Active systems are composed of constituents with interactions that are generically nonreciprocal in nature. Such nonreciprocity often gives rise to situations where conflicting objectives exist, such as in the case of a predator pursuing its prey, while the prey attempts to evade capture. This situation is somewhat reminiscent of those encountered in geometrically frustrated systems where conflicting objectives also exist, which result in the absence of configurations that simultaneously minimize all interaction energies. In the latter, a rich variety of exotic phenomena are known to arise due to the presence of accidental degeneracy of ground states. Here, we establish a direct analogy between these two classes of systems. The analogy is based on the observation that nonreciprocally interacting systems with antisymmetric coupling and geometrically frustrated systems have in common that they both exhibit marginal orbits, which can be regarded as a dynamical system counterpart of accidentally degenerate ground states. The former is shown by proving a Liouville-type theorem. These “accidental degeneracies” of orbits are shown to often get “lifted” by stochastic noise or weak random disorder due to the emergent “entropic force” to give rise to a noise-induced spontaneous symmetry breaking, in a similar manner to the order-by-disorder phenomena known to occur in geometrically frustrated systems. Furthermore, we report numerical evidence of a nonreciprocity-induced spin-glass-like state that exhibits a short-ranged spatial correlation (with stretched exponential decay) and an algebraic temporal correlation associated with the aging effect. Our work establishes an unexpected connection between the physics of complex magnetic materials and nonreciprocal matter, offering a fresh and valuable perspective for comprehending the latter.

We describe simulations of the quantum dynamics of a confocal cavity QED system that realizes an intrinsically driven-dissipative spin glass. A close connection between open quantum dynamics and replica symmetry breaking is established, in which individual quantum trajectories are the replicas. We observe that entanglement plays an important role in the emergence of replica symmetry breaking in a fully connected, frustrated spin network of up to 15 spin-$1/2$ particles. Quantum trajectories of entangled spins reach steady-state spin configurations of lower energy than that of semiclassical trajectories. Cavity emission allows monitoring of the continuous stochastic evolution of spin configurations, while backaction from this projects entangled states into states of broken Ising and replica symmetry. The emergence of spin glass order manifests itself through the simultaneous absence of magnetization and the presence of nontrivial spin overlap density distributions among replicas. Moreover, these overlaps reveal incipient ultrametric order, in line with the Parisi replica symmetry breaking solution for the Sherrington-Kirkpatrick model. A nonthermal Parisi order parameter distribution, however, highlights the driven-dissipative nature of this quantum optical spin glass. This practicable system could serve as a test bed for exploring how quantum effects enrich the physics of spin glasses.

Strong mutual interaction which correlates elementary excitations of quantum matter plays a key role in a range of emergent phenomena, from binding and condensation to quantum thermalization and many-body localization. Here, we employ a Rydberg quantum simulator to experimentally demonstrate strongly correlated spin transport in anisotropic Heisenberg magnets, where the magnon-magnon interaction can be tuned 2 orders of magnitude larger than the magnon hopping strength. In our approach, the motion of magnons is controlled by an induced spin-exchange interaction through far off-resonant driving, which enables coherent transport of a single Rydberg excitation across a chain of ground-state atoms. As the most prominent signature of a giant anisotropy, we show that nearby Rydberg excitations form distinct types of magnon-bound states, where a tightly bound pair exhibits frozen dynamics in a fragmented Hilbert space, while a loosely bound pair propagates and establishes correlations beyond a single lattice site. Our scheme complements studies using resonant dipole-dipole interactions between Rydberg states and opens the door to exploring quantum thermodynamics with ultrastrong interactions and kinetic constraints.

