Quantum-entangled states underpin many emergent phenomena in quantum materials, yet their direct experimental identification remains a challenge. ${\mathrm{NiPS}}_3$, a van der Waals antiferromagnet exhibiting a resolution-limited magnetic exciton in its ordered phase, has been proposed to host a many-body entangled Zhang-Rice triplet state. Here, using ${}^{33}\mathrm{S}$ nuclear magnetic resonance (NMR) on ${}^{33}\mathrm{S}$-enriched ${\mathrm{NiPS}}_3$ single crystals, we provide microscopic evidence for this charge-transfer state. The ${}^{33}\mathrm{S}$ and ${}^{31}\mathrm{P}$ Knight shifts as a function of temperature reveal a unified spin-triplet configuration arising from strong hybridization between a self-doped hole in the S $3p$ orbitals and a hole in Ni $3d$ orbitals. Furthermore, the ${}^{33}\mathrm{S}$ nuclear spin-lattice relaxation rate exhibits a power-law divergence as it approaches the Néel temperature $T_N=155\mathrm{K}$, indicating critical slowing down of collective charge fluctuations consistent with spin-nematic correlations. These results reveal a spin-charge-intertwined ground state and establish the microscopic foundation for the exceptional coherence of the magnetic exciton in ${\mathrm{NiPS}}_3$.

Although the absorption of light in a bulk homogeneous semiconductor produces photocarriers with nonzero momenta, it generally does not produce a current in the absence of an applied electric field because equal amounts of carriers with opposite momenta are injected. The interference of absorption processes, for example, between one-photon and two-photon absorption can produce a current because constructive interference for carriers with one momentum can correspond to destructive interference for carriers with the opposite momentum. We show that for the interference between two-photon and three-photon absorption, the current has a narrower angular spread, i.e., a “beam” of electrons in a specified direction is produced in the semiconductor.

The time-dependent $CP$ asymmetry in $B^0\to J/\psi \rho (770{)}^0$ decays is measured using proton-proton collision data corresponding to an integrated luminosity of $6{\mathrm{fb}}^{-1}$, collected with the LHCb detector at a center-of-mass energy of 13 TeV during the years 2015–2018. The $CP$-violation parameters for this process are determined to be $2{\beta }_{c\overline{c}d}^{\mathrm{eff}}=0.710\pm 0.084\pm 0.051\mathrm{rad}$ and $|\lambda |=1.019\pm 0.034\pm 0.024$, where the first uncertainty is statistical and the second systematic. This constitutes the first observation of time-dependent $CP$ violation in $B^0\to J/\psi \rho (770{)}^0$ decays. Assuming approximate SU(3) flavor symmetry, these results are combined with the previous consistent LHCb measurement to set the most stringent constraint on the penguin contribution, $\mathrm{\Delta }{\varphi }_s$, to the $CP$-violating phase ${\varphi }_s$ in $B_s^0\to J/\psi \varphi (1020)$ decays, yielding $\mathrm{\Delta }{\varphi }_s=5.0\pm 4.6\mathrm{mrad}$.

An elementary particle such as a photon cannot be cut in two pieces. Still it must be possible to truncate a photon with an optical shutter. The result is neither another photon nor a mix of a photon and a vacuum. Instead it is a superposition and mix of photon numbers up to infinity. This state is rather complicated, but nevertheless locally equivalent to a single photon or vacuum to the left and right, respectively, of a narrow transition region.

We uncover a class of nonlinear odd viscoelastic effects in three spatial dimensions. We show that these dissipationless effects arise upon combining geometric distortions in two orthogonal directions, yielding momentum flow in the third direction. We demonstrate that the effect arises from nontrivial geometric tensors in quantum states, and can be scaled up with integer topological invariants. We further show that the effect fingerprints the multiband Hilbert-space geometry of the underlying quantum states, as encoded in the nonmetricity and three-state quantum geometric tensors. Our findings unravel the role of multistate geometry in viscoelastic phenomena, paving a path for experimental observation of uncharted nonlinear odd viscoelastic responses in quantum systems.

We report an unprecedented hidden density-wave instability in the trimer-based ruthenate ${\mathrm{Ba}}_4{\mathrm{Ru}}_3{\mathrm{O}}_{10}$, previously regarded as a purely antiferromagnetic insulator. This instability develops in two distinct stages: an electronically driven reconstruction at $T_{\mathrm{A}}=100\mathrm{K}$ manifested in structural, thermodynamic, and transport anomalies that remain remarkably insensitive to magnetic fields up to at least 14 T, followed only at much lower temperatures $T^{*}\sim 20\mathrm{K}$ by the emergence of strongly nonlinear transport. Below $T^{*}$, charge conduction exhibits distinct depinning thresholds, sharp negative differential resistance, and unusually slow collective dynamics in the Hertz range. Direct measurements show that Joule heating is negligible, and all nonlinear signatures vanish upon only 3% Ir substitution for Ru, demonstrating the intrinsic origin. These results identify ${\mathrm{Ba}}_4{\mathrm{Ru}}_3{\mathrm{O}}_{10}$ as a rare correlated system hosting a strongly pinned collective electronic mode intertwined with antiferromagnetism.

