${\mathrm{CeRh}}_2{\mathrm{As}}_2$ is rare among superconductors, in that the magnetic field tunes it between two distinct superconducting phases. Combined with a lack of local inversion symmetry and an upper critical field exceeding the Pauli paramagnetic limit, this excitingly suggests triplet multicomponent superconductivity. Preceding the superconducting onset, $f$-electron correlations cause long-range order, attributed both to local antiferromagnetism and itinerant (quadrupole) density waves. A magnetic field provides a significant perturbation of the $f$ electrons and may reveal the nature of the many-body correlations. Therefore, we report comprehensive magnetization and magnetotransport studies on microstructured devices in fields of up to 73 T. Applied along the $c$ axis, the field causes a low-temperature change of majority (hole) carrier density at ${\mu }_{0}H\approx 24\mathrm{T}$. By contrast, in-plane fields produce a cascade of phase transitions; the field-induced in-plane conductivity anisotropy and lack of accompanying magnetic features, plus the closed-dome nature of the overall phase boundary is consistent with a hierarchy of field-induced density-wave states.

Secure multiparty computation enables the joint evaluation of multivariate functions across distributed users while ensuring the privacy of their local inputs. This field has become urgent due to the demand for computationally intensive deep learning inference. These computations are typically offloaded to cloud servers, leading to vulnerabilities. To solve this problem, we introduce a linear algebra engine that leverages the quantum nature of light for information-theoretically secure multiparty inference using telecommunication components. We apply this linear algebra engine to deep learning and derive rigorous upper bounds on the information leakage of both the deep neural network weights and the client’s data, enabling double-blind operations. Applied to the modified National Institute of Standards and Technology classification task, we obtain test accuracies exceeding 95% while guaranteeing leakage of less than 0.1 bits per weight and data element. This leakage is an order of magnitude below the minimum bit precision required for accurate deep learning using state-of-the-art quantization techniques. Our work lays the foundation for practical quantum-secure computation and unlocks secure cloud deep learning as a field.

The recent observation of superconductivity in the vicinity of Fermi surface reconstructed insulating or metallic states has established twisted bilayers of ${\mathrm{WSe}}_2$ as an exciting platform to study the interplay of strong electron-electron interactions, broken symmetries, and topology. In this work, we use a first-principles, material-specific theoretical treatment that is unbiased with respect to electronic instabilities to study the emergence of electronic ordering in twisted ${\mathrm{WSe}}_2$ driven by gate-screened Coulomb interactions. We construct exponentially localized moiré Wannier orbitals that faithfully capture the band structure and topology of the system, project the gate-screened Coulomb interaction onto them, and use unbiased functional renormalization group techniques to resolve the momentum and orbital structure of the leading instabilities and the relevant energy scales. We find an interplay between intervalley-coherent antiferromagnetic (IVC-AFM) order and chiral, mixed-parity $d/p$-wave superconductivity for carrier concentrations near a displacement field and twist-angle-tunable van Hove singularity. Our microscopic approach establishes incommensurate IVC-AFM spin fluctuations as the dominant electronic mechanism driving the formation of superconductivity in $\theta =5.08°$ twisted ${\mathrm{WSe}}_2$ and explains key aspects of recent experiments including the asymmetric density dependence of the spin ordering with respect to the van Hove line, the single- and double-peak structure of the DOS in the ordered (hole-doped) IVC-AFM phase, the emergence of superconductivity as the density is varied across the van Hove line, and the evolution of the displacement field-density phase diagram with twist angles between $3.7°\dots 5°$. We show that the interplay of electronic correlations and nontrivial quantum geometry in ${\mathrm{tWSe}}_2$ manifests in orbital-selective order parameters associated to the IVC-AFM and SC states that are detectable by local spectroscopy measurements.

