We study a one-dimensional system of two-component fermions in the limit of strong attractive particle-particle interactions. First, we analyze scattering in the corresponding few-body problem, which is analytically solvable via Bethe ansatz. This allows us to engineer effective interactions between the system’s effective degrees of freedom: fermions and bosonic dimers (tightly bound pairs of fermions). We argue that, although these interactions are strong, the resulting effective problem can be mapped onto a weakly interacting one, paving the way for the use of perturbation theory. This finding simplifies studies of many-fermion systems under confinement that are beyond reach of state-of-the-art numerical methods. We illustrate this statement by considering an impurity atom in a Fermi gas.

We identify a three-dimensional system that exhibits long-range entanglement at sufficiently small but nonzero temperature—it therefore constitutes a quantum topological order at finite temperature. The model of interest is known as the fermionic toric code, a variant of the usual 3D toric code, which admits emergent fermionic pointlike excitations. The fermionic toric code, importantly, possesses an anomalous two-form symmetry, associated with the spacelike Wilson loops of the fermionic excitations. We argue that it is this symmetry that imbues low-temperature thermal states with a novel topological order and long-range entanglement. Based on the current classification of three-dimensional topological orders, we expect that the low-temperature thermal states of the fermionic toric code belong to a phase of matter that, in the context of equilibrium phases of matter, only exists at nonzero temperatures. We conjecture that further examples of topological orders at nonzero temperatures are given by discrete gauge theories with anomalous two-form symmetries. Our Letter therefore opens the door to studying quantum topological order at nonzero temperature in physically realistic dimensions.

Atomically thin hexagonal boron nitride (h-BN), especially monolayer, has emerged as a pivotal quantum material due to its intriguing optical and light-matter-interaction properties. Nevertheless, fundamental ambiguities persist regarding its intrinsic band structure and deep-UV optical responses. Here, a multispectroscopic approach—combining near-resonance deep-UV photoluminescence, Raman spectroscopy, and reflectance contrast measurements—is employed to systematically resolve the layer-dependent optoelectronic evolution of h-BN. It is revealed that the absence of band-edge luminescence in 1–3 layers h-BN is indicative of their indirect band gap nature, thereby rectifying longstanding misinterpretations of monolayer BN as a direct band gap semiconductor. Strikingly, band-edge luminescence signals and indirect band gap absorption start to appear in 4-layer, and the luminescence intensity increases with the number of layers, suggesting that interlayer interactions and periodicity along the $z$ axis enhance phonon-assisted indirect band gap transition, even in the 4-layer case, and furthermore indicating the formation process of flat bands at $K/M$ valleys as the periodicity along z direction increases. Moreover, the prominent resonance Raman signals in atomically thin h-BN reveals exceptionally strong electron-phonon coupling, a critical parameter for quantum optoelectronic applications. Our findings provide definitive experimental benchmarks for the long-debated monolayer BN’s band structure.

We report the first observation of a momentum-resolved superconducting gap in the Hg-based trilayer cuprate, which holds the highest record of superconducting transition temperature ($T_{\mathrm{c}}$) at ambient pressure. By angle-resolved photoemission spectroscopy utilizing a microfocused beam, clear quasiparticle dispersions originating from the inner and outer ${\mathrm{CuO}}_2$ planes (IP and OP, respectively) were separately identified. The magnitude of the superconducting gap for the IP was comparable to that of the Bi-based trilayer cuprate with a lower $T_{\mathrm{c}}$. In contrast, the superconducting gap for the OP was significantly larger than that of the Bi-based one. While strong pairing in the IP has been highlighted as the key element of trilayer cuprates, the present results suggest that the enhanced pairing energy in the OP is essential for the highest $T_{\mathrm{c}}$ at ambient pressure realized in the Hg-based trilayer cuprate.