The identification of distinct charge transport features, deriving from nontrivial bulk band and surface states, has been a challenging subject in the field of topological systems. In topological Dirac and Weyl semimetals, nontrivial conical bands with Fermi-arc surface states give rise to negative longitudinal magnetoresistance due to chiral anomaly effect and unusual thickness dependent quantum oscillation from Weyl-orbit effect, which were demonstrated recently in experiments. In this work, we report the experimental observations of large nonlinear and nonreciprocal transport effects for both longitudinal and transverse channels in an untwinned Weyl metal of ${\mathrm{SrRuO}}_3$ thin film grown on a ${\mathrm{SrTiO}}_3$ substrate. From rigorous measurements with bias current applied along various directions with respect to the crystalline principal axes, the magnitude of nonlinear Hall signals from the transverse channel exhibits a simple $\sin \alpha$ dependence at low temperatures, where $\alpha$ is the angle between bias current direction and orthorhombic $[001{]}_{\mathrm{o}}$, reaching a maximum when current is along orthorhombic $[1\overline{1}0{]}_{\mathrm{o}}$. On the contrary, the magnitude of nonlinear and nonreciprocal signals in the longitudinal channel attains a maximum for bias current along $[001{]}_{\mathrm{o}}$, and it vanishes for bias current along $[1\overline{1}0{]}_{\mathrm{o}}$. The observed $\alpha$-dependent nonlinear and nonreciprocal signals in longitudinal and transverse channels reveal a magnetic Weyl phase with an effective Berry curvature dipole along $[1\overline{1}0{]}_{\mathrm{o}}$ from surface states, accompanied by 1D chiral edge modes along $[001{]}_{\mathrm{o}}$.

We show that time-reversal symmetry-broken, centrosymmetric antiferromagnets with nonrelativistic spin splitting of $d$-wave symmetry—the so-called $d$-wave altermagnets—are conveniently described in terms of the ferroic ordering of magnetic octupoles. The magnetic octupoles are the lowest-order ferroically ordered magnetic quantity in this case and so are the natural order parameter for the transition into the magnetically ordered state. They provide a unified description of the broken time-reversal symmetry and the nonrelativistic spin splitting, as well as a platform for manipulating the latter, and account for other phenomena, such as piezomagnetism, characteristic of this class of antiferromagnets. Unusually for antiferromagnets, we show that the magnetic octupoles cause a nonzero magnetic Compton scattering, providing a route for their direct experimental detection. We illustrate these concepts using density-functional and model calculations for the prototypical nonrelativistic spin-split antiferromagnet, rutile-structure manganese difluoride ${\mathrm{MnF}}_2$.

The motion of electrons in the vast majority of conductors is diffusive, obeying Ohm’s law. However, the recent discovery and growth of high-purity materials with extremely long electronic mean free paths has sparked interest in non-Ohmic alternatives, including viscous and ballistic flow. Although non-Ohmic transport regimes have been discovered across a range of materials—including two-dimensional electron gases, graphene, topological semimetals, and the delafossite metals—determining their nature has proved to be challenging. Here, we report on a new approach to the problem, employing broadband microwave spectroscopy of the delafossite metal ${\mathrm{PdCoO}}_2$ in three distinct sample geometries that would be identical for diffusive transport. The observed differences, which go as far as differing power laws, take advantage of the hexagonal symmetry of the conducting Pd planes of ${\mathrm{PdCoO}}_2$. This permits a particularly elegant symmetry-based diagnostic for nonlocal electrodynamics, with the result favoring predominantly ballistic over strictly hydrodynamic flow. Furthermore, it uncovers a new effect for ballistic electron flow, owing to the highly faceted shape of the hexagonal Fermi surface. We combine our extensive data set with an analysis of the Boltzmann equation to characterize the nonlocal regime in ${\mathrm{PdCoO}}_2$, and we include out-of-plane impurity scattering as a source of apparent momentum-conserving scattering at low temperatures. More broadly, our results highlight the potential of broadband microwave spectroscopy to play a central role in investigating exotic transport regimes in the new generation of ultrahigh-conductivity materials.

A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. For this task, there is a well-studied quantum algorithm that performs quantum phase estimation on an initial trial state that has a non-negligible overlap with a low-energy state. However, it is notoriously hard to give theoretical guarantees that such a trial state can be prepared efficiently. Moreover, the heuristic proposals that are currently available, such as with adiabatic state preparation, appear insufficient in practical cases. This paper shows that, for most random sparse Hamiltonians, the maximally mixed state is a sufficiently good trial state, and phase estimation efficiently prepares states with energy arbitrarily close to the ground energy. Furthermore, any low-energy state must have non-negligible quantum circuit complexity, suggesting that low-energy states are classically nontrivial and phase estimation is the optimal method for preparing such states (up to polynomial factors). These statements hold for two models of random Hamiltonians: (i) a sum of random signed Pauli strings and (ii) a random signed $d$-sparse Hamiltonian. The main technical argument is based on some new results in nonasymptotic random matrix theory. In particular, a refined concentration bound for the spectral density is required to obtain complexity guarantees for these random Hamiltonians.