We introduce the pushy random walk, where a walker can push multiple obstacles, thereby penetrating large distances in environments with finite obstacle density. This process provides a minimal model for experimentally observed interactions of active particles with dense, deformable media. Using scaling arguments and numerical simulations, we show that in one dimension the walker carves out an obstacle-free cavity whose length grows subdiffusively with time. In two dimensions, increasing obstacle density drives a transition from free diffusion to localized behavior, where the walker is trapped within a cavity whose radius again grows subdiffusively with time. These results show how tracer-induced rearrangements qualitatively reshape transport in crowded media.

Chiral active materials are abundant in nature, including the cytoskeleton with attached motor proteins, rotary clusters of bacterial flagella, and self-spinning starfish embryos. These materials break both time reversal and mirror-image (parity) symmetries due to injection of torques at the microscale. It was recently discovered that chiral active materials show a new type of elastic response termed “odd” elasticity. Currently, odd elasticity is understood microscopically only in ordered structures, e.g., lattice designs of metamaterials. It remains to explore how odd elasticity emerges in natural or biological systems, which are usually disordered. To address this, we propose a minimal generic model for disordered “odd solids,” using micropolar (Cosserat) elasticity in the presence of local active torques. We find that odd elasticity naturally emerges as a nonlinear effect of internal particle rotations. Exploring the viscoelasticity of such a solid, when immersed in an odd fluid, we discover new dynamically unstable regions driven by the odd solid-fluid coupling and, in the underdamped regime, also by inertia. Remarkably, in the overdamped limit, this odd solid-fluid coupling allows for bulk wave propagation near these unstable regions.

A terrestrial population of room-temperature millicharged particles can arise if they make up a dark matter subcomponent or if they are light enough to be produced in cosmic ray air showers. In a companion paper, we showed that a simple electrified shell acts as an efficient accumulator for such particles, parametrically enhancing their local density by many orders of magnitude. Here we demonstrate that Cavendish tests of Coulomb’s Law, performed since the late 18th century, function as both quasistatic accumulators and detectors for this overdensity. Reinterpretations of these past Cavendish tests thus provide some of the strongest bounds on a terrestrial millicharge population. We also propose surrounding a Cavendish test with an additional charged shell, which significantly improves the sensitivity and can even enable detection of the irreducible density of millicharged particles generated from cosmic rays. Using decades-old technology, this can outperform future accelerator searches for sub-GeV masses.

Gravitational waves (GWs) in the $0.01\sim 1\mathrm{Hz}$ band encode unique signatures of the early Universe and merging compact objects, but they are beyond the reach of existing observatories. Theoretical models suggest that the Moon could act as a resonant detector, but the unknown influence of its rugged surface and heterogeneous interior poses a challenge to the accurate modeling of its response. Here, we address this long-standing uncertainty by constructing the first high-resolution, two-dimensional model of the lunar GW response, more realistic than previous ones. We achieve this by combining high-fidelity spectral-element simulations with the analytical power of normal-mode perturbation theory, thereby resolving topographical effects down to 2 km grid spacing while maintaining the capacity to discern global free-oscillation patterns. This dual-methodology approach not only recovers the expected predominant quadrupole ($l=2$) oscillation mode, but also exposes a systematic signal amplification in thick-crust regions. This enhancement is traced by our normal-mode analysis to a mode-coupling process, in which the original quadrupolar oscillation induced by the passing GW distributes energy into a series of higher-order modes, the hybridized eigenmodes of a laterally heterogeneous Moon. In certain narrow frequency ranges, we observe up to tenfold amplification spanning into the deci-hertz band, highlighting the power of numerical simulations in resolving these structurally fine-tuned features for designing future detectors. Our Letter establishes the Moon as a resonant GW detector albeit its complex topographical structures, and the resulting amplification maps provide a quantitative guide for the optimal landing site selection.

