistribution in the tMoTe2, which serves as gauge fields for generating topological moir\'e bands. Importantly, the electronic states of the low-energy moir\'e flat bands primarily concentrate at the XM and MX regions as revealed by STS imaging. Such spatial distributions are nicely reproduced by our first principal calculations with a large-scale basis, suggesting the low-energy moir\'e flat bands are formed through the hybridization of K valley bands of the top layer and K' valley bands of the bottom layer. Overall, our findings provide compelling real-space evidence of electronic structure under pressure and topological flat bands of tMoTe2, paving the way for further STM/STS investigations of correlated topological states within the topological flat band in gate-tunable tMoTe2 devices.

The combination of deep learning and ab initio materials calculations is emerging as a trending frontier of materials science research, with deep-learning density functional theory (DFT) electronic structure being particularly promising. In this work, we introduce a neural-network method for modeling the DFT density matrix, a fundamental yet previously unexplored quantity in deep-learning electronic structure. Utilizing an advanced neural network framework that leverages the nearsightedness and equivariance properties of the density matrix, the method demonstrates high accuracy and excellent generalizability in multiple example studies, as well as capability to precisely predict charge density and reproduce other electronic structure properties. Given the pivotal role of the density matrix in DFT as well as other computational methods, the current research introduces a novel approach to the deep-learning study of electronic structure properties, opening up new opportunities for deep-learning enhanced computational materials study.

The transport of Bloch electrons under strong fields is traditionally understood through two mechanisms: intraband Bloch oscillations and interband Zener tunneling. Here we propose a new oscillation mechanism induced by the interband quantum metric, which would significantly affect the electron dynamics under strong fields. By considering the multiband dynamics to the second order of the density matrix, we reveal that quantum metric-induced oscillations (QMO) persist regardless of band dispersion, even in exactly flat bands. The resultant drift current can reach a magnitude comparable to the Bloch oscillations-induced drift current in systems where interband tunneling is negligible. Notably, the {QMO}-induced drift current increases linearly with electric field strength under the constraints of time-reversal or spatial-inversion symmetry, emerging as the primary delocalized current. We further show that both one-dimensional and two-dimensional superlattices are potential platforms for investigating QMO.

Realizing large materials models has emerged as a critical endeavor for materials research in the new era of artificial intelligence, but how to achieve this fantastic and challenging objective remains elusive. Here, we propose a feasible pathway to address this paramount pursuit by developing universal materials models of deep-learning density functional theory Hamiltonian (DeepH), enabling computational modeling of the complicated structure-property relationship of materials in general. By constructing a large materials database and substantially improving the DeepH method, we obtain a universal materials model of DeepH capable of handling diverse elemental compositions and material structures, achieving remarkable accuracy in predicting material properties. We further showcase a promising application of fine-tuning universal materials models for enhancing specific materials models. This work not only demonstrates the concept of DeepH's universal materials model but also lays the groundwork for developing large materials models, opening up significant opportunities for advancing artificial intelligence-driven materials discovery.

Recent experimental discovery of fractional Chern insulator in moir\'e Chern band in twisted transition metal dichalocogenide homobilayers has sparked intensive interest in exploring the ways of engineering band topology and correlated states in moir\'e systems. In this letter, we demonstrate that, with an additional exchange interaction induced by proximity effect, the topology and bandwidth of the moir\'e minibands of twisted $\mathrm{MoTe_2}$ homobilayers can be easily tuned. Fractional Chern insulators at -2/3 filling are found to appear at enlarged twist angles over a large range of twist angles with enhanced many-body gaps. We further discover a topological phase transition between the fractional Chern insulator, quantum anomalous Hall crystal, and charge density wave. Our results shed light on the interplay between topology and correlation physics., Comment: 7 pages, 4 figures

Moir\'e-twisted materials have garnered significant research interest due to their distinctive properties and intriguing physics. However, conducting first-principles studies on such materials faces challenges, notably the formidable computational cost associated with simulating ultra-large twisted structures. This obstacle impedes the construction of a twisted materials database crucial for datadriven materials discovery. Here, by using high-throughput calculations and state-of-the-art neural network methods, we construct a Deep-learning Database of density functional theory (DFT) Hamiltonians for Twisted materials named DDHT. The DDHT database comprises trained neural-network models of over a hundred homo-bilayer and hetero-bilayer moir\'e-twisted materials. These models enable accurate prediction of the DFT Hamiltonian for these materials across arbitrary twist angles, with an averaged mean absolute error of approximately 1.0 meV or lower. The database facilitates the exploration of flat bands and correlated materials platforms within ultra-large twisted structures.