More than 50 years ago, excitonic insulators formed by the pairing of electrons and holes due to Coulomb interactions were first predicted [A. N. Kozlov and L. A. Maksimov, Sov. J. Exp. Theor. Phys. 21, 790 (1965); L. V. Keldysh and Y. V. Kopaev, Sov. Phys. Solid State 6, 2219 (1965); D. Jérome, T. M. Rice, and W. Kohn, Phys. Rev. 158, 462 (1967)]. Since then, excitonic insulators have been observed in various classes of materials, including quantum Hall bilayers, graphite, transition metal chalcogenides, and more recently in moiré superlattices. In these excitonic insulators, an electron and a hole with the same spin bind together, and the resulting exciton is a spin singlet. Here, we report the experimental observation of a spin-triplet excitonic insulator in the ultra-quantum limit of a three-dimensional topological material ${\mathrm{HfTe}}_5$. We observe that the spin-polarized zeroth Landau bands dispersing along the field direction cross each other beyond a characteristic magnetic field in ${\mathrm{HfTe}}_5$, forming the one-dimensional Weyl mode. Transport measurements reveal the emergence of a gap of about $250\mathrm{\mu }\mathrm{eV}$ when the field surpasses a critical threshold. By performing the material-specific modeling, we identify this gap as a consequence of a spin-triplet exciton formation, where electrons and holes with opposite spin form bound states, and the translational symmetry is preserved. The system reaches charge neutrality following the gap opening, as evidenced by the zero Hall conductivity over a wide magnetic field range (10–72 T). Our finding of the spin-triplet excitonic insulator paves the way for studying novel spin transport including spin superfluidity, spin Josephson currents, and Coulomb drag of spin currents in analogy to the transport properties associated with the layer pseudospin in quantum Hall bilayers.

Experiments have shown that over 10% of proteins are degraded nonexponentially. Gene expression models for nonexponentially degraded proteins are notoriously difficult to solve since the underlying stochastic dynamics is non-Markovian. Here we develop an effective Markovian dynamics (EMD) method which converts a large class of non-Markovian models into effective Markovian ones so that they have the same mRNA and protein distributions at any fixed time. Using the EMD approach, we analytically solve some classical gene expression models with nonexponential or delayed protein decay, whose exact distributions are previously unknown and fail to be obtained using conventional queueing theory. Our theory successfully explains why nonexponentially degraded proteins on average have smaller mRNA-protein correlation than exponentially degraded proteins, and it predicts that bimodality is significantly enhanced in the presence of delayed protein degradation.

Sliding ferroelectrics constructed from stacked nonpolar monolayers enable out-of-plane polarization in two dimensions with exceptional properties. However, the widely accepted switching mechanism, involving synchronized long-distance in-plane translation of entire atomic layers, contradicts experimental findings. We demonstrate that this spinodal decompositionlike homogeneous switching process violates Neumann’s principle and is therefore highly improbable. Instead, polarization reversal relies on symmetry-breaking domain walls (DWs) and the tensorial nature of Born effective charges, highlighting the quantum nature of sliding ferroelectrics. We reveal that wide, wavelike DWs coherently propagate, a stark departure from the narrow DW mechanism recognized for decades. These wavelike DWs exhibit superlubric dynamics, achieving ultrahigh velocities of approximately $4000\mathrm{m}/\mathrm{s}$ at room temperature and displaying an anomalous cooling-promoted switching speed. The unexpected emergence of DW superlubricity presents new avenues for enhancing key performance metrics and offers exciting opportunities for applications in cryogenic environments.

Understanding which parts of a dynamical system cause each other is extremely relevant in fundamental and applied sciences. However, inferring causal links from observational data, namely, without direct manipulations of the system, is still computationally challenging, especially if the data are high dimensional. In this Letter we introduce a framework for constructing causal graphs from high-dimensional time series, whose computational cost scales linearly with the number of variables. The approach is based on the automatic identification of dynamical communities, groups of variables which mutually influence each other and can therefore be described as a single node in a causal graph. These communities are efficiently identified by optimizing the information imbalance, a statistical quantity that assigns a weight to each putative causal variable based on its information content relative to a target variable. The communities are then ordered starting from the fully autonomous ones, whose evolution is independent from all the others, to those that are progressively dependent on other communities, building in this manner a community causal graph. We demonstrate the computational efficiency and the accuracy of our approach on discrete-time and continuous-time dynamical systems including up to 80 variables.