The recent success of gravitational-wave (GW) astronomy together with renewed plans for lunar geophysical instrumentation has revived interest in using the Moon as a resonant detector for midfrequency (mHz–Hz) GWs. In realistic observational scenarios, the GW strain amplitude is expected to be constrained independently by networks of GW detectors, which motivates an inverse, tomographic question: to what extent can measurements of the Moon’s seismic response to known GWs be used to infer its internal structure? In this Letter, we develop a first-principles, perturbative framework that maps spherically symmetric perturbations of the elastic and density structure to measurable changes in observables, especially GW-driven modal amplitudes of the Moon. The formalism combines (i) a normal-mode representation of the elastic response, (ii) first-order perturbation theory for eigenvalues and eigenfunctions, and (iii) a linearized observation model that links frequency and amplitude observables to model parameters (bulk and shear moduli, density, and interface locations) and their perturbations. We show that the estimation errors of the Moon’s elastic parameters can be reduced by about an order of magnitude with observations of calibrated GWs.

An analysis of the $B^0\to K^{*0}(\to K^{+}{\pi }^{-}){\mu }^{+}{\mu }^{-}$ decay is presented using proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of $8.4{\mathrm{fb}}^{-1}$. The full set of $CP$-averaged and $CP$-asymmetric angular observables is determined in bins of the invariant mass squared of the dimuon system, as well as the branching fraction relative to the $B^0\to J/\psi (\to {\mu }^{+}{\mu }^{-})K^{+}{\pi }^{-}$ decay. For the first time, the full set of observables pertaining to the $K^{+}{\pi }^{-}$ S-wave contribution to the final state are presented and consideration is given to effects arising from the mass of the muons. The extracted $CP$-asymmetry observables show no significant deviations from zero. The measurements of the $CP$-averaged observables and the branching fractions continue to exhibit the pattern of tensions with the standard model predictions that have been seen in previous analyses that use part of the dataset considered in this Letter.

Engineering proximity effects in twisted van der Waals heterostructures offers a powerful platform for designing electronic properties. While theoretical predictions of quantum interference in transition metal dichalcogenide-encapsulated graphene can selectively control the spin-orbit coupling component, experimental realizations have remained elusive. Here, we report pure valley-Zeeman spin-orbit coupling in monolayer graphene achieved by encapsulation between two parallel twisted ${\mathrm{WSe}}_2$ monolayers. We observed a symmetry-enforced reordering of Landau levels, which is driven by the competition between the fixed valley-Zeeman energy and the magnetic-field-dependent cyclotron energy. This reordering is characterized by a transition from symmetry-broken states in the quantum Hall effect to a restored fourfold degeneracy with integer or half-integer quantum Hall sequences. We also demonstrate the ability to completely quench the proximity spin-orbit coupling by tuning the encapsulated geometry.

The final state of a binary black hole merger is predicted with high precision by numerical relativity, but could there be a simple thermodynamic principle within general relativity that governs the selection of the remnant? Using post-Newtonian relations between the mass $M$ (including the binding energy) and angular momentum $J$ of quasicircular, nonspinning binaries, we uncover a puzzling result: When the binary’s instantaneous $M$ and $J$ are mapped to those of a hypothetical Kerr black hole, the corresponding entropy exhibits a maximum during the evolution. This maximum occurs at values of $M$ and $J$, strikingly close to those of the final remnant predicted by numerical relativity. Consistent behavior is observed when using the relation between $M$ and $J$ obtained from numerical relativity evolution. Although this procedure is somewhat ad hoc, the agreement between the masses and spins of the final state obtained from numerical relativity and the results of this maximum entropy procedure is remarkable, with agreement to within a few percent when using either post-Newtonian or numerical relativity results for $M$ and $J$. These findings allow us to propose an entropy maximization conjecture for binary black hole mergers, hinting that thermodynamic principles may govern the selection of the final black hole state.

With the release of the fourth LIGO-Virgo-KAGRA gravitational-wave catalog (GWTC-4), we are starting to gain a detailed view of the population of merging binary black holes. The formation channels of these black holes is not clearly understood, but different formation mechanisms may lead to subpopulations with different properties visible in gravitational-wave data. Adopting a phenomenological approach, we find GWTC-4.0 data supports the presence of at least three subpopulations, each associated with a different range of black hole mass and with sharp transition boundaries between them. Each subpopulation is characterized by different distributions for either the mass ratios, the black-hole spin magnitudes or both. Subpopulation $\mathcal{A}$ with primary mass $m_1\le {27.7}_{-3.4}^{+4.1}{M}_{\odot }$ (90% credibility), is characterized by a nearly flat mass ratio distribution $q=m_2/m_1$, and by small spin magnitudes ($\chi \le {0.5}_{-0.1}^{+0.1}$). Subpopulation $\mathcal{B}$, with ${27.7}_{-3.4}^{+4.1}{M}_{\odot }\le m_1\le {40.2}_{-3.2}^{+4.7}{M}_{\odot }$, has a much sharper preference for mass ratio $q\approx 1$. Subpopulation $\mathcal{C}$, with $m_1\ge {40.2}_{-3.2}^{+4.7}{M}_{\odot }$, has support for large spin magnitudes, and tentative support for mass ratios $q\approx 0.5$. We interpret these transitions as evidence for multiple subpopulations, each potentially associated with a different formation pathways. We suggest putative formation scenarios for each subpopulation, and explore chemically homogeneous evolution, population III stars and dynamical formation channels as an explanation for subpopulation $\mathcal{B}$. Our findings for subpopulation $\mathcal{C}$ are largely consistent with recent claims of hierarchical mergers but with some curious differences in properties.