Twisted bilayer graphene (tBLG) provides a fascinating platform for engineering flat bands and inducing correlated phenomena. By designing the stacking architecture of graphene layers, twisted multilayer graphene can exhibit different symmetries with rich tunability. For example, in twisted monolayer-bilayer graphene (tMBG) which breaks the C2z symmetry, transport measurements reveal an asymmetric phase diagram under an out-of-plane electric field, exhibiting correlated insulating state and ferromagnetic state respectively when reversing the field direction. Revealing how the electronic structure evolves with electric field is critical for providing a better understanding of such asymmetric field-tunable properties. Here we report the experimental observation of field-tunable dichotomic electronic structure of tMBG by nanospot angle-resolved photoemission spectroscopy (NanoARPES) with operando gating. Interestingly, selective enhancement of the relative spectral weight contributions from monolayer and bilayer graphene is observed when switching the polarity of the bias voltage. Combining experimental results with theoretical calculations, the origin of such field-tunable electronic structure, resembling either tBLG or twisted double-bilayer graphene (tDBG), is attributed to the selectively enhanced contribution from different stacking graphene layers with a strong electron-hole asymmetry. Our work provides electronic structure insights for understanding the rich field-tunable physics of tMBG., Comment: 4 figures

The interplay of polarization and magnetism in materials with light can create rich nonlinear magneto-optical (NLMO) effects, and the recent discovery of two-dimensional (2D) van der Waals magnets provides remarkable control over NLMO effects due to their superb tunability. Here, based on first-principles calculations, we reported giant NLMO effects in CrI3-based 2D magnets, including a dramatic change of second-harmonics generation (SHG) polarization direction (90 degrees) and intensity (on/off switch) under magnetization reversal, and a 100% SHG circular dichroism effect. We further revealed that these effects could not only be used to design ultra-thin multifunctional optical devices, but also to detect subtle magnetic orderings. Remarkably, we analytically derived conditions to achieve giant NLMO effects and propose general strategies to realize them in 2D magnets. Our work not only uncovers a series of intriguing NLMO phenomena, but also paves the way for both fundamental research and device applications of ultra-thin NLMO materials., Comment: 10 pages,5 figures, npj Computational Materials accepted

Magic-angle twisted bilayer graphene (MATBG) exhibits correlated phenomena such as superconductivity and Mott insulating state related to the weakly dispersing flat band near the Fermi energy. Beyond its moir\'e period, such flat band is expected to be sensitive to lattice relaxations. Thus, clarifying the evolution of the electronic structure with twist angle is critical for understanding the physics of MATBG. Here, we combine nanospot angle-resolved photoemission spectroscopy and atomic force microscopy to resolve the fine electronic structure of the flat band and remote bands, and their evolution with twist angles from 1.07$^\circ$ to 2.60$^\circ$. Near the magic angle, dispersion is characterized by a flat band near the Fermi energy with a strongly reduced bandwidth. Moreover, near 1.07$^\circ$, we observe a spectral weight transfer between remote bands at higher binding energy and extract the modulated interlayer spacing near the magic angle. Our work provides direct spectroscopic information on flat band physics and highlights the role of lattice relaxations., Comment: 22 pages, 5 figures, Nature Materials, in press

