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A peculiar feature of quantum states is that they may embody so-called projective representations of symmetries rather than ordinary representations. Projective representations of space groups-the defining symmetry of crystals-remain largely unexplored. Despite recent advances in artificial crystals, whose intrinsic gauge structures necessarily require a projective description, a unified theory is yet to be established. Here, we establish such a unified theory by exhaustively classifying and representing all 458 projective symmetry algebras of time-reversal-invariant crystals from 17 wallpaper groups in two dimensions-189 of which are algebraically non-equivalent. We discover three physical signatures resulting from projective symmetry algebras, including the shift of high-symmetry momenta, an enforced nontrivial Zak phase, and a spinless eight-fold nodal point. Our work offers a theoretical foundation for the field of artificial crystals and opens the door to a wealth of topological states and phenomena beyond the existing paradigms. Projective representations of crystal symmetries are indispensable for understanding artificial crystals. Here, authors establish a unified theory of projective crystal symmetries with time-reversal invariance, and construct models for all 458 projective symmetry algebras for the 17 two-dimensional wallpaper groups.

The sublattice symmetry on a bipartite lattice is commonly regarded as the chiral symmetry in the AIII class of the tenfold Altland–Zirnbauer classification. Here, we reveal the spatial nature of sublattice symmetry and show that this assertion holds only if the periodicity of primitive unit cells agrees with that of the sublattice labeling. In cases where the periodicity does not agree, sublattice symmetry is represented as a glide reflection in energy–momentum space, which inverts energy and simultaneously translates some k by π , leading to substantially different physics. Particularly, it introduces novel constraints on zero modes in semimetals and completely alters the classification table of topological insulators compared to class AIII. Notably, the dimensions corresponding to trivial and nontrivial classifications are switched, and the nontrivial classification becomes Z 2 instead of Z . We have applied these results to several models, including the Hofstadter model both with and without dimerization. Sublattice symmetry has long been synonymous with chiral symmetry when it comes to topological classification. Here, the authors challenge this notion by systematically investigating sublattice symmetry and revealing its spatial nature with a precise description in terms of symmetry algebra and representation.

Intestinal IgA, which is regulated by gut microbiota, has a crucial role in maintenance of intestinal homeostasis and in protecting the intestines from inflammation. However, the means by which microbiota promotes intestinal IgA responses remain unclear. Emerging evidence suggests that the host can sense gut bacterial metabolites in addition to pathogen-associated molecular patterns and that recognition of these small molecules influences host immune response in the intestines and beyond. We reported here that microbiota metabolite short-chain fatty acid acetate promoted intestinal IgA responses, which was mediated by “metabolite-sensing” GPR43. GPR43−/− mice demonstrated lower levels of intestinal IgA and IgA+ gut bacteria compared with those in wild type (WT) mice. Feeding WT but not GPR43−/− mice acetate but not butyrate promoted intestinal IgA response independent of T cells. Acetate promoted B-cell IgA class switching and IgA production in vitro in the presence of WT but not GPR43−/− dendritic cells (DCs). Mechanistically, acetate-induced DC expression of Aldh1a2, which converts Vitamin A into its metabolite retinoic acid (RA). Moreover, blockade of RA signaling inhibited the acetate induction of B-cell IgA production. Our studies thus identified a new pathway by which microbiota promotes intestinal IgA response through its metabolites.

