Hongming Weng

The axion insulator exhibits a topological magnetoelectric effect characterized by an axion angle θ = π , while the time-reversal-doubled axion insulator ( T -DAXI) can be viewed as two copies of an axion insulator related by time-reversal symmetry. In this work, we show that a nonsymmorphic topological crystalline insulator with glide (or screw) symmetry can host the nonsymmorphic T -DAXI phase, diagnosed by the nontrivial hourglass (screw) invariant δ h = 1 ( δ s = 1 ). In this phase, the partial axion angles ( θ ± = π ) are quantized by the glide and/or screw symmetry, and the gapped surfaces realize half-quantized quantum spin Hall states. Furthermore, we show that nonsymmorphic T -DAXIs also exhibit the spin-magnetoelectric effect. Namely, an external magnetic field can induce a topological nonlocal spin polarization in real space. When the magnetic field is time periodic, this leads to an alternating spin current detectable in experiment. Using calculations, we demonstrate that mixed bismuth monohalides Bi 4 Br x I 4 − x realize the nonsymmorphic T -DAXI. Our findings not only reveal the symmetry-enforced T -DAXIs in nonsymmorphic topological crystalline insulators, but also demonstrate the spin-magnetoelectric effect as a detectable topological spin response in nonsymmorphic T -DAXIs.

We report uniaxial-strain control of spin interference in the Shubnikov–de Haas (SdH) oscillations of ZrTe5. With increasing tensile strain along the crystallographic a axis, the SdH amplitude develops a pronounced node followed by a sign reversal of the oscillatory component, signaling a strain-tunable spin-zero condition. In contrast, the Landau fan intercept remains close to the value expected for a π Berry phase, indicating that the sign reversal is not caused by a global change in the Berry phase inferred from the fan diagram. We show that this behavior is captured by a strain-driven evolution of the relative phase between Zeeman-split cyclotron orbits. This evolution arises from the combined effects of strain-dependent splitting of the extremal Fermi-surface areas and an effective spin-dependent geometric phase in the Zeeman-split Dirac bands. Our results establish uniaxial strain as an in situ mechanical tuning parameter for accessing and traversing the spin-zero condition in topological quantum transport in ZrTe5.

Spin space groups (SSGs) impose fundamentally different constraints on magnetic configurations in real and reciprocal spaces. As a consequence, the correspondence between real-space and momentum-space spin arrangements is far richer than traditionally assumed. Building on the complete enumeration of SSGs, we develop a systematic, symmetry-based framework that classifies all possible spin arrangements allowed by these groups. This unified approach naturally incorporates conventional magnetic orders, altermagnetism, and coplanar odd-wave magnetism (including the previously proposed p -wave case) as distinct symmetry classes. Moreover, by determining the symmetry-allowed wave patterns of spin-polarized phases, our framework classifies coplanar odd-wave magnets beyond the p -wave case into higher-wave types ( f , h , j , and l wave). Crucially, our classification predicts a variety of novel magnetic phases, highlighted by the discovery of the coplanar even-wave magnet(including d , g , and i wave): A state that is noncollinear in real space but hosts a collinear even-wave spin polarization in k space. Analysis of a minimal model reveals that this phase is characterized by nonquantized spin polarization and exhibits a novel mechanism for symmetry-enforced zero polarization on nondegenerate bands. Extending the framework from bulk crystals to layer SSGs appropriate for two-dimensional systems, we further predict layered counterparts and provide symmetry guidelines for designing bilayer coplanar odd-wave and even-wave magnets. We further validate this finding through first-principles calculations and propose CoCrO 4 as a promising candidate for its experimental realization, thereby demonstrating the completeness and predictive power of the SSG-based classification of magnetic orders.

Topologically nontrivial materials are distinguished by their inherent robustness against symmetry-preserving perturbations. However, the resilience of the topologically protected degeneracies against electronic instabilities remains largely unexplored. Here, by employing transport measurements, we demonstrate a layer-number-dependent metal-insulator transition in the topological semimetal Nb₃SiTe₆, which has a layered structure and exhibits Fermi-liquid-like metallicity with a hole carrier density of ∼3.3 × 10²¹ cm^-3 down to the bilayers. An unexpected insulating ground state only emerges in the monolayer and can be effectively tuned by electrostatic gating. The charge neutrality point coincides with a sign change of the Hall signal. Such ambipolar gating behavior contradicts the degeneracy protection under the glide-mirror symmetry in the single-particle picture. Combined with theoretical calculations, we suggest that electronic instabilities could offer a plausible mechanism for gap opening at the symmetry-protected nodal lines. Our findings provide crucial insights for understanding the rich dimension-related metal-insulator transitions in topological materials.

Anderson localization is a quantum phenomenon in which disorder localizes electronic wave functions. In this work, we propose a new approach to study Anderson localization based on the density matrix formalism. Drawing an analogy to the standard transfer matrix method, we extract the localization length from the modular density matrix in quasi-one-dimensional systems. This approach successfully captures the metal-insulator transition in the three-dimensional Anderson model and in the two-dimensional Anderson model with spin-orbit coupling. It can be also readily extended to multi-orbital systems. We further generalize the formalism to interacting systems, showing that the one-dimensional spinless attractive model exhibits the expected metallic phase, consistent with previous studies. More importantly, we demonstrate the existence of a two-dimensional metallic tendency in the presence of Hubbard interactions and disorder. This method offers a new perspective on Anderson localization and its interplay with interactions.

The discovery of topological materials has advanced rapidly due to high-throughput computation and machine learning, but the research progress is hampered by inconsistent classification standards and fragmented data resources. Existing databases differ in computational methods, material coverage and labeling criteria, making it difficult to compare findings across studies. To overcome these challenges, we present a unified topological materials dataset that systematically combines and reconciles two major databases: Materiae and the Topological Materials Database. This dataset provides consistent topological classifications for 35,608 materials, accessible through the Materials Galaxy platform for interactive exploration and available for bulk download via MatElab. We describe the featurization methodology that converts crystal structures into 4,710 machine-learning-ready descriptors and present a comprehensive analysis of topological material distributions. This work serves as a complete guide for accessing, utilizing, and interpreting this unified resource, designed to enable reproducible machine learning applications and accelerate the discovery of topological materials.