We analyze the 1D Anderson model with stealthy disorder, defined by a power spectrum that vanishes over a continuous band of wave numbers. Perturbative expansion of the self-energy and numerical results show that for small disorder $W$ and prescribed stealthiness $\chi$, the system is effectively delocalized, i.e., the localization length $\xi$ exceeds large system sizes. This unusual behavior follows from the systematic cancellation of leading terms so that $\xi$ scales as $W^{-2n}$ with large $n$. Since the underlying mechanism depends only on the stealthy disorder, our findings also apply to photonic and phononic waves.

We develop a theoretical framework for probing superconductivity with momentum resolution using the quantum twisting microscope (QTM), a planar tunneling device where a graphene tip is rotated relative to a two-dimensional sample. Because of in-plane momentum conservation, the QTM directly measures the superconducting spectral function along well-defined trajectories in momentum space. The relative intensities of electron and hole excitations encode the Bogoliubov coherence factors, revealing the momentum dependence of the pairing magnitude. Three $C_{3z}$-related tunneling channels enable direct detection of rotational symmetry breaking, as well as nodal points in the superconducting order parameter. We apply our framework to superconductivity within the Bistritzer-MacDonald model of noninteracting electrons and the topological heavy-fermion model, which accounts for electron-electron interactions. Together, these capabilities establish the QTM as a direct probe of the pairing symmetry and microscopic origin of superconductivity in two-dimensional materials.

Moiré flat bands in rhombohedral multilayer graphene provide a platform for exploring interaction-driven topological phases, where a single isolated band often forms a Chern band. However, non-Abelian degenerate Chern bands with internal symmetries such as $\mathrm{SU}(N)$ have so far been realized only in highly engineered systems. Here, we show that a doubly degenerate non-Abelian Chern band with Chern number $|C|=1$ emerges spontaneously at filling $\nu =2$ in rhombohedral three-, four-, and five-layer graphene, regardless of the presence of a hexagonal boron nitride substrate. Using self-consistent Hartree-Fock calculations, we map out phase diagrams as functions of displacement field and electronic periodicity and analytically demonstrate that the Fock term drives spontaneous symmetry breaking and generates non-Abelian Berry curvature. We further show that this non-Abelian topology is characterized by SU(2) gauge flux threading the noncontractible cycles of the Brillouin zone, leading to a global non-Abelian holonomy. Our findings unveil a new class of interaction-driven non-Abelian topological phases, distinct from quantum anomalous Hall and fractional Chern phases.

The operator wave function provides a fine-grained description of quantum chaos and of the irreversible growth of simple operators into increasingly complex ones. Remarkably, at finite temperature, this wave function can acquire a phase that increases linearly with the operator’s size, a phenomenon called size winding. Although size winding occurs naturally in a holographic setting, the emergence of a coherent phase in a scrambled operator remains mysterious from the standpoint of a thermalizing quantum many-body system. In this work, we elucidate this phenomenon by introducing the related concept of Krylov winding, whereby the operator wave function acquires a phase that winds linearly with the Krylov index. We show that Krylov winding is a generic feature of quantum chaotic systems and is a direct consequence of the universal operator growth bound hypothesis. It gives rise to size winding under two additional conditions: (i) a low-rank mapping between the Krylov and size bases, which ensures phase alignment among operators of the same size, and (ii) the saturation of the “chaos-operator growth” bound ${\lambda }_L\le 2\alpha$ (with ${\lambda }_L$ the Lyapunov exponent and $\alpha$ the growth rate), which ensures a linear phase dependence on size. For systems that do not saturate this bound, with $h={\lambda }_L/2\alpha <1$, the winding with Pauli size $\ell$ becomes superlinear, behaving as ${\ell }^{1/h}$. We illustrate these results with two classes of microscopic models: the Sachdev-Ye-Kitaev (SYK) model and its variants, and a disordered $k$-local spin model.

Breaking the intrinsic chiral symmetry of massless Dirac fermions in graphene at the two inequivalent valleys gives rise to rich intriguing phenomena. A prototypical example of this is the Kekulé order. Here, we use STM to directly visualize the bond texture associated with Kekulé spiral order in graphene. The Kekulé order originates from the intervalley scattering at 1D grain boundaries, and its strength can be significantly suppressed when a periodic potential is applied. By mapping atomic-scale electronic wave functions, we uncover that the bond texture localized near the 1D boundaries exhibits a complex spatial dependence indicative of phase winding, and it evolves dramatically with electronic energy. Our local-probe measurements thus establish the emergence of Kekulé spiral order in graphene, highlighting topological defects as versatile building blocks for engineering valley-ordered phases.