Two-dimensional hybrid metal-halide perovskites (2D-MHPs) have emerged as important solution-processed semiconductors with favorable optical and electronic properties for diverse applications in photovoltaics, optoelectronics, and spintronics. The quasi-2D layered structures, featuring large acoustic impedance mismatches between the organic and inorganic sublattices, are expected to result in distinct and anisotropic thermal transport properties along the cross-plane and in-plane directions. Here, we introduce transducer-free vibrational-pump-visible-probe (VPVP) approaches that enable accurate quantification of anisotropic thermal transport properties in various archetypical single-crystalline 2D-MHPs. Specifically, using VPVP spectroscopy and VPVP microscopy, we measure the anisotropic thermal diffusivities of 2D-MHPs with systematically varied Pb-I octahedral layer thicknesses, as well as organic spacer types and lengths, revealing how these structural parameters alter the cross-plane and in-plane thermal transport properties in distinct ways. While diffuse interface scattering plays an important role in dictating cross-plane thermal transport, in-plane thermal transport is primarily determined by phonon transport within interconnected inorganic layers. Density functional theory incorporating four-phonon scatterings provides further insight into the low thermal conductivity and modest thermal conduction anisotropy in 2D-MHPs. Our work demonstrates a new all-optical and noncontact method, which requires minimal sample preparation and allows direct visualization of cross-plane and in-plane thermal transport, potentially compatible with in situ sample environments. The demonstrated VPVP approaches can advance understanding of thermal transport in 2D-MHPs as well as wide-ranging hybrid and polymeric semiconductors beyond 2D-MHPs.

Stabilizing and shaping autonomous flows of active fluids is a fundamental challenge and a prerequisite for applications. We embed a light-responsive microtubule-based nematic in a proportional-integral control loop that adjusts the applied light intensity in response to real-time measurements of the spatially averaged flow speed. The self-regulating hardware-software-wetware system maintains a target flow speed against external or internal perturbations, including protein aging and aggregation, sample-to-sample variability, and temperature variation. Varying the controller’s gains reveals antagonistic roles between feedback and intrinsic processes, leading to nontrivial dynamics observed in fluctuation spectra. In particular, oscillations emerge from the interplay between the controller, motor binding kinetics, and active hydrodynamic relaxation. Accounting for the underlying binding timescale, our coarse-grained model and nematohydrodynamics simulations corroborate these observations. This work provides insight into the coupled dynamics of controlled active matter, laying the foundation for spatiotemporal patterning of active stress to generate and stabilize new dynamical configurations.

We show that Clifford algebras provide a natural language to describe the physics of liquid crystal defects in 3D. This framework shows that most of these defects have fermionic nature, as the director field profile on a 2D cross section can algebraically be represented by a spinor. Defects in uniaxial, biaxial nematics, and cholesterics are represented by elements belonging to different Clifford algebras, suggesting that there are fundamental distinctions between topological defects in each of these phases. Our theory allows nematic defects to be interpreted as Majorana-like spinors, as defects and antidefects are topologically equivalent, while some cholesteric defects, such as screw dislocations, are better viewed as Weyl-like spinors of well-defined chirality. Defects can be described by a “defect bivector,” an algebraic element that quantifies the rototranslation associated with them. In cholesterics, fermionic defects of different types can combine to yield composite quasiparticles with either fermionic or bosonic nature. Under cylindrical confinement, these quasiparticles provide the way to understand the structure of screw dislocations. In the bulk, they may condensate to form topological phases, such as blue phases or skyrmion lattices. Our results provide a surprising link between liquid crystals, particle physics, and topological quantum matter.

A major challenge of AI plus science lies in its inherent incompatibility: Today’s AI is primarily based on connectionism, while science depends on symbolism. To bridge the two worlds, we propose a framework to seamlessly synergize Kolmogorov-Arnold networks (KANs) and science. The framework highlights KANs’ usage for three aspects of scientific discovery: identifying relevant features, revealing modular structures, and discovering symbolic formulas. The synergy is bidirectional: science to KAN (incorporating scientific knowledge into KANs), and KAN to science (extracting scientific insights from KANs). We highlight major new functionalities in pykan: (1) MultKAN, KANs with multiplication nodes, (2) kanpiler, a KAN compiler that compiles symbolic formulas into KANs; (3) tree converter, convert KANs (or any neural networks) into tree graphs. Based on these tools, we demonstrate KANs’ capability to discover various types of physical laws, including conserved quantities, Lagrangians, symmetries, and constitutive laws.