Repeated black-hole mergers in dense stellar clusters are a plausible mechanism to populate the predicted gap in black hole masses due to the pair-instability supernova process. These hierarchical mergers carry distinct spin characteristics relative to first-generation black holes. We introduce an astrophysically motivated model in the joint space of effective inspiral and precessing spins, which captures the dominant spin dynamics expected for hierarchical mergers. We find decisive evidence for a transition at $m_1={46.2}_{-7.2}^{+12.6}{M}_{\odot }$, above which the population is nearly entirely hierarchical, a location consistent with the anticipated onset of the pair-instability gap. We also infer a global peak in the hierarchical merger rate at $m_1={15.7}_{-1.1}^{+3.2}{M}_{\odot }$. The existence of low- and high-mass subpopulations of higher-generation black holes suggests the contribution of both near-solar-metallicity and metal-poor star clusters to the hierarchical merger population. Our results reinforce the growing evidence for detailed, mass-dependent substructure in the spin distribution of the binary black hole population.

The strong interplay between geometry and electronic structure in clusters consisting of a countable number of atoms critically governs their properties, making precise knowledge of geometry essential. This challenge is particularly acute for transition-metal clusters, where many unpaired electrons lead to multiple low-lying spin and geometric isomers, implying cumbersome and contradicting theoretical predictions of the ground state. In this Letter, we conclusively assign geometries and spin states of iron clusters of 3 to 12 atoms, which significantly reduces uncertainties of spin magnetic moments inferred from x-ray magnetic circular dichroism experiments [Niemeyer et al. Phys. Rev. Lett. 108, 057201 (2012)]. Hereto we use infrared multiple photon dissociation spectroscopy with Ar as messenger atom to measure the vibrational spectra of cationic iron clusters in the $110–400{\mathrm{cm}}^{-1}$ range and compare those with density functional theory calculations. We show that in addition to direct structural information the spectra provide an accurate determination of spin multiplicities. This methodology is broadly applicable to transition-metal clusters of any charge state and provides a general route to benchmark theory.

Unidirectional guided resonances (UGRs)—topological polarization singularities in momentum space with intrinsic unidirectional radiation—have recently garnered widespread attention. However, previous studies have been largely limited to realizing only a few discrete UGRs. We demonstrate an unprecedented continuous ring of UGRs in a hexagonal bilayer cylinder array, whose formation is governed by isotropic interband coupling, ensuring robust and azimuthally continuous unidirectional emission. Furthermore, by leveraging an in-plane inversion symmetry-protected bound state in the continuum at the $\mathrm{\Gamma }$ point, the continuous ring of UGRs acquires its topological properties from the enclosed bound state in the continuum, manifesting as a phase vortex with a nontrivial topological charge. This unique combination of continuous unidirectionality and a global topological charge provides a robust platform for developing novel devices, such as unidirectional vortex lasers.

Self-consistent approaches in many-electron problems typically converge to an unphysical solution in strongly correlated regimes. By deriving the mathematical condition for the stability of the physical solution, we unveil the precise relation between two distinct issues previously considered equivalent: the misleading convergence in self-consistent schemes and the multivaluedness of the Luttinger-Ward functional. Although these problems are fundamentally linked through the divergences of the irreducible vertex function, we show that misleading convergence can occur even in the absence of such divergences. Eventually, a systematic procedure for stabilizing the physical solution is proposed.

Although coupled ion-electron transfer (CIET) has emerged as a powerful framework to rationalize the kinetics of Faradaic reactions, its mechanism has lacked a fully microscopic, first-principles description. Here we show that the coupling of electron transfer to ion transfer can be understood as an extension of Marcus theory in which the ensemble of diabatic nuclear configurations is conditioned on a classical collective variable describing the interfacial anisotropy. This formalism enables direct construction of the CIET free-energy surface from constrained ab initio trajectories, providing a first-principles route to electrochemical current-overpotential relations. We demonstrate this method for ${\mathrm{CO}}_2$ redox on a gold electrode and find that the resulting two-dimensional saddle-point barriers differ substantially from one-dimensional treatments that consider only electron- or ion-transfer coordinates individually.