While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number of time steps $n$. Here, we introduce a numerically exact algorithm to calculate process tensors—compact representations of environmental influences—which provides a scaling advantage over previous algorithms by leveraging self-similarity of the tensor networks that represent the environment. It is applicable to environments with Gaussian statistics, such as for spin-boson-type open quantum systems. Based on a divide-and-conquer strategy, our approach requires only $\mathcal{O}(n\log n)$ singular value decompositions for environments with infinite memory. Where the memory can be truncated after $n_c$ time steps, a nominal scaling $\mathcal{O}(n_c\log n_c)$ is found, which is independent of $n$. This improved scaling is enabled by identifying process tensors with repeatable blocks. To demonstrate the power and utility of our approach, we provide three examples. (1) We calculate the fluorescence spectra of a quantum dot under both strong driving and strong dot-phonon couplings, a task requiring simulations over millions of time steps, which we are able to perform in minutes. (2) We efficiently find process tensors describing superradiance of multiple emitters. (3) We explore the limits of our algorithm by considering coherence decay with a very strongly coupled environment. The observed computation time is not necessarily proportional to the number of singular value decompositions because the matrix dimensions also depend on the number of time steps. Nevertheless, quasilinear and sublinear scaling of computation time is found in practice for a wide range of parameters. While there are instances where existing methods can achieve comparable nominal scaling by precalculating effective propagators for time-independent or periodic system Hamiltonians, process tensors contain all the information needed to extract arbitrary multitime correlation functions of the system when driven by arbitrary time-dependent system Hamiltonians. The algorithm we present here not only significantly extends the scope of numerically exact techniques to open quantum systems with long memory times, but it also has fundamental implications for the simulation complexity of tensor network approaches.

The dipolar-octupolar (DO) pyrochlores, $R_2{M}_2{\mathrm{O}}_7$ ($R=\mathrm{Ce},\mathrm{Sm},\mathrm{Nd}$), are key players in the search for realizable novel quantum spin liquid (QSL) states as a large parameter space within the DO pyrochlore phase diagram is theorized to host QSL states of both dipolar and octupolar nature. New single crystals and powders of ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$, synthesized by hydrothermal techniques, present an opportunity for a new characterization of the exchange parameters in ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ using the near-neighbor $XYZ$ model Hamiltonian associated with DO pyrochlores. Utilizing quantum numerical linked cluster expansion fits to heat capacity and magnetic susceptibility measurements, and classical Monte Carlo calculations to the diffuse neutron diffraction of the new hydrothermally grown ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ samples, we place ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$’s ground state within the ordered dipolar all-in-all-out (AIAO) Néel phase, with quantum Monte Carlo calculations showing a transition to long-range order at temperatures below those accessed experimentally. Indeed, our new neutron diffraction measurements on the hydrothermally grown ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ powders show a broad signal at low scattering wave vectors, reminiscent of a dipolar spin ice, in striking contrast from previous powder neutron diffraction on samples grown from solid-state synthesis, which found diffuse scattering at high scattering wave vectors associated with magnetic octupoles and suggested an octupolar quantum spin ice state. We conclude that new hydrothermally grown ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ samples host a finite-temperature proximate dipolar spin ice phase, above the expected transition to AIAO Néel order.

Moiré materials provide fertile ground for the correlated and topological quantum phenomena. Among them, the quantum anomalous Hall (QAH) effect, in which the Hall resistance is quantized even under zero magnetic field, is a direct manifestation of the intrinsic topological properties of a material and an appealing attribute for low-power electronics applications. The QAH effect has been observed in both graphene and transition metal dichalcogenide (TMD) moiré materials. It is thought to arise from the interaction-driven valley polarization of the narrow moiré bands. Here, we show that the newly discovered QAH state in AB-stacked ${\mathrm{MoTe}}_2/{\mathrm{W}\mathrm{S}\mathrm{e}}_2$ moiré bilayers is not valley polarized but valley coherent. The layer- and helicity-resolved optical spectroscopy measurement reveals that the QAH ground state possesses spontaneous spin (valley) polarization aligned (antialigned) in two TMD layers. In addition, saturation of the out-of-plane spin polarization in both layers occurs only under high magnetic fields, supporting a canted spin texture. Our results call for a new mechanism for the QAH effect and highlight the potential of TMD moiré materials with strong electronic correlations and spin-orbit interactions for exotic topological states.

