Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve (nodes’ dynamics). Despite substantial progress, little is known about why some subtle changes in the network structure, at the so-called critical points, can provoke drastic shifts in its dynamics. We tackle this challenging problem by introducing a method that reduces any network to a simplified low-dimensional version. It can then be used to describe the collective dynamics of the original system. This dimension reduction method relies on spectral graph theory and, more specifically, on the dominant eigenvalues and eigenvectors of the network adjacency matrix. Contrary to previous approaches, our method is able to predict the multiple activation of modular networks as well as the critical points of random networks with arbitrary degree distributions. Our results are of both fundamental and practical interest, as they offer a novel framework to relate the structure of networks to their dynamics and to study the resilience of complex systems.

Photonic cavities are gathering a large amount of interest to enhance the energy transfer between two dipoles, with far-reaching consequences for applications in photovoltaics, lighting sources, and molecular biosensing. However, experimental difficulties in controlling the dipoles’ positions, orientations, and spectra have limited the earlier work in the visible part of the spectrum, and have led to inconsistent results. Here, we directly map the energy transfer of microwaves between two dipoles inside a resonant half-wavelength cavity with ultrahigh control in space and frequency. Our approach extends Förster resonance energy-transfer (FRET) theory to microwave frequencies and bridges the gap between the descriptions of FRET using quantum electrodynamics and microwave engineering. Beyond the conceptual interest, we show how this approach can be used to optimize the design of photonic cavities to enhance dipole-dipole interactions and FRET.

Bianisotropy is common in electromagnetism whenever a cross-coupling between electric and magnetic responses exists. However, the analogous concept for elastic waves in solids, termed as Willis coupling, is more challenging to observe. It requires coupling between stress and velocity or momentum and strain fields, which is difficult to induce in non-negligible levels, even when using metamaterial structures. Here, we report the experimental realization of a Willis metamaterial for flexural waves. Based on a cantilever bending resonance, we demonstrate asymmetric reflection amplitudes and phases due to Willis coupling. We also show that, by introducing loss in the metamaterial, the asymmetric amplitudes can be controlled and can be used to approach an exceptional point of the non-Hermitian system, at which unidirectional zero reflection occurs. The present work extends conventional propagation theory in plates and beams to include Willis coupling and provides new avenues to tailor flexural waves using artificial structures.

Weyl and Dirac (semi)metals in three dimensions have robust gapless electronic band structures. Their massless single-body energy spectra are protected by symmetries such as lattice translation, (screw) rotation, and time reversal. In this paper, we discuss many-body interactions in these systems. We focus on strong interactions that preserve symmetries and are outside the single-body mean-field regime. By mapping a Dirac (semi)metal to a model based on a three-dimensional array of coupled Dirac wires, we show (1) the Dirac (semi)metal can acquire a many-body excitation energy gap without breaking the relevant symmetries, and (2) interaction can enable an anomalous Weyl (semi)metallic phase that is otherwise forbidden by symmetries in the single-body setting and can only be present holographically on the boundary of a four-dimensional weak topological insulator. Both of these topological states support fractional gapped (gapless) bulk (respectively, boundary) quasiparticle excitations.

The temperature–magnetic field phase diagram of the mixed honeycomb-triangular lattice system ${\mathrm{K}}_2{\mathrm{Mn}}_3({\mathrm{VO}}_4{)}_2{\mathrm{CO}}_3$ is investigated by means of magnetization, heat-capacity, and neutron-scattering measurements. The results indicate that triangular and honeycomb magnetic layers undergo sequential magnetic orderings and act as nearly independent magnetic sublattices. The honeycomb sublattice orders at about 85 K in a Neél-type antiferromagnetic structure, while the triangular sublattice displays two consecutive ordered states at much lower temperatures, 3 and 2.2 K. The ground state of the triangular sublattice consists of a planar “$Y$” magnetic structure that emerges from an intermediate collinear “up-up-down” state. Applied magnetic fields parallel or perpendicular to the $c$ axis induce exotic ordered phases characterized by various spin-stacking sequences of triangular layers that yield bilayer, three-layer, or four-layer magnetic superstructures. The observed superstructures cannot be explained in the framework of quasiclassical theory based only on nearest-neighbor interlayer coupling and point towards the presence of effective second-nearest-neighbor interactions mediated by fluctuations of the magnetic moments in the honeycomb sublattice.