Deep-learning density functional theory (DFT) shows great promise to significantly accelerate material discovery and potentially revolutionize materials research. However, current research in this field primarily relies on data-driven supervised learning, making the developments of neural networks and DFT isolated from each other. In this work, we present a theoretical framework of neural-network DFT, which unifies the optimization of neural networks with the variational computation of DFT, enabling physics-informed unsupervised learning. Moreover, we develop a differential DFT code incorporated with deep-learning DFT Hamiltonian, and introduce algorithms of automatic differentiation and backpropagation into DFT, demonstrating the capability of neural-network DFT. The physics-informed neural-network architecture not only surpasses conventional approaches in accuracy and efficiency, but also offers a new paradigm for developing deep-learning DFT methods., Comment: 6 pages, 4 figures

Topological and valleytronic materials are promising for spintronic and quantum applications due to their unique properties. Using first principles calculations, we demonstrate that germanene (Ge)-based ferromagnetic heterostructures can exhibit multiple quantum states such as quantum anomalous Hall effect (QAHE) with Chern numbers of C=-1 or C=-2, quantum valley Hall effect (QVHE) with a valley Chern number of C$v$=2, valley-polarized quantum anomalous Hall effect (VP-QAHE) with two Chern numbers of C=-1 and C$v$=-1 as well as time-reversal symmetry broken quantum spin Hall effect (T-broken QSHE) with a spin Chern number of C$s$~1. Furthermore, we find that the transitions between different quantum states can occur by changing the magnetic orientation of ferromagnetic layers through applying a magnetic field. Our discovery provides new routes and novel material platforms with a unique combination of diverse properties that make it well suitable for applications in electronics, spintronics and valley electronics., Comment: 15 pages, 3 figures

Neural network force fields have significantly advanced ab initio atomistic simulations across diverse fields. However, their application in the realm of magnetic materials is still in its early stage due to challenges posed by the subtle magnetic energy landscape and the difficulty of obtaining training data. Here we introduce a data-efficient neural network architecture to represent density functional theory total energy, atomic forces, and magnetic forces as functions of atomic and magnetic structures. Our approach incorporates the principle of equivariance under the three-dimensional Euclidean group into the neural network model. Through systematic experiments on various systems, including monolayer magnets, curved nanotube magnets, and moir\'e-twisted bilayer magnets of $\text{CrI}_{3}$, we showcase the method's high efficiency and accuracy, as well as exceptional generalization ability. The work creates opportunities for exploring magnetic phenomena in large-scale materials systems., Comment: 10 pages, 4 figures

Calculating perturbation response properties of materials from first principles provides a vital link between theory and experiment, but is bottlenecked by the high computational cost. Here a general framework is proposed to perform density functional perturbation theory (DFPT) calculations by neural networks, greatly improving the computational efficiency. Automatic differentiation is applied on neural networks, facilitating accurate computation of derivatives. High efficiency and good accuracy of the approach are demonstrated by studying electron-phonon coupling and related physical quantities. This work brings deep-learning density functional theory and DFPT into a unified framework, creating opportunities for developing ab initio artificial intelligence.

Deep-learning electronic structure calculations show great potential for revolutionizing the landscape of computational materials research. However, current neural-network architectures are not deemed suitable for widespread general-purpose application. Here we introduce a framework of equivariant local-coordinate transformer, designed to enhance the deep-learning density functional theory Hamiltonian referred to as DeepH-2. Unlike previous models such as DeepH and DeepH-E3, DeepH-2 seamlessly integrates the simplicity of local-coordinate transformations and the mathematical elegance of equivariant neural networks, effectively overcoming their respective disadvantages. Based on our comprehensive experiments, DeepH-2 demonstrates superiority over its predecessors in both efficiency and accuracy, showcasing state-of-the-art performance. This advancement opens up opportunities for exploring universal neural network models or even large materials models.