A Brillouin zone is the unit for the momentum space of a crystal. It is topologically a torus, and distinguishing whether a set of wave functions over the Brillouin torus can be smoothly deformed to another leads to the classification of various topological states of matter. Here, we show that under Z 2 gauge fields, i.e., hopping amplitudes with phases ±1, the fundamental domain of momentum space can assume the topology of a Klein bottle. This drastic change of the Brillouin zone theory is due to the projective symmetry algebra enforced by the gauge field. Remarkably, the non-orientability of the Brillouin Klein bottle corresponds to the topological classification by a Z 2 invariant, in contrast to the Chern number valued in Z for the usual Brillouin torus. The result is a novel Klein bottle insulator featuring topological modes at two edges related by a nonlocal twist, radically distinct from all previous topological insulators. Our prediction can be readily achieved in various artificial crystals, and the discovery opens a new direction to explore topological physics by gauge-field-modified fundamental structures of physics. Topological states are exploited based on crystalline symmetry, but under artificial gauge fields, symmetries may satisfy projective algebras, which remains less studied. Here, the authors reveal that projective symmetry algebra leads to momentum-space nonsymmorphic symmetry, resulting in new topological states over a momentum-space Klein bottle.

Improving the strength of a metal alloy is hard to do without sacrificing the ductility. Yang et al. designed an iron-nickel-cobalt (Fe-Ni-Co) alloy laced with aluminum-titanium (Al-Ti) nanoparticles with both high strength and ductility. The key was getting the composition tuned correctly, because the Fe-Ni-Co matrix reacts with the Al-Ti nanoparticles. This was vital for avoiding environmental embrittlement, enhancing work hardening, and improving ductility. Science , this issue p. 933 Multicomponent nanoparticles enhance both the strength and ductility of an iron-nickel-cobalt alloy. Alloy design based on single–principal-element systems has approached its limit for performance enhancements. A substantial increase in strength up to gigapascal levels typically causes the premature failure of materials with reduced ductility. Here, we report a strategy to break this trade-off by controllably introducing high-density ductile multicomponent intermetallic nanoparticles (MCINPs) in complex alloy systems. Distinct from the intermetallic-induced embrittlement under conventional wisdom, such MCINP-strengthened alloys exhibit superior strengths of 1.5 gigapascals and ductility as high as 50% in tension at ambient temperature. The plastic instability, a major concern for high-strength materials, can be completely eliminated by generating a distinctive multistage work-hardening behavior, resulting from pronounced dislocation activities and deformation-induced microbands. This MCINP strategy offers a paradigm to develop next-generation materials for structural applications.

Band topology of materials describes the extent Bloch wavefunctions are twisted in momentum space. Such descriptions rely on a set of topological invariants, generally referred to as topological charges, which form a characteristic class in the mathematical structure of fiber bundles associated with the Bloch wavefunctions. For example, the celebrated Chern number and its variants belong to the Chern class, characterizing topological charges for complex Bloch wavefunctions. Nevertheless, under the space-time inversion symmetry, Bloch wavefunctions can be purely real in the entire momentum space; consequently, their topological classification does not fall into the Chern class, but requires another characteristic class known as the Stiefel-Whitney class. Here, in a three-dimensional acoustic crystal, we demonstrate a topological nodal-line semimetal that is characterized by a doublet of topological charges, the first and second Stiefel-Whitney numbers, simultaneously. Such a doubly charged nodal line gives rise to a doubled bulk-boundary correspondence—while the first Stiefel-Whitney number induces ordinary drumhead states of the nodal line, the second Stiefel-Whitney number supports hinge Fermi arc states at odd inversion-related pairs of hinges. These results experimentally validate the two Stiefel-Whitney topological charges and demonstrate their unique bulk-boundary correspondence in a physical system. Symmetry plays a crucial role in defining the band topology. Here, the authors experimentally demonstrate that spacetime inversion symmetry can lead to Stiefel-Whitney topological charges and protect hinge states in an acoustic nodal-line semimetal.