Perhaps the most basic question we can ask about cosmological correlations is how their strength changes as we smoothly vary kinematic parameters. The answer is encoded in differential equations that govern this evolution in kinematic space. In this Letter, we introduce a new perspective on these differential equations. We show that, in the simplified setting of conformally coupled scalars in power-law Friedmann-Robertson-Walker spacetimes, the equations for arbitrary tree-level processes can be obtained from a small number of simple combinatorial rules. While this “kinematic flow” is defined purely in terms of boundary data, it reflects the physics of bulk time evolution. The unexpected regularity of the equations suggests the existence of an autonomously defined mathematical structure from which cosmological correlations and the time evolution of the associated spacetime emerge.

Seeded free-electron lasers (FELs) capable of operating at repetition rates up to the MHz level are in high demand for advanced time-resolved spectroscopies, which require both full longitudinal coherence and high average photon flux in the extreme ultraviolet (EUV) and x-ray regimes. However, conventional external-seeding methods require ultraviolet seed lasers with peak powers on the order of 100 MW, constraining them to lower repetition rates. Here, we report the first lasing and stable operation of a direct-amplification enabled harmonic generation FEL driven by a weak seed laser with only MW-level peak power. Beginning with an ultraviolet seed laser with only $0.75\mathrm{\mu }\mathrm{J}$ pulse energy, we demonstrate its direct amplification to over $10\mathrm{\mu }\mathrm{J}$ within an 8-m-long modulator. We observe coherent harmonic generation up to the $12th$ harmonic of the seed and achieve saturation of the $7th$ harmonic in the radiator. These results represent a crucial milestone toward the realization of MHz-class, fully coherent EUV and x-ray light sources.

Optically active spin defects in solids are promising platforms for quantum technologies. Here, we present a first-principles framework to investigate intersystem crossing processes, which represent crucial steps in the optical spin-polarization cycle used to address spin defects. Considering the nitrogen-vacancy center in diamond as a case study, we demonstrate that our framework effectively captures electron correlation effects in the calculation of many-body electronic states and their spin-orbit coupling and electron-phonon interactions, while systematically addressing finite-size effects. We validate our predictions by carrying out measurements of fluorescence lifetimes, finding excellent agreement between theory and experiments. The framework presented here provides a versatile and robust tool for exploring the optical cycle of varied spin defects entirely from first principles.

The pertinent need for a microscopic understanding of magnetic exchange motivated us to go beyond the existing theories and develop a systematic method to quantify all possible mechanisms that contribute to magnetic exchange for an arbitrary pair of atoms in a given material. We apply it to the archetypal 2D magnetic monolayers ${\mathrm{CrI}}_3$ and ${\mathrm{NiI}}_2$, to reveal the previously underrated $d_{x^2-y^2}$,$d_{x^2-y^2}$ contribution as either the leading or the second largest contribution to the total magnetic exchange. We proceed to explore the microscopic mechanisms behind all the nonzero orbital contributions in both ${\mathrm{CrI}}_3$ and ${\mathrm{NiI}}_2$, and generalize the findings to other magnetic monolayers dominated by $d^8$ and $d^3$ electronic configurations of the magnetic atoms.

Observations from the Juno satellite have indicated very low electron densities, as low as ${10}^{-3}{\mathrm{cm}}^{-3}$, at high-latitudes in Jupiter’s magnetosphere. This region is strongly magnetized, with surface magnetic fields at the one-bar level up to 20 G, or 2 mT, leading to the unusual situation that the electron plasma frequency is less than the ion gyrofrequency. In this extremely low-density plasma, the Alfven wave becomes a plasma oscillation at the electron plasma frequency at shorter perpendicular wavelengths. Analysis of this mode with a kinetic low-frequency dispersion solver indicates that at large wave number, this mode has the characteristics of the Langmuir wave. Thus, this mode can be called an Alfvén-Langmuir mode. Below the plasma frequency, the high-wave number behavior of this mode exhibits a resonance cone, with frequency determined by the angle of the wave vector with the background magnetic field. These waves can be excited by the upward electron beams observed by Juno.