Recently discovered Ising superconductors have garnered considerable interest due to their anomalously large in-plane upper critical fields ($B_{c2}$). However, the requisite strong spin-orbital coupling in the Ising pairing mechanism generally renders these superconductors heavy-element dominant with notably low superconducting transition temperatures ($T_c$). Here, based on the Migdal-Eliashberg theory and the mean-field Bogoliubov-de Gennes Hamiltonian, we demonstrate a significant enhancement of Ising superconductivity in monolayer NbSe$_2$ through surface fluorination, as evidenced by concomitant improvements in $T_c$ and $B_{c2}$. This enhancement arises from three predominant factors. Firstly, fluorine atoms symmetrically and stably adhere to both sides of the monolayer NbSe$_2$, thereby maintaining the out-of-plane mirror symmetry and locking carrier spins out-of-plane. Secondly, fluorination suppresses the charge density wave in monolayer NbSe$_2$ and induces a van Hove singularity in the vicinity of the Fermi level, leading to a marked increase in the number of carriers and, consequently, strengthening the electron-phonon coupling (EPC). Lastly, the appearance of fluorine-related, low-frequency phonon modes further augments the EPC. Our findings suggest a promising avenue to elevate $T_c$ in two-dimensional Ising superconductors without compromising their Ising pairing., Comment: 5 figures

Time-periodic light field can dress the electronic states and lead to light-induced emergent properties in quantum materials. While below-gap pumping is regarded favorable for Floquet engineering, so far direct experimental evidence of momentum-resolved band renormalization still remains missing. Here, we report experimental evidence of light-induced band renormalization in black phosphorus by pumping at photon energy of 160 meV which is far below the band gap, and the distinction between below-gap pumping and near-resonance pumping is revealed. Our work demonstrates light-induced band engineering upon below-gap pumping, and provides insights for extending Floquet engineering to more quantum materials.

Learning the electron scattering around atomic impurities is a fundamental step to fully understand the basic electronic transport properties of realistic conducting materials. Although many efforts have been made in this field for several decades, atomic scale transport around single point-like impurities has yet been achieved. Here, we report the direct visualization of the electric current induced dipoles around single atomic impurities in epitaxial bilayer graphene by multi-probe low temperature scanning tunneling potentiometry as the local current density is raised up to around 25 A/m, which is considerably higher than that in previous studies. We find the directions of these dipoles which are parallel or anti-parallel to local current are determined by the charge polarity of the impurities, revealing the direct evidence for the existence of the carrier density modulation effect proposed by Landauer in 1976. Furthermore, by $in$ $situ$ tuning local current direction with contact probes, these dipoles are redirected correspondingly. Our work paves the way to explore the electronic quantum transport phenomena at single atomic impurity level and the potential future electronics toward or beyond the end of Moore's Law.

We generalize the nested Wilson loop formalism, which has been playing an important role in the study of topological quadrupole insulators, to two-dimensional (2D) and 3D nonsymmorphic materials with higher-order topology. In particular, certain 3D Dirac semimetals exhibit 1D higher-order Fermi arc (HOFA) states localizing on hinges where two surfaces meet and connecting the projection of the bulk Dirac points. We discover that the generalized nested Berry phase (gNBP) derived from this formalism is the bulk topological indicator determining the existence/absence of HOFAs, revealing a direct bulk-hinge correspondence in 3D Dirac semimetals. Finally, we study the Dirac semimetals NaCuSe and KMgBi based on first-principles calculations and explicitly show that the change in gNBP adjacent to the Dirac point corresponds to the termination of HOFAs at the projection of Dirac points on the hinge. Our findings not only improve the understanding of the bulk-hinge correspondence in topological Dirac semimetals but also provide a general formalism for studying the higher-order topology in nonsymmorphic systems.

Chiral magnetic states in two-dimensional (2D) layered noncentrosymmetric magnets, which are promising advanced spintronic materials, are usually attributed to Dzyaloshinskii-Moriya interactions (DMI). However, the role of underlying higher-order spin couplings in determining the properties of chiral spin textures has much less reported. In this work, taking the lithium-decorated monolayer CrTe$_{2}$ (monolayer LiCrTe$_{2}$) as an example, we develop a first-principles-based comprehensive spin model constructed by using the symmetry-adapted cluster expansion method. Based on this spin model, we identify the ground state of monolayer LiCrTe$_{2}$ as a chiral spin spiral state, which can further assemble macroscopic chiral labyrinth domains (LD) under zero-field conditions as well as evolve into skyrmions under a finite magnetic field. Moreover, higher-order biquadratic and three-site interactions are identified to be responsible for modulating both the size and the field stability of the spin spiral state. Our study sheds light on complex magnetic couplings in 2D magnets., Comment: 10 pages, 5 figures