The discrepancies between reality and simulation impede the optimization and scalability of solid-state quantum devices. Disorder induced by the unpredictable distribution of material defects is one of the major contributions to the reality gap. We bridge this gap using physics-aware machine learning, in particular, using an approach combining a physical model, deep learning, Gaussian random field, and Bayesian inference. This approach enables us to infer the disorder potential of a nanoscale electronic device from electron-transport data. This inference is validated by verifying the algorithm’s predictions about the gate-voltage values required for a laterally defined quantum-dot device in AlGaAs/GaAs to produce current features corresponding to a double-quantum-dot regime.

The elementary excitations in weakly interacting quantum fluids have a nontrivial nature which is at the basis of defining quantum phenomena such as superfluidity. These excitations and the physics they lead to have been explored in closed quantum systems at thermal equilibrium both theoretically within the celebrated Bogoliubov framework and experimentally in quantum fluids of ultracold atoms. Over the past decade, the relevance of Bogoliubov excitations has become essential to understand quantum fluids of interacting photons. Their driven-dissipative character leads to distinct properties with respect to their equilibrium counterparts. For instance, the condensate coupling to the photonic vacuum environment leads to a nonzero generation rate of elementary excitations with many striking implications. In this work, considering that quantum fluids of light are often hosted in solid-state systems, we show within a joint theory-experiment analysis that the vibrations of the crystal constitute another environment that the condensate is fundamentally coupled to. This coupling leads to a unique heat transfer mechanism, resulting in a large generation rate of elementary excitations in typical experimental conditions, and to a fundamental nonzero contribution at vanishing temperatures. Our work provides a complete framework for solid-embedded quantum fluids of light, which is invaluable in view of achieving a regime dominated by photon-vacuum fluctuations.

Quantifying electron-phonon interactions for the surface states of topological materials can provide key insights into surface-state transport, topological superconductivity, and potentially how to manipulate the surface state using a structural degree of freedom. We perform time-resolved x-ray diffraction (XRD) and angle-resolved photoemission (ARPES) measurements on ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, following the excitation of coherent $A_{1g}$ optical phonons. We extract and compare the deformation potentials coupling the surface electronic states to local $A_{1g}$-like displacements in these two materials using the experimentally determined atomic displacements from XRD and electron band shifts from ARPES. We find the coupling in ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ to be similar and in general in agreement with expectations from density functional theory. We establish a methodology that quantifies the mode-specific electron-phonon coupling experimentally, allowing detailed comparison to theory. Our results shed light on fundamental processes in topological insulators involving electron-phonon coupling.

The Mott insulator provides an excellent foundation for exploring a wide range of strongly correlated physical phenomena, such as high-temperature superconductivity, quantum spin liquid, and colossal magnetoresistance. A Mott insulator with the simplest degree of freedom is an ideal and highly desirable system for studying the fundamental physics of Mottness. In this study, we have unambiguously identified such an anticipated Mott insulator in a van der Waals layered compound ${\mathrm{Nb}}_3{\mathrm{Cl}}_8$. In the high-temperature phase, where interlayer coupling is negligible, density functional theory calculations for the monolayer of ${\mathrm{Nb}}_3{\mathrm{Cl}}_8$ suggest a half-filled flat band at the Fermi level, whereas angle-resolved photoemission spectroscopy experiments observe a large gap. This observation is perfectly reproduced by dynamical mean-field theory calculations considering strong electron correlations, indicating a correlation-driven Mott insulator state. Since this half-filled band derived from a single $2a_1$ orbital is isolated from all other bands, the monolayer of ${\mathrm{Nb}}_3{\mathrm{Cl}}_8$ is an ideal realization of the celebrated single-band Hubbard model. Upon decreasing the temperature, the bulk system undergoes a phase transition, where structural changes significantly enhance the interlayer coupling. This results in a bonding-antibonding splitting in the Hubbard bands, while the Mott gap remains dominant. Our discovery provides a simple and seminal model system for investigating Mott physics and other emerging correlated states.