The bulk-edge correspondence links the Chern topological numbers with the net number of unidirectional states supported at an interface of the relevant materials. This fundamental principle is perhaps the most consequential result of topological photonics, as it determines the precise physical manifestations of nontrivial topological features. Even though the bulk-edge correspondence has been extensively discussed and used in the literature, it seems that in the general photonic case with dispersive materials it has no solid mathematical foundation and is essentially a conjecture. Here, I present a rigorous physically-motivated demonstration of this fundamental principle by showing that the thermal fluctuation-induced light-angular momentum spectral density in a closed cavity can be expressed in terms of the photonic gap Chern number, as well as in terms of the net number of unidirectional edge states. In particular, I highlight the rather fundamental connections between topological numbers in Chern-type photonic insulators and the fluctuation-induced light momentum.

Metasurfaces have enabled unprecedented control over electromagnetic waves, providing new opportunities in areas such as wireless communications, energy harvesting, imaging, and cloaking. Despite significant progress in this area, most metasurface designs provide static functionalities. Here, we theoretically propose and experimentally validate a transparent metasurface with dynamically tunable properties. Notably, we present an electronically tunable metasurface that is capable of rotating the polarization of an arbitrarily polarized incident wave, without changing its axial ratio. The designed polarization rotator consists of a tunable birefringent structure sandwiched between two $\pm 45°$ rotated metasurface-based quarter-wave plates. The birefringent structure is a bandpass metasurface which relies on integrated varactor diodes for tunability. Through a simple biasing mechanism, different voltages are applied to the diodes to rotate the polarization of a transmitted wave. The proposed idea may find application in various areas where dynamic polarization control is required.

${\mathrm{V}}_2{\mathrm{O}}_3$ famously features all four combinations of paramagnetic versus antiferromagnetic and metallic versus insulating states of matter in response to percent-level doping, pressure in the GPa range, and temperature below 300 K. Using time-of-flight neutron spectroscopy combined with density functional theory calculations of magnetic interactions, we have mapped and analyzed the inelastic magnetic neutron scattering cross section over a wide range of energy and momentum transfer in the chromium-stabilized antiferromagnetic and paramagnetic insulating phases. Our results reveal an important magnetic frustration and degeneracy of the paramagnetic insulating phase which is relieved by the rhombohedral-to-monoclinic transition at $T_N=185\mathrm{K}$. This leads to the recognition that magnetic frustration is an inherent property of the paramagnetic phase in $({\mathrm{V}}_{1-x}{\mathrm{Cr}}_x{)}_2{\mathrm{O}}_3$ and plays a key role in suppressing the magnetic long-range-ordering temperature and exposing a large phase space for the paramagnetic Mott metal-insulator transition to occur.

We analyze state preparation within a restricted space of local control parameters between adiabatically connected states of control Hamiltonians. We formulate a conjecture that the time integral of energy fluctuations over the protocol duration is bounded from below by the geodesic length set by the quantum geometric tensor. The conjecture implies a geometric lower bound for the quantum speed limit (QSL). We prove the conjecture for arbitrary, sufficiently slow protocols using adiabatic perturbation theory and show that the bound is saturated by geodesic protocols, which keep the energy variance constant along the trajectory. Our conjecture implies that any optimal unit-fidelity protocol, even those that drive the system far from equilibrium, are fundamentally constrained by the quantum geometry of adiabatic evolution. When the control space includes all possible couplings, spanning the full Hilbert space, we recover the well-known Mandelstam-Tamm bound. However, using only accessible local controls to anneal in complex models such as glasses or to target individual excited states in quantum chaotic systems, the geometric bound for the quantum speed limit can be exponentially large in the system size due to a diverging geodesic length. We validate our conjecture both analytically by constructing counter-diabatic and fast-forward protocols for a three-level system, and numerically in nonintegrable spin chains and a nonlocal SYK model.

In topological insulators doped with magnetic ions, spin-orbit coupling and ferromagnetism give rise to the quantum anomalous Hall effect. Here, we show that in $s$-wave superconductors with strong spin-orbit coupling, magnetic impurity ions can generate topological vortices in the absence of external magnetic fields. Such vortices, dubbed quantum anomalous vortices, support robust Majorana zero-energy modes when superconductivity is induced in the topological surface states. We demonstrate that the zero-energy bound states observed in Fe(Te,Se) superconductors are possible realizations of the Majorana zero modes in quantum anomalous vortices produced by the interstitial magnetic Fe. The quantum anomalous vortex matter not only advances fundamental understandings of topological defect excitations of Cooper pairing but also provides new and advantageous platforms for manipulating Majorana zero modes in quantum computing.