Two-dimensional (2D) transition metal dichalcogenides (TMDs) hold great potential for future low-energy optoelectronics owing to their unique electronic, optical, and mechanical properties. Chemical vapor deposition (CVD) is the technique widely used for the synthesis of large-area TMDs. However, due to high sensitivity to the growth environment, reliable synthesis of monolayer TMDs via CVD remains challenging. Here we develop a controllable CVD process for large-area synthesis of monolayer WS2 crystals, films, and in-plane graphene-WS2 heterostructures by cleaning the reaction tube with hydrochloric acid, sulfuric acid and aqua regia. The concise cleaning process can remove the residual contaminates attached to the CVD reaction tube and crucibles, reducing the nucleation density but enhancing the diffusion length of WS2 species. The photoluminescence (PL) mappings of a WS2 single crystal and film reveal that the extraordinary PL around the edges of a triangular single crystal is induced by ambient water intercalation at the WS2-sapphire interface. The extraordinary PL can be controlled by the choice of substrates with different wettabilities.

The intact transfer and assembly of two-dimensional (2D) materials and their heterostructures are critical for their integration into advanced electronic and optical devices. Herein, we report a facile technique called volatile polymer stamping (VPS) to achieve efficient transfer of 2D materials and assembly of large-scale heterojunctions with clean interfaces. The central feature of the VPS technique is the use of volatile polyphthalaldehyde (PPA) together with hydrophobic polystyrene (PS). While PS enables the direct delamination of 2D materials from hydrophilic substrates owing to water intercalation, PPA can protect 2D materials from solution attack and maintain their integrity during PS removal. Thereafter, PPA can be completely removed by thermal annealing at 180 {\deg}C. The proposed VPS technique overcomes the limitations of currently used transfer techniques, such as chemical etching during the delamination stage, solution tearing during cleaning, and contamination from polymer residues.

The respective unique merit of antiferromagnets and two-dimensional (2D) materials in spintronic applications inspire us to exploit 2D antiferromagnetic spintronics. However, the detection of the N\'eel vector in 2D antiferromagnets remains a great challenge because the measured signals usually decrease significantly in the 2D limit. Here we propose that the N\'eel vector of 2D antiferromagnets can be efficiently detected by the intrinsic nonlinear Hall (INH) effect which exhibits unexpected significant signals. As a specific example, we show that the INH conductivity of the monolayer manganese chalcogenides Mn$X$ ($X$=S, Se, Te) can reach the order of nm$\cdot$mA/V$^2$, which is orders of magnitude larger than experimental values of paradigmatic antiferromagnetic spintronic materials. The INH effect can be accurately controlled by shifting the chemical potential around the band edge, which is experimentally feasible via electric gating or charge doping. Moreover, we explicitly demonstrate its $2\pi$-periodic dependence on the N\'eel vector orientation based on an effective $k.p$ model. Our findings enable flexible design schemes and promising material platforms for spintronic memory device applications based on 2D antiferromagnets.

Van der Waals superlattices are important for tailoring the electronic structures and properties of layered materials. Here we report the superconducting properties and electronic structure of a natural van der Waals superlattice (PbSe)$_{1.14}$NbSe$_2$. Anisotropic superconductivity with a transition temperature $T_c$ = 5.6 $\pm$ 0.1 K, which is higher than monolayer NbSe$_2$, is revealed by transport measurements on high-quality samples. Angle-resolved photoemission spectroscopy (ARPES) measurements reveal the two-dimensional electronic structure and a charge transfer of 0.43 electrons per NbSe$_2$ unit cell from the blocking PbSe layer. In addition, polarization-dependent ARPES measurements reveal a significant circular dichroism with opposite contrast at K and K' valleys, suggesting a significant spin-orbital coupling and distinct orbital angular momentum. Our work suggests natural van der Waals superlattice as an effective pathway for achieving intriguing properties distinct from both the bulk and monolayer samples., Comment: 8 pages, 4 figures

