Electron spin resonance scanning tunneling microscopy (ESR-STM) is a groundbreaking technique that combines atomic-scale spatial resolution with quantum coherent manipulation capability. Over the past decade, rapid advancements in this field have expanded its scope beyond the initial focus on control of single electron spins. This review summarizes the latest developments in this field that transcend the single-spin paradigm, highlighting three directions: tip-based ESR-STM for quantum sensing, multi-spin ESR-STM for quantum gate operations, and nuclear-spin ESR-STM for high-fidelity qubits. The versatility of ESR-STM lies in its ability to detect and coherently control various spin species while simultaneously providing atomic-scale information. This multifaceted capability, combined with recent paradigm-shifting advances, suggests that ESR-STM’s full potential is yet to be realized.

Understanding and controlling the dynamic interactions between fluid flows and solid materials and structures-a field known as fluid-structure interaction-is central not only to established disciplines such as aerospace and naval engineering, but also to emerging technologies such as energy harvesting, soft robotics, and biomedical devices. In recent years, the advent of metamaterials has provided exciting opportunities to rethink and redesign fluid-structure interactions. The idea of engineering the internal structure of materials that interface with fluid flows opens a new horizon for the precise and effective manipulation and control of coupled fluidic, acoustic, and elastodynamic responses. This review focuses on this relatively unexplored interdisciplinary theme with broad technological significance. Salient potential applications, such as reduction of fuel consumption in transport systems, efficiency of renewable energy extraction, noise mitigation, and resilience against structural fatigue, depend on controlling interactions among flow, acoustic, and vibration mechanisms. Flow control, for example, which spans a wealth of regimes such as laminar, transitional, turbulent, and unsteady separated flows, is strongly influenced by fluid-structure interaction. This review surveys and discusses conceptual frameworks that describe the interplay between fluids and elastic solids, with a focus on contemporary and emerging concepts. The paper is organised into three main sections: fluid-structure and flow-phonon interactions, flow-induced acoustic interactions with metamaterials, and exotic metamaterial concepts with potential impact on fluid-structure interaction. It concludes with perspectives on current challenges and future directions in this rapidly expanding area of research.

Extremal materials are a specific class of Cauchy materials whose elasticity tensor has one or more zero eigenvalues. Each zero eigenvalue corresponds to a soft mode requiring zero strain energy, while non-zero eigenvalues correspond to hard modes that cost energy. According to the number, N, of zero eigenvalues, these materials can be referred to as unimode (N=1), bimode (N=2), etc. Extremal materials have enabled novel functions beyond conventional Cauchy media, e.g., phonon polarizers, Rayleigh wave isolators and underwater acoustic cloaks. These functions typically require a single extremal material. Interfaces between two extremal materials exhibit rich wave behaviors, yet have been seldom explored. Here, we proposed the concept of complementary extremal materials, i.e., the soft mode of one extremal material is a hard mode of the other. As one example, we study the interface between an isotropic unimode material and an isotropic bimode material. We show that the interface allows perfect mode conversion from longitudinal waves to transverse waves. A low-frequency underwater acoustic insulator based on complementary extremal materials is proposed. Our finding has been verified with designed metamaterials and using effective-medium modeling. This work demonstrates the potential of complementary extremal materials in controlling elastic wave polarization and waterborne sound.

The asymmetric transformation elasticity provides a promising method for controlling elastic waves. However, it requires elastic materials capable of supporting asymmetric stresses, which are not admissible within the linearized Cauchy elasticity under small deformations. In contrast, asymmetric stress tensors naturally arise in micropolar continuum theory, yet the connection between micropolar media and the asymmetric transformation elasticity has remained largely unexplored. In this work, we demonstrate that extremal micropolar media, which are micropolar materials exhibiting soft modes, can be used to design elastic cloaks via asymmetric transformation elasticity. Our first contribution is to establish a rigorous theoretical formulation of the asymmetric transformation method within the micropolar continuum framework. Second, we propose a micropolar meta-material model that exhibits required soft modes for cloaking. A two-dimensional metamaterial cloak is then constructed and its cloaking performance is verified through full-wave numerical simulations. This study unveils a novel strategy for controlling elastic waves through micropolar media and also sheds light on interesting physical properties of extremal micropolar materials.

The design of elastic metamaterials with prescribed dispersion curves, which define the relationship between wave frequency and wavenumber, poses significant challenges due to its nonlinear and non-convex nature. This study introduces a novel optimization framework to tailor 2D elastic metamaterials dispersion relations utilizing a genetic algorithm. The proposed method encodes beam configurations in a binary vector and employs topology optimization to evolve structures toward desired dispersion characteristics. By representing dispersion curves with polynomial functions, constraints are applied to ensure the desired properties of monotonic and non-monotonic dispersion bands, such as roton-like and plateau-shaped behaviors. The approach demonstrates its robustness and versatility in achieving diverse dispersion profiles, validated through numerical simulations. Results reveal the ability to create unique wave phenomena by nonlocal interaction, paving the way for on-demand wave manipulation in advanced engineering applications.

