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A topological insulator reveals its nontrivial bulk through the presence of gapless edge states: This is called the bulk-boundary correspondence. However, the recent discovery of “fragile” topological states with no gapless edges casts doubt on this concept. We propose a generalization of the bulk-boundary correspondence: a transformation under which the gap between the fragile phase and other bands must close. We derive specific twisted boundary conditions (TBCs) that can detect all the two-dimensional eigenvalue fragile phases. We develop the concept of real-space invariants, local good quantum numbers in real space, which fully characterize these phases and determine the number of gap closings under the TBCs. Realizations of the TBCs in metamaterials are proposed, thereby providing a route to their experimental verification.

Steering the evolution of single spin systems is crucial for quantum computing and quantum sensing.The dynamics of quantum systems has been theoretically investigated with parity-time–symmetric Hamiltonians exhibiting exotic properties. Although parity-time symmetry has been explored in classical systems, its observation in a single quantum system remains elusive.We developed amethod to dilate a general parity-time–symmetric Hamiltonian into a Hermitian one.The quantum state evolutions ranging from regions of unbroken to broken PT symmetry have been observed with a single nitrogen-vacancy center in diamond.Owing to the universality of the dilation method, our result provides a route for further exploiting and understanding the exotic properties of parity-time symmetric Hamiltonian in quantum systems.

Exploiting topological properties of a system allows certain properties to be protected against the disorder and scattering caused by defects. Barik et al. demonstrate a strong light-matter interaction in a topological photonic structure (see the Perspective by Amo). They created topological edge states at the interface between two photonic, topologically distinct regions and coupled them to a single quantum emitter. The chiral nature of single-photon emission was used to inject single photons of opposite polarization into counterpropagating topological edge states. Such a topological quantum optics interface may provide a powerful platform for developing robust integrated quantum optical circuits. Science , this issue p. 666 ; see also p. 638 Light-matter coupling is achieved between topologically protected photonic edge states and a quantum emitter. The application of topology in optics has led to a new paradigm in developing photonic devices with robust properties against disorder. Although considerable progress on topological phenomena has been achieved in the classical domain, the realization of strong light-matter coupling in the quantum domain remains unexplored. We demonstrate a strong interface between single quantum emitters and topological photonic states. Our approach creates robust counterpropagating edge states at the boundary of two distinct topological photonic crystals. We demonstrate the chiral emission of a quantum emitter into these modes and establish their robustness against sharp bends. This approach may enable the development of quantum optics devices with built-in protection, with potential applications in quantum simulation and sensing.

Predicting the properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a ‘classical shadow’, can be used to predict many different properties; order log ( M ) measurements suffice to accurately predict M different functions of the state with high success probability. The number of measurements is independent of the system size and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods. An efficient method has been proposed through which the properties of a complex, large-scale quantum system can be predicted without fully characterizing the quantum state.

Graphene is an atomically thin material that supports highly confined plasmon polaritons, or nano-light, with very low loss. The properties of graphene can be made richer by introducing and then rotating a second layer so that there is a slight angle between the atomic registry. Sunku et al. show that the moiré patterns that result from such twisted bilayer graphene also provide confined conducting channels that can be used for the directed propagation of surface plasmons. Controlling the structure thereby provides a pathway to control and route surface plasmons for a nanophotonic platform. Science , this issue p. 1153 Twisted bilayer graphene hosts periodic arrays of conducting channels for the directed propagation of surface plasmons. Graphene is an atomically thin plasmonic medium that supports highly confined plasmon polaritons, or nano-light, with very low loss. Electronic properties of graphene can be drastically altered when it is laid upon another graphene layer, resulting in a moiré superlattice. The relative twist angle between the two layers is a key tuning parameter of the interlayer coupling in thus-obtained twisted bilayer graphene (TBG). We studied the propagation of plasmon polaritons in TBG by infrared nano-imaging. We discovered that the atomic reconstruction occurring at small twist angles transforms the TBG into a natural plasmon photonic crystal for propagating nano-light. This discovery points to a pathway for controlling nano-light by exploiting quantum properties of graphene and other atomically layered van der Waals materials, eliminating the need for arduous top-down nanofabrication.

Skeletal muscles possess the combinational properties of high fatigue resistance (1,000 J/m²), high strength (1 MPa), low Young’s modulus (100 kPa), and high water content (70 to 80 wt %), which have not been achieved in synthetic hydrogels. The muscle-like properties are highly desirable for hydrogels’ nascent applications in load-bearing artificial tissues and soft devices. Here, we propose a strategy of mechanical training to achieve the aligned nanofibrillar architectures of skeletal muscles in synthetic hydrogels, resulting in the combinational muscle-like properties. These properties are obtained through the training-induced alignment of nanofibrils, without additional chemical modifications or additives. In situ confocal microscopy of the hydrogels’ fracturing processes reveals that the fatigue resistance results from the crack pinning by the aligned nanofibrils, which require much higher energy to fracture than the corresponding amorphous polymer chains. This strategy is particularly applicable for 3D-printed microstructures of hydrogels, in which we can achieve isotropically fatigue-resistant, strong yet compliant properties.