Distinguishing and controlling the extent of Mottness is important for materials where the energy scales of the onsite Coulomb repulsion U and the bandwidth W are comparable. Here we report the ultrafast electronic dynamics of 1T-TaS$_2$ by ultrafast time- and angle-resolved photoemission spectroscopy. A comparison of the electron dynamics for the newly-discovered intermediate phase (I-phase) as well as the low-temperature commensurate charge density wave (C-CDW) phase shows distinctive dynamics. While the I-phase is characterized by an instantaneous response and nearly time-resolution-limited fast relaxation (~200 fs), the C-CDW phase shows a delayed response and a slower relaxation (a few ps). Such distinctive dynamics refect the different relaxation mechanisms and provide nonequilibrium signatures to distinguish the Mott insulating I-phase from the C-CDW band insulating phase. Moreover, a light-induced bandwidth reduction is observed in the C-CDW phase, pushing it toward the Mott insulating phase. Our work demonstrates the power of ultrafast light-matter interaction in both distinguishing and controlling the extent of Mottness on the ultrafast timescale.

Hybrid density functional calculation is indispensable to accurate description of electronic structure, whereas the formidable computational cost restricts its broad application. Here we develop a deep equivariant neural network method (named DeepH-hybrid) to learn the hybrid-functional Hamiltonian from self-consistent field calculations of small structures, and apply the trained neural networks for efficient electronic-structure calculation by passing the self-consistent iterations. The method is systematically checked to show high efficiency and accuracy, making the study of large-scale materials with hybrid-functional accuracy feasible. As an important application, the DeepH-hybrid method is applied to study large-supercell Moir\'{e} twisted materials, offering the first case study on how the inclusion of exact exchange affects flat bands in the magic-angle twisted bilayer graphene.

Time-periodic light field has emerged as a control knob for manipulating quantum states in solid-state materials, cold atoms and photonic systems via hybridization with photon-dressed Floquet states in the strong coupling limit, dubbed as Floquet engineering. Such interaction leads to tailored properties of quantum materials, for example, modifications of the topological properties of Dirac materials and modulation of the optical response. Despite extensive research interests over the past decade, there is no experimental evidence of momentum-resolved Floquet band engineering of semiconductors, which is a crucial step to extend Floquet engineering to a wide range of solid-state materials. Here, based on time- and angle-resolved photoemission spectroscopy measurements, we report experimental signatures of Floquet band engineering in a model semiconductor - black phosphorus. Upon near-resonance pumping at photon energy of 340 to 440 meV, a strong band renormalization is observed near the band edges. In particular, light-induced dynamical gap opening is resolved at the resonance points, which emerges simultaneously with the Floquet sidebands. Moreover, the band renormalization shows a strong selection rule favoring pump polarization along the armchair direction, suggesting pseudospin selectivity for the Floquet band engineering as enforced by the lattice symmetry. Our work demonstrates pseudospin-selective Floquet band engineering in black phosphorus, and provides important guiding principles for Floquet engineering of semiconductors.

The quantum anomalous Hall effect (QAHE) has unique advantages in topotronic applications, but it is still challenging to realize the QAHE with tunable magnetic and topological properties for building functional devices. Through systematic first-principles calculations, we predict that the in-plane magnetization induced QAHE with Chern numbers C = $\pm$1 and the out-of-plane magnetization induced QAHE with high Chern numbers C = $\pm$3 can be realized in a single material candidate, which is composed of van der Waals (vdW) coupled Bi and MnBi$_2$Te$_4$ monolayers. The switching between different phases of QAHE can be controllable by multiple ways, such as applying strain or (weak) magnetic field or twisting the vdW materials. The prediction of an experimentally available material system hosting robust, highly tunable QAHE will stimulate great research interest in the field. Our work opens a new avenue for the realization of tunable QAHE and provides a practical material platform for the development of topological electronics., Comment: 14 pages, 4 figures