The Mott insulator ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$ is the subject of much recent attention following reports of emergent nonequilibrium steady states driven by applied electric fields or currents. In this paper, we carry out infrared nano-imaging and optical-microscopy measurements on bulk single crystal ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$ under conditions of steady current flow to obtain insight into the current-driven insulator-to-metal transition. We observe macroscopic growth of the current-induced metallic phase, with nucleation regions for metal and insulator phases determined by the polarity of the current flow. A remarkable metal-insulator-metal microstripe pattern is observed at the phase front separating metal and insulator phases. The microstripes have orientations tied uniquely to the crystallographic axes, implying a strong coupling of the electronic transition to lattice degrees of freedom. Theoretical modeling further illustrates the importance of the current density and confirms a submicron-thick surface metallic layer at the phase front of the bulk metallic phase. Our work confirms that the electrically induced metallic phase is nonfilamentary and is not driven by Joule heating, revealing remarkable new characteristics of electrically induced insulator-metal transitions occurring in functional correlated oxides.

While the equilibrium properties, states, and phase transitions of interacting systems are well described by statistical mechanics, the lack of suitable state parameters has hindered the understanding of nonequilibrium phenomena in diverse settings, from glasses to driven systems to biology. The length of a losslessly compressed data file is a direct measure of its information content: The more ordered the data file is, the lower its information content and the shorter the length of its encoding can be made. Here, we describe how data compression enables the quantification of order in nonequilibrium and equilibrium many-body systems, both discrete and continuous, even when the underlying form of order is unknown. We consider absorbing state models on and off lattice, as well as a system of active Brownian particles undergoing motility-induced phase separation. The technique reliably identifies nonequilibrium phase transitions, determines their character, quantitatively predicts certain critical exponents without prior knowledge of the order parameters, and reveals previously unknown ordering phenomena. This technique should provide a quantitative measure of organization in condensed matter and other systems exhibiting collective phase transitions in and out of equilibrium.

The interaction of carbon-based aromatic molecules and nanostructures with metals can strongly depend on the topology of their $\pi$-electron systems. This is shown with a model system using the isomers azulene, which has a nonalternant $\pi$ system with a 5-7 ring structure, and naphthalene, which has an alternant $\pi$ system with a 6-6 ring structure. We found that azulene can interact much more strongly with metal surfaces. On copper (111), its zero-coverage desorption energy is 1.86 eV, compared to 1.07 eV for naphthalene. The different bond strengths are reflected in the adsorption heights, which are 2.30 Å for azulene and 3.04 Å for naphthalene, as measured by the normal incidence x-ray standing wave technique. These differences in the surface chemical bond are related to the electronic structure of the molecular $\pi$ systems. Azulene has a low-lying LUMO that is close to the Fermi energy of Cu and strongly hybridizes with electronic states of the surface, as is shown by photoemission, near-edge x-ray absorption fine-structure, and scanning tunneling microscopy data in combination with theoretical analysis. According to density functional theory calculations, electron donation from the surface into the molecular LUMO leads to negative charging and deformation of the adsorbed azulene. Noncontact atomic force microscopy confirms the deformation, while Kelvin probe force microscopy maps show that adsorbed azulene partially retains its in-plane dipole. In contrast, naphthalene experiences only minor adsorption-induced changes of its electronic and geometric structure. Our results indicate that the electronic properties of metal-organic interfaces, as they occur in organic (opto)electronic devices, can be tuned through modifications of the $\pi$ topology of the molecular organic semiconductor, especially by introducing 5-7 ring pairs as functional structural elements.

Models for confluent biological tissues often describe the network formed by cells as a triple-junction network, similar to foams. However, higher-order vertices or multicellular rosettes are prevalent in developmental and in vitro processes and have been recognized as crucial in many important aspects of morphogenesis, disease, and physiology. In this work, we study the influence of rosettes on the mechanics of a confluent tissue. We find that the existence of rosettes in a tissue can greatly influence its rigidity. Using a generalized vertex model and the effective medium theory, we find a fluid-to-solid transition driven by rosette density and intracellular tensions. This transition exhibits several hallmarks of a second-order phase transition such as a growing correlation length and a universal critical scaling in the vicinity of a critical point. Furthermore, we elucidate the nature of rigidity transitions in dense biological tissues and other cellular structures using a generalized Maxwell constraint counting approach, which answers a long-standing puzzle of the origin of solidity in these systems.