We report the emergence of two-dimensional itinerant half-metallicity in a two-atomic-layer thick iron-palladium alloy. Against the common belief that spin-orbit coupling is adverse to half-metallicity, the complex interplay between exchange and spin-orbit coupling counterintuitively enables it via electronic band hybridization. The 2D ferromagnet is engineered directly via controlled alloying and is verified experimentally via spin-resolved band structure analyses. First-principles calculations corroborate its tunability by providing a systematic bottom-up approach through stepwise ground-state construction. The appearance of hybridization points at specific $k$ points, via interplay between exchange and spin-orbit interactions, is responsible for the emergence of half-metallicity.

We present a search for the diffuse extremely-high-energy neutrino flux using 12.6 years of IceCube data. The nonobservation of neutrinos with energies well above 10 PeV constrains the all-flavor neutrino flux at ${10}^{18}\mathrm{eV}$ to a level of $E^2{\mathrm{\Phi }}_{{\nu }_e+{\nu }_{\mu }+{\nu }_{\tau }}\simeq {10}^{-8}\mathrm{GeV}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{sr}}^{-1}$, the most stringent limit to date. Using these data, we constrain the proton fraction of ultrahigh-energy cosmic rays (UHECRs) above $\simeq 30\mathrm{EeV}$ to be $\lesssim 70\%$ (at 90% CL) if the cosmological evolution of the sources is comparable to or stronger than the star formation rate. This is the first result to disfavor the “proton-only” hypothesis for UHECR in this evolution regime using neutrino data. This result complements direct air-shower measurements by being insensitive to uncertainties associated with hadronic interaction models. We also evaluate the tension between IceCube’s nonobservation and the $\sim 200\mathrm{PeV}$ KM3NeT neutrino candidate (KM3-230213A), finding it to be $\sim 2.9\sigma$ based on a joint-livetime fit between neutrino datasets.

We report a single-ion optical atomic clock with a fractional frequency uncertainty of $5.5\times {10}^{-19}$ and fractional frequency stability of $3.5\times {10}^{-16}/\sqrt{\tau /\mathrm{s}}$, based on quantum logic spectroscopy of a single ${}^{27}{\mathrm{Al}}^{+}$ ion. A cotrapped ${}^{25}{\mathrm{Mg}}^{+}$ ion provides sympathetic cooling and quantum logic readout of the ${}^{27}{\mathrm{Al}}^{+}{{}^{1}S}_0\leftrightarrow {{}^{3}P}_0$ clock transition. A Rabi probe duration of 1 s, enabled by laser stability transfer from a remote cryogenic silicon cavity across a 3.6 km fiber link, results in a threefold reduction in instability compared to previous ${}^{27}{\mathrm{Al}}^{+}$ clocks. Systematic uncertainties are lower due to an improved ion trap electrical design, which reduces excess micromotion, and a new vacuum system, which reduces collisional shifts. We also perform a direction-sensitive measurement of the ac magnetic field due to the rf ion trap, eliminating systematic uncertainty due to field orientation.