Ab initio study of magnetic superstructures (e.g., magnetic skyrmion) is indispensable to the research of novel materials but bottlenecked by its formidable computational cost. For solving the bottleneck problem, we develop a deep equivariant neural network method (named xDeepH) to represent density functional theory Hamiltonian $H_\text{DFT}$ as a function of atomic and magnetic structures and apply neural networks for efficient electronic structure calculation. Intelligence of neural networks is optimized by incorporating a priori knowledge about the important locality and symmetry properties into the method. Particularly, we design a neural-network architecture fully preserving all equivalent requirements on $H_\text{DFT}$ by the Euclidean and time-reversal symmetries ($E(3) \times \{I, T\}$), which is essential to improve method performance. High accuracy (sub-meV error) and good transferability of xDeepH are shown by systematic experiments on nanotube, spin-spiral, and Moir\'{e} magnets, and the capability of studying magnetic skyrmion is also demonstrated. The method could find promising applications in magnetic materials research and inspire development of deep-learning ab initio methods.

Finding guiding principles to optimize properties of quantum anomalous Hall (QAH) insulators is of pivotal importance to fundamental science and applications. Here, we build a first-principles QAH material database of chirality and band gap, explore microscopic mechanisms determining the QAH material properties, and obtain a general physical picture that can comprehensively understand the QAH data. Our results reveal that the usually neglected Coulomb exchange is unexpectedly strong in a large class of QAH materials, which is the key to resolve experimental puzzles. Moreover, we identify simple indicators for property evaluation and suggest material design strategies to control QAH chirality and gap by tuning cooperative or competing contributions via magnetic co-doping, heterostructuring, spin-orbit proximity, etc. The work is valuable to future research of magnetic topological physics and materials.

Combination of deep learning and ab initio calculation has shown great promise in revolutionizing future scientific research, but how to design neural network models incorporating a priori knowledge and symmetry requirements is a key challenging subject. Here we propose an E(3)-equivariant deep-learning framework to represent density functional theory (DFT) Hamiltonian as a function of material structure, which can naturally preserve the Euclidean symmetry even in the presence of spin-orbit coupling. Our DeepH-E3 method enables very efficient electronic-structure calculation at ab initio accuracy by learning from DFT data of small-sized structures, making routine study of large-scale supercells ($> 10^4$ atoms) feasible. Remarkably, the method can reach sub-meV prediction accuracy at high training efficiency, showing state-of-the-art performance in our experiments. The work is not only of general significance to deep-learning method development, but also creates new opportunities for materials research, such as building Moir\'e-twisted material database.

Magnetotransport such as the giant magnetoresistance and Hall effect lies at the heart of fundamental physics and technologies. Recently, some experiments have clearly demonstrated linear magnetotransport (LMT) proportional to magnetic field but the underlying physical mechanism is still unclear. In this work, we show that Berry curvature effect is a new mechanism dominating the LMT. The Berry-curvature-induced LMT widely exists in 66 out of 122 magnetic point groups. For typical magnetic Weyl semimetals Co$_3$Sn$_2$S$_2$ and ferromagnetic MnBi$_2$Te$_4$, Berry curvature induces LMT conductivities reaching orders of $10^4$ and $10^2$ ${\rm \Omega^{-1}m^{-1}}$ per tesla, respectively, which are tunable through magnetization canting induced by moderate magnetic fields. We further reveal that Berry-curvature-induced LMT can be detected by Hall effect and especially intrinsic magnetoresistance exceeding $100\%$ per tesla insensitive to the sample quality. Our results agree with recent experiments and uncover the important role of Berry curvature in LMT.

Identifying low-energy conformers with quantum mechanical accuracy for molecules with many degrees of freedom is challenging. In this work, we use the molecular dihedral angles as features and explore the possibility of performing molecular conformer search in a latent space with a generative model named variational auto-encoder (VAE). We bias the VAE towards low-energy molecular configurations to generate more informative data. In this way, we can effectively build a reliable energy model for the low-energy potential energy surface. After the energy model has been built, we extract local-minimum conformations and refine them with structure optimization. We have tested and benchmarked our low-energy latent-space (LOLS) structure search method on organic molecules with $5-9$ searching dimensions. Our results agree with previous studies., Comment: 17 pages, 9 figures