This work rigorously establishes a universal lower bound $z\ge 2$ for the dynamical exponent in frustration-free quantum many-body systems whose ground states exhibit power-law decaying correlations. The derivation relies on the Gosset-Huang inequality, providing a unified framework applicable across various lattice structures and spatial dimensions, independent of specific boundary conditions. Remarkably, our result can be applied to prove bounds for dynamics of classical stochastic processes. Specifically, we utilize a well-established mapping from the time evolution of local Markov processes with detailed balance to that of frustration-free quantum Hamiltonians, known as Rokhsar-Kivelson Hamiltonians. This proves $z\ge 2$ for such Markov processes, which is an improvement over existing bounds. Beyond these applications, the quantum analysis of the $z\ge 2$ bound is further broadened to include systems exhibiting hidden correlations, which may not be evident from purely local operators.

Because of the large-period superlattices emerging in moiré two-dimensional (2D) materials, electronic states in such systems exhibit low energy flat bands that can be used to simulate strongly correlated physics in a highly tunable setup. While many investigations have thus far focused on moiré flat bands and emergent correlated electron physics in triangular, honeycomb, and quasi-one-dimensional lattices, tunable moiré realizations of square lattices subject to strong correlations remain elusive. Here we propose a feasible scheme to construct moiré square lattice systems by twisting two or more layers of 2D materials in a rectangular lattice by 90°. We demonstrate the concept with twisted $\mathrm{GeX}/\mathrm{SnX}$ ($\mathrm{X}=\mathrm{S}$, Se) moiré superlattices and calculate their electronic structures from first principles. We show that the lowest conduction flat band in these systems can be described by a square lattice Hubbard model with parameters which can be controlled by varying the choice of host materials, number of layers, and external electric fields. In particular, twisted double bilayer GeSe realizes a square lattice Hubbard model with strong frustration due to the next-nearest-neighbor hopping that could host unconventional superconductivity, in close analogy to the Hubbard model for copper-oxygen planes of cuprate high-temperature superconductors. The presented scheme uses 90° twisted 2D materials with rectangular unit cells as a promising platform for realizing the physical phenomena of square lattice Hubbard models, establishing a new route for studying its rich phase diagram of magnetism, charge order, and unconventional superconductivity in a highly tunable setting.

Premelting plays a key role across physics, chemistry, materials, and biology sciences but remains poorly understood at the atomic level due to surface characterization limitations. We report the discovery of an amorphous ice layer (AIL) preceding the quasiliquid layer during ice premelting, enabled by a machine learning framework integrating atomic force microscopy (AFM) with molecular dynamics simulations. This approach overcomes AFM’s depth and signal limitations, allowing for three-dimensional surface structure reconstruction from AFM images. It further enables structural exploration of premelting interfaces across a wide temperature range that are experimentally inaccessible. We identify the AIL present between 121 and 180 K displaying a disordered two-dimensional hydrogen-bond network with solidlike dynamics. Our findings refine the ice premelting phase diagram and offer new insights into the surface growth dynamic, dissolution, and interfacial chemical reactivity. Methodologically, this work establishes a novel framework for AFM-based 3D structural discovery, marking a significant leap in our ability to probe complex disordered interfaces with unprecedented precision and paving the way for future disciplinary research, including surface reconstruction, crystallization, ion solvation, and biomolecular recognition.

Two-dimensional electron systems (2DESs) have represented an ever-expanding frontier in condensed matter physics. Over the past two decades, this growth has primarily been propelled by the emergence of novel 2DESs, exemplified by graphene and other two-dimensional (2D) crystals, each exhibiting distinctive properties. In this study, we synthesize high-quality $\beta$-phase bismuth thin films on exfoliated hexagonal boron nitride (hBN) and establish that bismuth surface states form a high-mobility 2DES with strong spin-orbit coupling (SOC). The extreme two dimensionality of the 2DES is characterized by an out-of-plane to in-plane effective-mass-anisotropy lower bound exceeding ${10}^3$. We further demonstrate that the spin degeneracy of the hole pockets is completely lifted, providing unambiguous transport evidence that they originate from Rashba states induced by strong SOC in the bismuth thin film. Under magnetic fields up to 40 Tesla, electrostatic gating drives the carriers into the lowest Landau levels, revealing signatures of rotational symmetry breaking and electronic nematicity. These findings position the bismuth 2DES as a compelling platform for exploring topological quantum phenomena in systems with strong SOC and high carrier mobility.