Engineering stress or strain into materials can improve their performance. Adding mechanical stress to silicon chips, for instance, produces transistors with enhanced electron mobility. Ghadimi et al. explore the possibility of enhancing the vibrational properties of a micromechanical oscillator by engineering stress within the structure (see the Perspective by Eichler). By careful design of the micromechanical oscillator, and by building in associated stresses, exceptional vibrational properties can be produced. Such enhanced oscillators could be used as exquisite force sensors. Science , this issue p. 764 ; see also p. 706 Engineered stress is used to fabricate micromechanical oscillators with enhanced vibrational properties. Extreme stresses can be produced in nanoscale structures; this feature has been used to realize enhanced materials properties, such as the high mobility of silicon in modern transistors. We show how nanoscale stress can be used to realize exceptionally low mechanical dissipation when combined with “soft-clamping”—a form of phononic engineering. Specifically, using a nonuniform phononic crystal pattern, we colocalize the strain and flexural motion of a free-standing silicon nitride nanobeam. Ringdown measurements at room temperature reveal string-like vibrational modes with quality ( Q ) factors as high as 800 million and Q × frequency exceeding 10 15 hertz. These results illustrate a promising route for engineering ultracoherent nanomechanical devices.

Samarium supersensorsPiezoelectric materials produce electric charge in response to changes in stress and are thus good sensor materials. One challenge has been growing single-crystal piezoelectrics with uniform properties. As of now, much of the crystal is discarded because of compositional variations. Li et al. synthesized single crystals of samarium-doped Pb(Mg1/3Nb2/3)O3-PbTiO3 that have uniform and extremely high piezoelectric properties (see the Perspective by Hlinka). These crystals are ideal for a variety of sensing applications and could reduce cost by eliminating waste.Science, this issue p. 264; see also p. 228High-performance piezoelectrics benefit transducers and sensors in a variety of electromechanical applications. The materials with the highest piezoelectric charge coefficients (d33) are relaxor-PbTiO3 crystals, which were discovered two decades ago. We successfully grew Sm-doped Pb(Mg1/3Nb2/3)O3-PbTiO3 (Sm-PMN-PT) single crystals with even higher d33 values ranging from 3400 to 4100 picocoulombs per newton, with variation below 20% over the as-grown crystal boule, exhibiting good property uniformity. We characterized the Sm-PMN-PT on the atomic scale with scanning transmission electron microscopy and made first-principles calculations to determine that the giant piezoelectric properties arise from the enhanced local structural heterogeneity introduced by Sm3+ dopants. Rare-earth doping is thus identified as a general strategy for introducing local structural heterogeneity in order to enhance the piezoelectricity of relaxor ferroelectric crystals.

Poly(vinylidene fluoride), PVDF, as one of important polymeric materials with extensively scientific interests and technological applications, shows five crystalline polymorphs with α, β, γ, δ and ε phases obtained by different processing methods. Among them, β phase PVDF presents outstanding electrical characteristics including piezo-, pyro-and ferroelectric properties. These electroactive properties are increasingly important in applications such as energy storage, spin valve devices, biomedicine, sensors and smart scaffolds. This article discusses the basic knowledge and character methods for PVDF fabrication and provides an overview of recent advances on the phase modification and recent applications of the β phase PVDF are reported. This study may provide an insight for the development and utilization for β phase PVDF nanofilms in future electronics.

In the present review, we focused on the fundamental concepts of hydrogels—classification, the polymers involved, synthesis methods, types of hydrogels, properties, and applications of the hydrogel. Hydrogels can be synthesized from natural polymers, synthetic polymers, polymerizable synthetic monomers, and a combination of natural and synthetic polymers. Synthesis of hydrogels involves physical, chemical, and hybrid bonding. The bonding is formed via different routes, such as solution casting, solution mixing, bulk polymerization, free radical mechanism, radiation method, and interpenetrating network formation. The synthesized hydrogels have significant properties, such as mechanical strength, biocompatibility, biodegradability, swellability, and stimuli sensitivity. These properties are substantial for electrochemical and biomedical applications. Furthermore, this review emphasizes flexible and self-healable hydrogels as electrolytes for energy storage and energy conversion applications. Insufficient adhesiveness (less interfacial interaction) between electrodes and electrolytes and mechanical strength pose serious challenges, such as delamination of the supercapacitors, batteries, and solar cells. Owing to smart and aqueous hydrogels, robust mechanical strength, adhesiveness, stretchability, strain sensitivity, and self-healability are the critical factors that can identify the reliability and robustness of the energy storage and conversion devices. These devices are highly efficient and convenient for smart, light-weight, foldable electronics and modern pollution-free transportation in the current decade.