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Three-dimensional (3D) topological Dirac semimetal, when thinned down to 2D few layers, is expected to possess gapped Dirac nodes via quantum confinement effect and concomitantly display the intriguing quantum spin Hall (QSH) insulator phase. However, the 3D-to-2D crossover and the associated topological phase transition, which is valuable for understanding the topological quantum phases, remain unexplored. Here, we synthesize high-quality Na3Bi thin films with √3×√3 reconstruction on graphene, and systematically characterize their thickness-dependent electronic and topological properties by scanning tunneling microscopy/spectroscopy in combination with first-principles calculations. We demonstrate that Dirac gaps emerge in Na3Bi films, providing spectroscopic evidences of dimensional crossover from a 3D semimetal to a 2D topological insulator. Importantly, the Dirac gaps are revealed to be of sizable magnitudes on 3 and 4 monolayers (72 and 65 meV, respectively) with topologically nontrivial edge states. Moreover, the Fermi energy of a Na3Bi film can be tuned via certain growth process, thus offering a viable way for achieving charge neutrality in transport. The feasibility of controlling Dirac gap opening and charge neutrality enables realizing intrinsic high-temperature QSH effect in Na3Bi films and achieving potential applications in topological devices.

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The combination of nontrivial topology and charge density wave (CDW) has been proposed as a powerful resource for realizing novel quantum phenomena such as axion electrodynamics and the anomalous Hall effect. Hence, topological materials with CDW states attract great interest, yet they are still very rare, particularly in the 2D limit. Here, it is predicted that monolayer NbTe 2 in its high-symmetry 1T phase stabilized by anharmonicity at room temperature exhibits nontrivial topology sensitive to electronic interactions: it changes from a quantum spin Hall (QSH) state to a quantum anomalous Hall (QAH) state when the Hubbard potential U exceeds a critical value. At low temperature, a 4 × 4 CDW order emerges and coexists with the nontrivial topology. Meanwhile, the critical U increases because CDW reduces density of states at Fermi level. More interestingly, in contrast to the high-symmetry structure that actually is a topologically nontrivial metal, the CDW structure shows an insulating nontrivial gap either in the QSH or the QAH phase, indicating CDW is an effective means to modulate the topological state for developing new functions and devices. These discoveries establish NbTe 2 as a promising candidate to explore exotic quantum states at the confluence of nontrivial topology, electronic correlation, and CDW.

Spin-orbit-coupled Mott iridates show great similarity with parent compounds of superconducting cuprates, attracting extensive research interest especially for their electron-doped states. However, previous experiments have been largely limited within a small doping range due to the absence of effective dopants, and therefore the electron-doped phase diagram remains elusive. Here, an ionic-liquid-gating-induced protonation method is utilized to achieve electron-doping into a 5d Mott-insulator built with a SrIrO 3 /SrTiO 3 superlattice (SL), and a systematic mapping of its electron-doped phase diagram is achieved with the evolution of the iridium valence state from 4+ to 3+, equivalent to doping of one electron per iridium ion. Along increasing doping level, the parent Mott-insulator is first turned into a localized metallic state with gradually suppressed magnetic ordering, and then further evolves into a nonmagnetic band insulating state. This work forms an important step forward for the study of electron-doped Mott iridate systems, and the strategy of manipulating the band filling in an artificially designed SL structure can be readily extended into other systems with more exotic states to explore.

Research on topological physics of phonons has attracted enormous interest but demands appropriate model materials. Our ab initio calculations identify silicon as an ideal candidate material containing extraordinarily rich topological phonon states. In silicon, we identify various topological nodal lines characterized by quantized Berry phase π, which gives drumhead surface states observable from any surface orientations. Remarkably, a novel type of topological nexus phonon is discovered which is featured by double Fermi-arc-like surface states but requires neither inversion nor time-reversal symmetry breaking. Versatile topological states can be created from the nexus phonons, such as Hopf nodal links by strain. Furthermore, we generalize the symmetry analysis to other centrosymmetric systems and find numerous candidate materials, demonstrating the ubiquitous existence of topological phonons in solids. These findings open up new opportunities for studying topological phonons in realistic materials and their influence on surface physics.

The 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 efficient electronic structure calculation at ab initio accuracy by learning from DFT data of small-sized structures, making the routine study of large-scale supercells (>104 atoms) feasible. 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 opportunities for materials research, such as building a Moiré-twisted material database.

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