We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers, based on the Keldysh path-integral formalism and replica trick. In the limit of rare measurements, $\gamma /J\ll 1$ (where $\gamma$ is measurement rate per site and $J$ is hopping constant in the tight-binding model), we derive a nonlinear sigma model (NLSM) as an effective field theory of the problem. Its replica-symmetric sector is described by a $\mathrm{U}(2)/\mathrm{U}(1)\times \mathrm{U}(1)\simeq S^2$ sigma model with diffusive behavior, and the replica-asymmetric sector is a two-dimensional NLSM defined on $\mathrm{SU}(R)$ manifold with the replica limit $R\to 1$. On the Gaussian level, valid in the limit $\gamma /J\to 0$, this model predicts a logarithmic behavior for the second cumulant of number of particles in a subsystem and for the entanglement entropy. However, the one-loop renormalization group analysis allows us to demonstrate that this logarithmic growth saturates at a finite value $\sim (J/\gamma {)}^2$ even for rare measurements, which corresponds to the area-law phase. This implies the absence of a measurement-induced entanglement phase transition for free fermions. The crossover between logarithmic growth and saturation, however, happens at exponentially large scale, $\ln l_{\mathrm{corr}}\sim J/\gamma$. This makes this crossover very sharp as a function of the measurement frequency $\gamma /J$, which can be easily confused with a transition from the logarithmic to area law in finite-size numerical calculations. We have performed a careful numerical analysis, which supports our analytical predictions.

First-order nonequilibrium phase transitions observed in active matter, fluid dynamics, biology, climate science, and other systems with irreversible dynamics are challenging to analyze, because they cannot be inferred from a simple free energy minimization principle. Rather, the mechanism of these transitions depends crucially on the system’s dynamics, which requires us to analyze them in trajectory space rather than in phase space. Here, we consider situations where the path of these transitions can be characterized as the minimizer of an action, whose minimum value can be used in a nonequilibrium generalization of the Arrhenius law to calculate the system’s phase diagram. We also develop efficient numerical tools for the minimization of this action. These tools are general enough to be transportable to many situations of interest, in particular, when the fluctuations present in the microscopic system are non-Gaussian and its dynamics is not governed by the standard Langevin equation. As an illustration, first-order phase transitions in two spatially extended nonequilibrium systems are analyzed: a modified Ginzburg-Landau equation with a chemical potential which is nongradient and a reaction-diffusion network based on the Schlögl model. The phase diagrams of both systems are calculated as a function of their control parameters, and the paths of the transitions, including their critical nuclei, are identified. These results clearly demonstrate the nonequilibrium nature of the transitions, with differing forward and backward paths.

Quantum critical systems constitute appealing platforms for exploring novel measurement-induced phenomena due to their innate sensitivity to perturbations. We study the impact of measurements on paradigmatic Ising quantum-critical chains using an explicit protocol, whereby correlated ancillae are entangled with the critical chain and then projectively measured. Using a perturbative analytic framework supported by extensive numerical simulations, we demonstrate that measurements can qualitatively alter critical correlations in a manner dependent on the choice of entangling gate, ancilla measurement basis, measurement outcome, and nature of ancilla correlations. We further show that measurement-altered Ising criticality can be pursued surprisingly efficiently in experiments featuring of order 100 qubits by postselecting for high-probability measurement outcomes or, in certain cases, by averaging observables separately over measurement outcomes residing in distinct symmetry sectors. Our framework naturally adapts to more exotic quantum-critical points and highlights opportunities for realization in noisy intermediate-scale quantum hardware and in Rydberg arrays.