China’s Mars rover, Zhurong, touched down on Utopia Planitia in the northern lowlands of Mars (109.925° E, 25.066° N) in May 2021, and has been conducting in situ investigations of the landing area in conjunction with the Tianwen-1 orbiter. Here we present surface properties derived from the Zhurong rover’s traverse during the first 60 sols of rover operations. Our analysis of the rover’s position from locomotion data and camera imagery over that time shows that the rover traversed 450.9 m southwards over a flat surface with mild wheel slippage. Soil parameters determined by terramechanics, which observes wheel–terrain interactions, indicate that the topsoil has high bearing strength and cohesion. The soil’s equivalent stiffness is estimated to range from 1,390 to 5,872 kPa per m N , and the internal friction angle ranges from 21° to 34° under a cohesion of 1.5 to 6 kPa. Aeolian bedforms in the area are primarily transverse aeolian ridges, indicating northeastern local wind directions. Surface rocks imaged by the rover cameras show evidence of physical weathering processes, such as wind erosion, and potential chemical weathering processes. Joint investigations utilizing the scientific payloads of the rover and the orbiter can provide insights into local aeolian and aqueous history, and the habitability evolution of the northern lowlands on Mars. Analysis of interactions between the wheels of the Zhurong rover and the terrain along the rover’s traverse reveals soils with high bearing strength and cohesion.

Double neutron star (DNS) merger events are promising candidates of short gamma-ray burst (sGRB) progenitors as well as high-frequency gravitational wave (GW) emitters. On August 17, 2017, such a coinciding event was detected by both the LIGO-Virgo gravitational wave detector network as GW170817 and Gamma-Ray Monitor on board NASA’s Fermi Space Telescope as GRB 170817A. Here, we show that the fluence and spectral peak energy of this sGRB fall into the lower portion of the distributions of known sGRBs. Its peak isotropic luminosity is abnormally low. The estimated event rate density above this luminosity is at least 19 0 - 160 + 440  Gpc −3  yr −1 , which is close to but still below the DNS merger event rate density. This event likely originates from a structured jet viewed from a large viewing angle. There are similar faint soft GRBs in the Fermi archival data, a small fraction of which might belong to this new population of nearby, low-luminosity sGRBs. A short-duration gamma-ray burst was detected along with a double neutron start merger gravitational wave by LIGO-Virgo on August 17th 2017. Here, the authors show that the fluence and spectral peak energy of this event fall into the lower portion of the distribution of known short-duration gamma-ray bursts.

Optical metamaterials are usually based on planarized, complex-shaped, resonant nano-inclusions. Three-dimensional geometries may provide a wider set of functionalities, including broadband chirality to manipulate circular polarization at the nanoscale, but their fabrication becomes challenging as their dimensions get smaller. Here we introduce a new paradigm for the realization of optical metamaterials, showing that three-dimensional effects may be obtained without complicated inclusions, but instead by tailoring the relative orientation within the lattice. We apply this concept to realize planarized, broadband bianisotropic metamaterials as stacked nanorod arrays with a tailored rotational twist. Because of the coupling among closely spaced twisted plasmonic metasurfaces, metamaterials realized with conventional lithography may effectively operate as three-dimensional helical structures with broadband bianisotropic optical response. The proposed concept is also shown to relax alignment requirements common in three-dimensional metamaterial designs. The realized sample constitutes an ultrathin, broadband circular polarizer that may be directly integrated within nanophotonic systems. Three-dimensional optical metamaterials provide a range of exciting features, such as broadband circular dichroism, yet their fabrication is challenging. Here, a broadband optical circular polarizer is presented based on twisted stacks of metasurfaces, avoiding the issues of three-dimensional fabrication.

First-order relationships between organic matter content and mineral surface area have been widely reported and are implicated in stabilization and long-term preservation of organic matter. However, the nature and stability of organomineral interactions and their connection with mineralogical composition have remained uncertain. In this study, we find that continentally derived organic matter of pedogenic origin is stripped from smectite mineral surfaces upon discharge, dispersal, and sedimentation in distal ocean settings. In contrast, organic matter sourced from ancient rocks that is tightly associated with mica and chlorite endures in the marine realm. These results imply that the persistence of continentally derived organic matter in ocean sediments is controlled to a first order by phyllosilicate mineralogy.