Ultracold molecules have experienced increasing attention in recent years. Compared to ultracold atoms, they possess several unique properties that make them perfect candidates for the implementation of new quantum-technological applications in several fields, from quantum simulation to quantum sensing and metrology. In particular, ultracold molecules of two-electron atoms (such as strontium or ytterbium) also inherit the peculiar properties of these atomic species, above all, the possibility to access metastable electronic states via direct excitation on optical clock transitions with ultimate sensitivity and accuracy. We report on the production and coherent manipulation of molecular bound states of two fermionic ${}^{173}\mathrm{Yb}$ atoms in different electronic (orbital) states ${}^1{S}_0$ and ${}^3{P}_0$ in the proximity of a scattering resonance involving atoms in different spin and electronic states, called orbital Feshbach resonance. We demonstrate that orbital molecules can be coherently photoassociated starting from a gas of ground-state atoms in a three-dimensional optical lattice by observing several photoassociation and photodissociation cycles. We also show the possibility to coherently control the molecular internal state by using Raman-assisted transfer to swap the nuclear spin of one of the atoms forming the molecule, thus demonstrating a powerful manipulation and detection tool of these molecular bound states. Finally, by exploiting this peculiar detection technique we provide the first information on the lifetime of the molecular states in a many-body setting, paving the way towards future investigations of strongly interacting Fermi gases in a still unexplored regime.

Atomically thin ferromagnetic and conducting electron systems are highly desired for spintronics, because they can be controlled with both magnetic and electric fields. We present $({\mathrm{SrRuO}}_3{)}_1-{({\mathrm{SrTiO}}_3)}_5$ superlattices and single-unit-cell-thick ${\mathrm{SrRuO}}_3$ samples that are capped with ${\mathrm{SrTiO}}_3$. We achieve samples of exceptional quality. In these samples, the electron systems comprise only a single ${\mathrm{RuO}}_2$ plane. We observe conductivity down to 50 mK, a ferromagnetic state with a Curie temperature of 25 K, and signals of magnetism persisting up to approximately 100 K.

The recent emergence of 2D van der Waals magnets down to atomic-layer thickness provides an exciting platform for exploring quantum magnetism and spintronics applications. The van der Waals nature stabilizes the long-range ferromagnetic order as a result of magnetic anisotropy. Furthermore, giant tunneling magnetoresistance and electrical control of magnetism have been reported. However, the potential of 2D van der Waals magnets for magnonics, magnon-based spintronics, has not been explored yet. Here, we report the experimental observation of long-distance magnon transport in quasi-two-dimensional van der Waals antiferromagnet ${\mathrm{MnPS}}_3$, which demonstrates the 2D magnets as promising material candidates for magnonics. As the 2D ${\mathrm{MnPS}}_3$ thickness decreases, a shorter magnon diffusion length is observed, which could be attributed to the surface-impurity-induced magnon scattering. Our results could pave the way for exploring quantum magnonics phenomena and designing future magnonics devices based on 2D van der Waals magnets.

We measure valence-to-core x-ray emission spectra of compressed crystalline ${\mathrm{GeO}}_2$ up to 56 GPa and of amorphous ${\mathrm{GeO}}_2$ up to 100 GPa. In a novel approach, we extract the Ge coordination number and mean Ge-O distances from the emission energy and the intensity of the $\mathrm{K}{\beta }^{\prime \prime }$ emission line. The spectra of high-pressure polymorphs are calculated using the Bethe-Salpeter equation. Trends observed in the experimental and calculated spectra are found to match only when utilizing an octahedral model. The results reveal persistent octahedral Ge coordination with increasing distortion, similar to the compaction mechanism in the sequence of octahedrally coordinated crystalline ${\mathrm{GeO}}_2$ high-pressure polymorphs.

Chiral nano- or metamaterials and surfaces enable striking photonic properties, such as negative refractive index and superchiral light, driving promising applications in novel optical components, nanorobotics, and enhanced chiral molecular interactions with light. In characterizing chirality, although nonlinear chiroptical techniques are typically much more sensitive than their linear optical counterparts, separating true chirality from anisotropy is a major challenge. Here, we report the first observation of optical activity in second-harmonic hyper-Rayleigh scattering (HRS). We demonstrate the effect in a 3D isotropic suspension of Ag nanohelices in water. The effect is 5 orders of magnitude stronger than linear optical activity and is well pronounced above the multiphoton luminescence background. Because of its sensitivity, isotropic environment, and straightforward experimental geometry, HRS optical activity constitutes a fundamental experimental breakthrough in chiral photonics for media including nanomaterials, metamaterials, and chemical molecules.

Analytical approaches to model the structure of complex networks can be distinguished into two groups according to whether they consider an intensive (e.g., fixed degree sequence and random otherwise) or an extensive (e.g., adjacency matrix) description of the network structure. While extensive approaches—such as the state-of-the-art message passing approximation—typically yield more accurate predictions, intensive approaches provide crucial insights on the role played by any given structural property in the outcome of dynamical processes. Here we introduce an intensive description that yields almost identical predictions to the ones obtained with the message passing approximation using bond percolation as a benchmark. Our approach distinguishes nodes according to two simple statistics: their degree and their position in the core-periphery organization of the network. Our near-exact predictions highlight how accurately capturing the long-range correlations in network structures allows easy and effective compression of real complex network data.