Computing topological invariants in two-dimensional quasicrystals and supermoiré matter is a remarkable open challenge due to the absence of translational symmetry and the colossal number of sites inherent to these systems. Here, we establish a method to compute local topological invariants of exceptionally large systems using tensor networks, enabling the computation of invariants for Hamiltonians with hundreds of millions of sites, several orders of magnitude above the capabilities of conventional methodologies. Our approach leverages a tensor network representation of the density matrix using a Chebyshev tensor network algorithm, enabling large-scale calculations of topological markers in quasicrystalline and moiré systems. We demonstrate our methodology with two-dimensional quasicrystals featuring $C_8$ and $C_{10}$ rotational symmetries and mosaics of Chern phases. Our Letter establishes a powerful method to compute topological phases in exceptionally large-scale topological systems, providing the required tool to rationalize generic super-moiré and quasicrystalline topological matter.

Detection of the Higgs mode in superconductors using nonlinear terahertz spectroscopy is a key area of interest in condensed matter physics. We investigate the influence of disorder on the nonlinear terahertz response and the Higgs mode in NbN thin films with varying Ioffe-Regel parameters ($k_{F}l$). In strongly disordered films near the superconductor-insulator transition, we observe an anomalous third-harmonic generation (THG) signal above $T_c$, which is absent in both cleaner superconducting and nonsuperconducting counterparts. The persistence of this normal-state THG signal in a high magnetic field excludes superconducting fluctuations as its origin. Below $T_c$, the THG intensity increases sharply, indicating a dominant contribution from the driven Higgs mode. The THG spectrum of the strongly disordered sample exhibits a broadened, multipeak structure, which we attribute to quantum path interference between distinct channels involving unpaired electrons and Cooper pairs within emergent superconducting islands. Our findings not only demonstrate how disorder tunes the nonlinear terahertz response, but also uncover a strong coupling between electrons responsible for normal-state THG and the superconducting Higgs mode below $T_c$ in strongly disordered samples.

A nonspinning permanent ferromagnet is predicted to behave as a gyroscope at sufficiently low frequencies, which can be seen as a manifestation of gyromagnetism. This yet unexplored regime, conjectured for the first time by Maxwell [A Treatise on Electricity and Magnetism (Clarendon Press, Oxford, 1873).], has recently been proposed for ultrasensitive magnetometry and for atomiclike quantum stabilization of a levitated nanomagnet in a static field. Here, we observe signatures of gyroscopic effects in the rotational dynamics of a nonspinning permanent ferromagnet levitated in a superconducting trap. Specifically, we detect spin-rotation coupling between different librational modes, leading to elliptical trajectories, in good agreement with theoretical predictions. From our measurements, we can infer both the intrinsic angular momentum of the levitated magnet and its gyromagnetic $g$ factor.

We present high-precision spectroscopy of the ground state hyperfine structure of ${\mathrm{HD}}^{+}$ at 4 T. We determine the bound-electron $g$ factor, $g_{e,\text{bound}}=-2.00227854096(40)$, to a relative uncertainty of $2\times {10}^{-10}$, the most precise determination of a bound-electron $g$ factor of a molecular ion to date. The experimental value agrees with recently developed ab initio theory that now includes quantum-electrodynamical effects up to order ${\alpha }^5$ and has reduced the theoretical uncertainty by three orders of magnitude [O. Kullie et al., Precision calculation of the bound-electron $g$ factor in molecular hydrogen ions, Phys. Rev. A 112, 052813 (2025)]. In addition, we extract the scalar spin-spin interaction coefficients $E_4=925395.758(41)\mathrm{kHz}$ (electron-proton) and $E_5=142287.821(22)\mathrm{kHz}$ (electron-deuteron), which show a moderate tension with another state-of-the-art theoretical prediction [M. Haidar et al., Higher-order corrections to the spin-orbit and spin-spin tensor interactions in ${\mathrm{HD}}^{+}$, Phys. Rev. A 106, 042815 (2022)].

In frustrated magnetic systems with a subextensive number of classical ground states, quantum zero-point fluctuations can select a unique long-range ordered state, a celebrated phenomenon referred to as order by quantum disorder (ObQD). For frustrated spin-$\frac{1}{2}$ models, unbiased numerical methods able to expose ObQD are necessary. We show that ObQD can be identified from exact diagonalization calculations through an analysis akin to the Anderson tower of states associated with spontaneous symmetry breaking. By defining an effective quantum rotor model, we describe the competition between ObQD-induced localization of the rotor and its tunneling between symmetry-related ground states, identifying the crossover length scale from the finite-size regime where the rotor is delocalized to the infinite system-size limit where it becomes localized. This rotor model relates the characteristic splittings in the exact diagonalization energy spectrum to the ObQD selection energy scale, providing an estimate that can be compared to spin wave calculations. We demonstrate the general applicability of this approach in one-, two-, and three-dimensional frustrated spin models that exhibit ObQD.