Robust spin-photon interfaces in solids are essential components in quantum networking and sensing technologies. Ideally, these interfaces combine a long-lived spin memory, coherent optical transitions, fast and high-fidelity spin manipulation, and straightforward device integration and scaling. The tin-vacancy center (SnV) in diamond is a promising spin-photon interface with desirable optical and spin properties at 1.7 K. However, the SnV spin lacks efficient microwave control, and its spin coherence degrades with higher temperature. In this work, we introduce a new platform that overcomes these challenges—SnV centers in uniformly strained thin diamond membranes. The controlled generation of crystal strain introduces orbital mixing that allows microwave control of the spin state with 99.36(9)% gate fidelity and spin coherence protection beyond a millisecond. Moreover, the presence of crystal strain suppresses temperature-dependent dephasing processes, leading to a considerable improvement of the coherence time up to $223(10)\mathrm{\mu }\mathrm{s}$ at 4 K, a widely accessible temperature in common cryogenic systems. Critically, the coherence of optical transitions is unaffected by the elevated temperature, exhibiting nearly lifetime-limited optical linewidths. Combined with the compatibility of diamond membranes with device integration, the demonstrated platform is an ideal spin-photon interface for future quantum technologies.

Understanding the materials dependence together with the universal controlling parameter of superconductivity (SC) in copper oxide superconductors is one of the major challenges in condensed matter physics. Here, we numerically analyze SC by using ab initio low-energy effective Hamiltonians consisting of the antibonding combination of Cu $3d_{x^2-y^2}$ and O $2p_{\sigma }$ orbitals without adjustable parameters. We have performed the state-of-the-art variational Monte Carlo calculations for the four carrier doped cuprates with diverse experimental optimal SC critical temperature $T_c^{\mathrm{opt}}$: ${\mathrm{CaCuO}}_2$ ($T_c^{\mathrm{opt}}\sim 110\mathrm{K}$), ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CuO}}_6$ ($T_c^{\mathrm{opt}}\sim 10–40\mathrm{K}$), ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_8$ ($T_c^{\mathrm{opt}}\sim 85–100\mathrm{K}$), and ${\mathrm{HgBa}}_2{\mathrm{CuO}}_4$ ($T_c^{\mathrm{opt}}\sim 90\mathrm{K}$). Materials and hole doping concentration ($\delta$) dependencies of the SC order parameter $F_{\mathrm{SC}}$ and the competition with spin or charge order show essential and quantitative agreement with the available experiments on the four materials in the following points. (1) In a wide range $0.05\le \delta \le 0.25$, the ground state is commonly the uniform SC state, which is severely competing with the charge or spin stripe and antiferromagnetic states. (2) $F_{\mathrm{SC}}$ at the optimum doping shows amplitude consistent with the superfluid density measured in the muon spin resonance and its dome structure found in $\delta$ dependence shows consistency with that of the SC gap in the tunneling and photoemission measurements. Based on the confirmed materials dependence, we further find insights into the universal SC mechanism. (I) $F_{\mathrm{SC}}$ increases with the ratio $U/|t_1|$ within the available realistic materials, indicating that $U/|t_1|$ is the principal component controlling the strength of the SC in the real materials dependence. Here, $U$ and $t_1$ are the on-site Coulomb repulsion and the nearest neighbor hopping, respectively, in the ab initio Hamiltonians. (II) A universal scaling $T_c^{\mathrm{opt}}\sim 0.16|t_1|F_{\mathrm{SC}}$ holds. (III) SC is enhanced and optimized if $U$ is increased beyond the real available materials, and it is further enhanced when the off-site interaction is reduced, while the presence of the off-site interaction is important to make the SC ground state against other competing states. The present findings provide useful clues for the design of new SC materials with even higher $T_c^{\mathrm{opt}}$.

A solid loaded beyond the yield stress loses its elastic properties and becomes plastic. From a microscopic point of view, this limit corresponds to the condition where plastic regions become so densely packed that they give rise to system-spanning structures. This limit for glasses is abrupt, which makes experimental investigations challenging. Here, the yield point is reached by the alternative approach of increasing the density of plastic regions by generation of point defects during x-ray irradiation. For the case of a ${\mathrm{LiBO}}_2$ glass, we show that at low doses, i.e., for a low density of defects, the defects behave as isolated stress sources that induce atomic displacements typical of an elastic solid. As the density of defects increases, the mechanical response of the glass at the local scale changes from elastic to more and more plastic, until reaching the limit where it becomes characteristic of a flowing system, which signals that the yield point is reached.