The recent experimental observation of quantum anomalous Hall (QAH) effects in the rhombohedrally stacked pentalayer graphene has motivated theoretical discussions on the possibility of quantum anomalous Hall crystal (QAHC), a topological version of Wigner crystal. Conventional topological Wigner crystals typically have one electron per unit cell. In this Letter we propose new types of topological Wigner crystals labeled as QAHC-$z$, with $z$ electrons per unit cell. In the pentalayer graphene system, we find parameter regimes where QAHC-2 and QAHC-3 have lower energy than the conventional QAHC-1 at total filling $\nu =1$ per moiré unit cell. These states all have total Chern number $C_{\mathrm{tot}}=1$ and are consistent with the QAH effect observed in the experiments. The larger period QAHC states have lower kinetic energy due to the unique Mexican-hat dispersion of the pentalayer graphene, which can compensate for the loss in the interaction energy. Unlike QAHC-1, QAHC-2, and QAHC-3 break the moiré translation symmetry and are sharply distinct from a moiré band insulator. We also briefly discuss the competition between integer QAH and fractional QAH states at filling $\nu =2/3$. Moreover, we find that a stronger moiré potential can significantly change the phase diagram and even favors a QAHC-1 ansatz with $C=2$ Chern band.

The $\sim 60000$ solar-mass ($M_{\odot }$) star cluster R136 (NGC 2070) in the Tarantula Nebula in the Large Magellanic Cloud is the host of at least 55 massive stars ($M\gtrsim 10M_{\odot }$) which move away from the cluster at projected velocities $\ge 27.5\mathrm{km}/\mathrm{s}$. The origin of the high velocities of such runaway stars have been debated since the 1960s, resulting either from dynamical ejections or from supernova explosions. Because of the Gaia satellite’s outstanding precision, we can now retrace the most recently ejected binary star, Mel 34, back to the center of R136 and reconstruct the events that 52 000 years ago led to its removal from R136; i.e., we establish its dynamical interaction and ejection history. We find that this ejection requires the participation of five stars in a strong interaction between a triple composed of the tight massive binary Mel 39, orbited by the star VFTS 590, and the binary star Mel 34. The participation of five stars is unexpected because runaway stars were not expected to result from triple interactions. The deterministic nature of the Newtonian dynamics in the scattering enables us to reconstruct the encounter that ejected Mel 34. We then predict that Mel 39 is a binary star with an $80M_{\odot }$ companion star that orbits within $\sim 1°$ in the same plane as Mel 34 and escapes the cluster with a velocity of $\sim 64\mathrm{km}/\mathrm{s}$. The five stars will undergo supernova explosions in the coming 5 Myr at a distance of $\sim 180–332\mathrm{pc}$ from their birth location (R136). The resulting black hole binaries, however, are not expected to merge within a Hubble time.

Nonadiabatic effects profoundly influence lattice dynamics, resulting in phonon renormalizations not only at the center of Brillouin zone (BZ), but also across the entire dispersion at finite momenta. These nonadiabatic phenomena exhibit clear dimensional dependencies and remain largely unexplored experimentally in low-dimensional systems. Here, we utilize high-resolution electron energy loss spectroscopy to investigate nonadiabatic phonon dispersion renormalization in monolayer graphene (MLG) and Bernal bilayer graphene (BLG). We present comprehensive phonon spectra measurements for both MLG and BLG across the full BZ. The high-resolution data reveal an intriguing “W” -shaped dispersion for the longitudinal optical phonon in MLG and a “V” -shaped dispersion in BLG near the BZ center, in contrast to the conventional “U” -shaped parabolic dispersions. Combining theoretical analysis, these anomalous phonon renormalizations are demonstrated to originate from nonadiabatic electron-phonon couplings. The comparative study of MLG and BLG gives a generic understanding of the impact of nonadiabatic effects on phonon dispersions in doped two-dimensional systems.

We combine atomistic simulations and theories to predict the free energy of polymer crystallization, which highlights the roles of backbone stiffness and orientational coupling between monomers in the formation of metastable mesophases. We show that polyethylene (PE) with sufficient backbone stiffness in the conformationally disordered state can develop uniaxial order through metastable nematic and rotator phases before conformationally ordering into the crystalline state. Isotactic polypropylene (iPP), with a lower backbone stiffness, undergoes one-step crystallization directly from the isotropic phase to the crystalline phase. The predicted bulk phase transition temperatures for iPP and PE of different molecular weights agree well with experiments.