Charged particle reconstruction, the identification and characterization of particles from collision data, is fundamental to nearly all research at particle colliders like the Large Hadron Collider (LHC). With the High-Luminosity upgrade (HL-LHC), particle multiplicities will increase substantially, overwhelming traditional track reconstruction algorithms and presenting computational bottlenecks. Here, we introduce a proof of concept for a powerful new method for charged particle reconstruction inspired by state-of-the-art machine learning (ML) approaches in computer vision. Our model leverages transformer neural networks to efficiently filter relevant signals and fully reconstruct particle trajectories, directly tackling the computational complexity that traditional methods face. Evaluated on the widely used TrackML dataset, our approach achieves state-of-the-art tracking efficiency (97%) and a low fake rate (0.7%), requiring just 97 ms to reconstruct on average 1300 particle trajectories from 55,000 detector hits for particles with transverse momentum above 750 MeV. These results represent a significant milestone in both performance and speed, demonstrating a shift toward unified, scalable ML solutions that offer substantial improvements for collider experiments.

Geometrically frustrated magnetic systems, such as those based on the Shastry-Sutherland lattice (SSL), offer a rich playground for exploring unconventional magnetic states. The delicate balance between competing interactions in these systems leads to the emergence of novel phases. We present the characterization of ${\mathrm{Er}}_2{\mathrm{Be}}_2{\mathrm{GeO}}_7$, an SSL compound with ${\mathrm{Er}}^{3+}$ ions forming orthogonal dimers separated by nonmagnetic layers whose structure is invariant under the $P\overline{4}{2}_{1}m$ space group. Neutron scattering reveals an antiferromagnetic dimer structure at zero field, typical of Ising spins on that lattice and consistent with the anisotropic magnetization observed. However, magnetization measurements exhibit fractional plateaus at $1/4$ and $1/2$ of saturation, in contrast to the expected $1/3$ plateau of the SSL Ising model. By comparing the energy of candidate states with ground-state lower bounds we show that this behavior requires spatially anisotropic interactions, leading to an anisotropic Shastry-Sutherland Ising model symmetric under the $Cmm2$ space group. This anisotropy is consistent with the small orthorhombic distortion observed with single-crystal neutron diffraction. The other properties, including thermodynamics, which have been investigated theoretically using tensor networks, point to small residual interactions, potentially due to further couplings and quantum fluctuations. This study highlights ${\mathrm{Er}}_2{\mathrm{Be}}_2{\mathrm{GeO}}_7$ as a promising platform for investigating exotic magnetic phenomena.

Efficient, low-noise, and high-bandwidth transduction between optical and microwave photons is key to long-range quantum communication between distant superconducting quantum processors. Recent demonstrations of microwave-optical transduction using the broadband direct electro-optic (Pockels) effect in optical thin films made of AlN or ${\mathrm{LiNbO}}_3$ have shown promise. To improve efficiency and added noise, materials with larger Pockels coefficients, such as the soft ferroelectrics ${\mathrm{BaTiO}}_3$ or ${\mathrm{SrTiO}}_3$, are needed. However, these materials require adapted designs and fabrication approaches due to their nonlinear and, in some cases, hysteretic electro-optic response. Here, we engineer an on-chip, triply resonant transducer comprising low-loss ${\mathrm{BaTiO}}_3$-on-${\mathrm{SiO}}_2$ waveguides monolithically integrated with a superconducting microwave resonator made of Nb. We demonstrate bidirectional microwave-optical transduction and reach total off-chip efficiencies of $1\times {10}^{-6}$ using pulsed pumping. The device design permits in situ poling of the ferroelectric material without introducing excess microwave loss, exploiting superconducting air bridges fabricated using only subtractive patterning steps. In addition, we investigate optically induced heating, revealing fast thermalization and quasiparticle resilience of the microwave resonator. Our transducer concept and fabrication process are applicable to other materials with a large bias-induced Pockels effect like ${\mathrm{SrTiO}}_3$ and pave the way for efficient, low-power quantum interconnects.