Achieving optical nonlinearities at ultralow light intensities in solid-state platforms is essential for advancing nonlinear and quantum photonic technologies. A promising approach involves coupling excitons to photons in optical cavities to create exciton polaritons, where effective photon-photon interactions are mediated by the intrinsic excitonic nonlinearity. However, realizing strong polariton nonlinearities within a scalable architecture remains a significant experimental challenge. Here, we demonstrate highly nonlinear two-dimensional exciton polaritons by coupling a charge-tunable ${\mathrm{MoSe}}_2$ monolayer to a planar photonic crystal nanocavity. The pronounced excitonic resonance of the monolayer, combined with its seamless integration with the planar nanocavity, facilitates robust exciton-photon hybridization. Remarkably, the strong mode confinement of the nanocavity substantially enhances polariton-polariton interactions, enabling all-optical switching of the cavity spectrum with excitation energies as low as $\sim 4\mathrm{fJ}$—several orders of magnitude below previously reported thresholds in 2D exciton-polariton systems. Pump-probe spectroscopy reveals that this switching operates on an ultrafast timescale of a few picoseconds. Our Letter establishes a robust platform for nonlinear 2D polaritonics with broad applications in integrated photonic technologies, including all-optical neuromorphic computing and quantum photonic information processing.

The missing mass of the ${}^{12}\mathrm{C}(p,d)$ reaction has been measured near the ${\eta }^{\prime }$-meson emission threshold in coincidence with a high-momentum proton to selectively collect ${\eta }^{\prime }\text{−}{}^{11}\mathrm{C}$ mesic nucleus formation events at GSI, Germany. A 2.5 GeV proton excites a carbon nucleus in order to form an ${\eta }^{\prime }$-mesic nucleus emitting a deuteron forward with an energy of $\sim 1.5\mathrm{GeV}$. The deuteron is momentum analyzed by the fragment separator used as a high-resolution spectrometer to deduce the excitation energy of the residual system. The large-acceptance detector WASA surrounding the target identifies high-momentum protons emitted in the decay of the ${\eta }^{\prime }$-mesic nucleus. The measured semiexclusive spectrum exhibits structures below the threshold though the statistical significance is limited. The spectrum is fitted by theoretically calculated spectra varying optical-potential parameters of the ${\eta }^{\prime }$-nucleus interaction. The analysis results indicate possible formation of ${\eta }^{\prime }$-mesic nuclei for the real potential depth of $\sim -61\mathrm{MeV}$ with a local statistical significance of $3.5\sigma$ and, taking into account the look-elsewhere effect, a global significance of $2.1\sigma$.

Ion acceleration in $Z$-pinch plasmas is traditionally linked to the axial direction of current. Here, we report the radial emission of MeV protons from a low-mass, hydrogen-containing $X$ pinch. Proton energies up to 3 MeV are observed in a hybrid $X$ pinch with a $30\mathrm{\mu }\mathrm{m}$ polyethylene fiber at a 400 kA peak current. The low-mass load, correlation of protons with hard x-rays, and timing of hard x-ray emission point to proton acceleration driven by current disruption following fiber disintegration. A new insight into the acceleration mechanism arises from the use of an interelectrode gap that is too short for magnetic fields to bend axially accelerated protons by $\pi /2$ radians; thus, the observed radial emission implies a substantial radial acceleration component. The radial emission also enables $X$-pinch-driven proton radiography, the exceptional potential of which is demonstrated with exploding wires.

Combining high-speed photography with direct force measurements, we investigate the impact dynamics of drops of cornstarch-water mixtures—a premier example of shear-thickening fluids—across a wide range of impact conditions. Our Letter identifies three distinct impact regimes. In addition to the liquidlike and solidlike behaviors generally expected for the impact-induced response of shear-thickening fluids, we uncover a counterintuitive regime in which high-concentration cornstarch-water mixtures display a liquidlike response at the onset of impact when shear rates are high and only transition to a solidlike behavior at later times as shear rates reduce. By integrating the classic drop-impact theory with the Reynolds-Darcy mechanism for dilatancy, we develop a unified model that quantitatively describes the impact dynamics of shear-thickening drops across all regimes. Our Letter reveals the unexpected response of shear-thickening fluids to ultrafast deformation and advances the fundamental understanding of drop impact for complex fluids.