Twisted bilayer ${\mathrm{MoTe}}_2$ (${\mathrm{tMoTe}}_2$) is an emergent platform for exploring exotic quantum phases driven by the interplay between nontrivial band topology and strong electron correlations. Direct experimental access to its momentum-resolved electronic structure is essential for uncovering the microscopic origins of the correlated topological phases therein. Here, we report angle-resolved photoemission spectroscopy measurements of ${\mathrm{tMoTe}}_2$, revealing pronounced twist-angle-dependent band reconstruction shaped by orbital character, interlayer coupling, and moiré potential modulation. Density functional theory captures the qualitative evolution, yet underestimates key energy scales across twist angles, highlighting the importance of electronic correlations. Notably, the hole effective mass at the $K$ point exhibits a nonmonotonic dependence on twist angle, peaking near 2°, consistent with band flattening at the magic angle predicted by continuum models. Via electrostatic gating and surface dosing, we further visualize the evolution of electronic structure versus doping, enabling direct observation of the conduction band minimum and confirm ${\mathrm{tMoTe}}_2$ as a direct band gap semiconductor. These results establish a spectroscopic foundation for modeling and engineering emergent quantum phases in this moiré platform.

By combining ab initio downfolding with cluster dynamical mean-field theory, we study the degree of correlations in monolayer, bilayer, and bulk breathing-mode kagome van der Waals materials ${\mathrm{Nb}}_3(\mathrm{F},\mathrm{Cl},\mathrm{Br},\mathrm{I}{)}_8$. Our new material-specific many-body model library shows that in low-temperature bulk structures the Coulomb correlation strength steadily increases from I to Br, Cl, and F, allowing us to identify ${\mathrm{Nb}}_3{\mathrm{I}}_8$ as a weakly correlated insulator whose gap is only mildly affected by the local Coulomb interaction. ${\mathrm{Nb}}_3{\mathrm{Br}}_8$ and ${\mathrm{Nb}}_3{\mathrm{Cl}}_8$ are strongly correlated insulators, whose gaps are significantly influenced by Coulomb-induced vertex corrections. ${\mathrm{Nb}}_3{\mathrm{F}}_8$ is a prototypical bulk Mott insulator whose gap is initially opened by strong correlation effects. Angle-resolved photoemission spectroscopy measurements comparing ${\mathrm{Nb}}_3{\mathrm{Br}}_8$ and ${\mathrm{Nb}}_3{\mathrm{I}}_8$ allow us to experimentally confirm these findings by revealing spectroscopic footprints of the degree of correlation. Our calculations further uncover how the thickness and the stacking affect the degree of correlations and predict that the entire material family can be tuned into correlated charge transfer or Mott-insulating phases upon electron or hole doping. Our magnetic property analysis based on our model parameter library additionally confirms that interlayer magnetic interactions likely drive the lattice phase transition to the low-temperature structures. The accompanying bilayer hybridization through interlayer dimerization yields magnetic singlet-like ground states in the Cl, Br, and I compounds. We further prove that all low-temperature compounds are dynamically stable and that electron-phonon coupling to the low-energy subspace is suppressed. Our findings establish ${\mathrm{Nb}}_3{\mathrm{X}}_8$ as a robust, versatile, and tunable class for van der Waals-based Coulomb and Mott engineering with a rich phase diagram and allow us to speculate on the symmetry-breaking effects necessary for the recently observed Josephson diode effect in ${\mathrm{NbSe}}_2/{\mathrm{Nb}}_3{\mathrm{Br}}_8/{\mathrm{NbSe}}_2$ heterostructures.