We demonstrate high-resolution in situ imaging of density-wave ordering induced by cavity-mediated interactions in a unitary Fermi gas. We observe long-range spatial correlations throughout the formation of density waves, both for adiabatic preparation and following a quench, with a pattern controlled by the cavity mode structure. Our single-shot microscopic images together with the real-time readout of the cavity photons provide access to atom-photon correlations. We use this capability to investigate order fluctuations as a function of time following a quench and to directly confirm the correspondence between optical and atomic observables. Our system opens rich perspectives, from local patterning to correlation measurements in long-range interacting quantum gases.

Quantum interference phenomena in superconductors, such as Josephson interference and Little-Parks oscillations, serve as powerful probes of phase coherence, symmetry breaking, and vortex dynamics. However, they are typically observed in well-defined mesoscopic structures, and their behavior in the two-dimensional limit remains largely unexplored. Here, we report periodic magnetoresistance oscillations, superconducting interference patterns, and interfering diode effect in unpatterned few-layer ${\mathrm{NbSe}}_2$. These phenomena emerge exclusively within the superconducting fluctuation regime of thin samples, consistent with the enhanced anomalous metallic behavior of atomically thin ${\mathrm{NbSe}}_2$. The nonmonotonic temperature dependence of both the oscillation amplitude and the diode efficiency can be captured by a model in which thermally activated vortices traverse intrinsic supercurrent loops. Our results reveal that the observed interference phenomena originate from the lost of global phase coherence, providing a new route to accessing interference effects in unpatterned superconductors.

While equilibrium interfaces display universal large-scale statistics, interfaces in phase-separated active and driven systems are predicted to belong to distinct nonequilibrium universality classes. Yet, such behavior has proven difficult to observe, with most systems exhibiting equilibriumlike fluctuations despite their strongly nonequilibrium microscopic dynamics. We introduce a hard-disk model driven by active collisions, conceived as an effective two-dimensional description of a vibrofluidized granular system that, contrary to self-propelled models, displays clear nonequilibrium interfacial scaling. We observe for the first time, the $|\mathit{q}|\mathrm{KPZ}$ and wet-$|\mathit{q}|\mathrm{KPZ}$ universality classes while revealing a new, previously overlooked universality class arising in systems with slow solidlike or glassy dynamics. Conservation laws and slow dynamics select these distinct classes.

By leveraging nonlocal airborne acoustic metamaterials, we propose acoustic “ghost tunnels” that enable perfect tunneling while simultaneously functioning as an “empty” space for external waves incident upon their lateral boundaries. This remarkable property originates from two groups of eigenstates shifted along different directions in the momentum space: one exhibiting doubly degeneracy with directional linear dispersions, which is strictly protected by glide symmetries, and the other showing broad-angle impedance matching, characterized by arc-shaped equal-frequency contour. Upon selective excitation of such eigenstates through different boundaries, acoustic waves perceive the same metastructure, either as a perfect tunnel with strict bounds or as a reflectionless empty space. This exotic acoustic tunnel, verified through both simulations and experiments, establishes a versatile paradigm for novel acoustic manipulation.

Magnetoresistance studies of 2D systems are often shaped by the motion of electrons that occupy spatially confined wave functions, such as topological edge modes and disorder-induced bound states. Directly probing how such states form and behave in situ, under applied currents, provides a clear way of connecting microscopic physics to the macroscopic transport response. In this Letter, scanning tunneling potentiometry is used to probe the local, current-induced electrochemical potential of carriers in graphene near circular $p\text{−}n$ junctions in an out-of-plane magnetic field ranging from 0 to 1.4 T. These measurements provide detailed information about the motion of carriers at the nanometer scale, revealing how it evolves with increasing field. The electrochemical potential displays distinct patterns, such as dipoles, spirals, and concentric disks in weak, moderate, and high fields, respectively. The size and orientation of these patterns can be used to understand how local carrier dynamics change in different transport regimes as well as to directly extract physical parameters such as the electron mean free path and cyclotron diameter.

Bistability—two distinct stable states under identical parameters—is not only a fundamental physical concept but also of importance in practical applications. While plasmon-polaritonic bistability representing history-dependent stable states within plasmonic systems has been theoretically predicted, it has yet to be demonstrated experimentally due to challenges in realizing suitable nonlinearity at feasible electric-field strengths. Here, we report the experimental observation of electrically driven plasmon-polaritonic bistability in graphene/hexagonal-boron-nitride/graphene tunneling transistors, achieved through momentum-conserving resonant tunneling of Dirac electrons. Using a small twist angle between graphene layers, we engineered devices exhibiting both electronic and plasmon-polaritonic bistability. This bistable plasmonic behavior can be precisely tuned through load resistance and electrostatic gating. Our findings open new pathways for exploring nonlinear optical and electronic phenomena in van der Waals heterostructures and mark a significant advance in nanoplasmonics, with potential applications in optical memory, sensing, and optoelectronic switching.