Understanding how the vibrational and thermal properties of solids are influenced by atomistic structural disorder is of fundamental scientific interest and paramount to designing materials for next-generation energy technologies. While several studies indicate that structural disorder strongly influences the thermal conductivity, the fundamental physics governing the disorder-conductivity relation remains elusive. Here we show that order-of-magnitude, disorder-induced variations of conductivity in network solids can be predicted from a “bond-network” entropy, an atomistic structural descriptor that quantifies heterogeneity in the topology of the atomic-bond network. We employ the Wigner formulation of thermal transport to demonstrate the existence of a relation between the bond-network entropy and observables such as smoothness of the vibrational density of states and macroscopic conductivity. We also show that the smoothing of the vibrational density of states encodes information about the thermal resistance induced by disorder and can be directly related to phenomenological models for phonon-disorder scattering based on the semiclassical Peierls-Boltzmann equation. Our findings rationalize the conductivity variations of disordered carbon polymorphs ranging from nanoporous electrodes to defective graphite used as a moderator in nuclear reactors.

Quantum processors based on neutral atoms trapped in arrays of optical tweezers have appealing properties, including relatively easy qubit number scaling and the ability to engineer arbitrary gate connectivity with atom movement. However, these platforms are inherently prone to atom loss, and the ability to replace lost atoms during a quantum computation is an important but previously elusive capability. Here, we demonstrate the ability to measure and reinitialize, and if necessary replace, a subset of atoms while maintaining coherence in other atoms. This allows us to perform logical circuits that include single- and two-qubit gates as well as repeated midcircuit measurement while compensating for atom loss. We highlight this capability by performing up to 41 rounds of syndrome extraction in a repetition code, and combine midcircuit measurement and atom replacement with real-time conditional branching to demonstrate heralded state preparation of a logically encoded Bell state. Finally, we demonstrate the ability to replenish atoms in a tweezer array from an atomic beam while maintaining coherence of existing atoms—a key step toward execution of logical computations that last longer than the lifetime of an atom in the system.

A central mystery in high-temperature cuprate superconductors is the coexistence of multiple exotic orders, which is presumably associated with strong electronic correlation. The ongoing interest in this enigmatic phenomenon is further energized when similar electronic orders and states emerge and coexist in less correlated kagome superconductors. Here, by utilizing angle-resolved photoemission spectroscopy (ARPES), nuclear magnetic resonance (NMR) spectroscopy, scanning tunneling microscopy (STM) and first-principles calculations, we reveal the sudden emergence of a distinct short-range charge stripe order in Sn-doped ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ kagome superconductors when the long-range $2\times 2$ charge density wave order in pristine ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ is suppressed. This short-range stripe order features a modulation vector of approximately $1/3$ along one of the three lattice directions, induces remarkable quasiparticle scattering between the original quasi-1D kagome $d$ bands and their replica of folding, and clearly suppresses the electron density of states at the Fermi level. Our first-principles calculations reveal that $3\times 1$ supermodulation represents a hidden secondary instability in pristine ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$. This instability is further enhanced by in-plane chemical pressure induced by Sn substitution, and coupled to the electronic correlation, leading to a unique charge stripe order in the system. As such, our results reveal a new route toward emergent electronic orders via cooperative interactions between the lattice and electronic degrees of freedom.

From the vasculature of animals to the porous media making up batteries, the core task of flow networks is to transport solutes and perfuse all cells or media equally with resources. Yet, living flow networks have a key advantage over porous media: They are adaptive, and they self-organize their geometry for homogeneous perfusion throughout the network. Here, we show that artificial flow networks can also self-organize toward homogeneous perfusion by the versatile adaption of controlled erosion. Flowing a pulse of cleaving enzyme through a network patterned into an erodible hydrogel, with initial channels disparate in width, we observe a homogenization in channel resistances. Experimental observations are matched with numerical simulations of the diffusion-advection-sorption dynamics of an eroding enzyme within a network. Analyzing transport dynamics theoretically, we show that homogenization only occurs if the pulse of the eroding enzyme lasts longer than the time it takes any channel to equilibrate to the pulse concentration. The equilibration time scale derived analytically is in agreement with simulations. Lastly, we show both numerically and experimentally that erosion leads to the homogenization of complex networks containing loops. Erosion being an omnipresent reaction, our results pave the way for a very versatile self-organized increase in the performance of porous media.