Recently, we revealed anomalous static response in metamaterials with strong beyond-nearest-neighbor interactions or nonlocal interactions. Therein, the displacement field of a metamaterial beam when stretched is not simply linear in space like for ordinary materials, but rather exhibits pronounced spatial oscillations. The unusual behavior originates from evanescent Bloch modes at zero frequency, or frozen evanescent modes, with large decaying length. Here, we start from a discrete nonlocal mass-and-spring model and adopt an effective-medium approach based on higher-order differential equation to describe the anomalous behaviors. We demonstrate that the theory well captures the frozen evanescent modes and predicates the exact spatial oscillations of the displacement field. The strong dependence of the displacement field on the beam length is also revealed. The feasibility of the effective-medium approach is validated by comparison with the uniaxial tensile test results of metamaterials designed to support the anomalous frozen evanescent phonons. This theory can potentially be used for exploring other intriguing phenomena in nonlocal materials.

Yujeong Bae, Paola Ceroni, and Yi Chen introduce the Nanoscale and Nanoscale Advances themed collection on ‘Quantum nanomaterials – emerging platforms for next-generation quantum science and technology’.

The fractional quantum anomalous Hall effect (FQAHE) exhibited in fractional Chern insulators has recently been demonstrated in twisted MoTe2 and rhombohedral graphene/hBN moiré superlattices, promising new routes toward topological quantum computation. Central to realizing this promise is the understanding of the underlying microscopic mechanism. This, however, remains elusive in the case of rhombohedral graphene, with the crux being its two seemingly paradoxical conditions: a pronounced small-twist-angle (θ) moiré interface, yet only when electrons are kept distant from it. Here, by scanning tunnelling microscopic imaging with both conditions fulfilled, we capture dramatic electronic structure reshaping in rhombohedral hexalayer graphene by unforeseen 'trans-moiré orbitals', which emerge on the other, distant side of the moiré interface but nevertheless enforce the moiré periodicity at all measured fillings. We visualize a hierarchy of spatially and energetically distinct trans-moiré orbitals which doped electrons must sequentially occupy–the lowest-energy orbital, expectedly responsible for the FQAHE at small fillings, carries a hollow-cage-like shape. Remarkably, these trans-moiré orbitals vanish at θ ≳ 1°, and so do QAHE plateaus in similar devices. Simulations reveal an interaction-driven charge-redistribution mechanism which shapes the trans-moiré orbitals and corresponding Chern minibands. With our findings providing the missing microscopic link, the paradoxical conditions find a natural explanation: electrons are not simply kept distant from a small-θ moiré interface; they are forced into topological trans-moiré orbitals, forged precisely under such conditions. Our microscopic diagnostics unlocks a wide range of possible 'synthetic' FQAHE platforms.

Zero modes, which are deformations that cost zero energy, underlie many exotic behaviors in elastic metamaterials. While classical linear Cauchy elasticity explains many of these modes, those linked to the rotations of metamaterial inner components often lie beyond its scope. Micropolar elasticity, which incorporates translation and rotation degrees of freedom, provides a framework for capturing these rotational modes. Herein, we present the first complete symmetry-based classification of zero modes in two-dimensional micropolar solids, with an emphasis on rotation-related modes. Guided by this classification, we construct threefold rotationally symmetric micropolar metamaterials and realize typical rotational micropolar zero modes. We further show that these metamaterials exhibit wave phenomena forbidden in Cauchy continua, including the emergence of three bulk waves in the long-wavelength limit and associated triple refraction, chiral acoustic modes, as well as strong wave anisotropy. All intriguing properties are quantitatively captured by micropolar continuum descriptions, whereas the classical Cauchy continuum theory fails to predict these behaviors, even at a qualitative level. Our results establish a general framework for engineering rotation-based zero modes, opening avenues for designing metamaterials with novel wave properties.

Ohm's law of electric conduction is local in the sense that the current density at one position only depends on the electric field at that same position. For a nonlocal medium, the current density at one position depends on the electric field at other positions within the medium as well. As a result of Ohm's law, doubling the length of a wire doubles its resistance. Here, electrically conducting nonlocal architectures are discussed theoretically and experimentally for which changing the length of the metawire rather leads to a complex oscillatory behavior versus wire length. This oscillatory behavior is connected to local currents inside of the metawire flowing in the opposite direction than the externally applied field. The theoretical and experimental results for electric conduction can directly be transferred to thermal conduction or particle diffusion and may enable remote sensing applications.

Interface states and edge states in periodic structures have been extensively investigated in the context of topological dynamics over the past decades. In this study, we propose an impedance method based on surface impedance to analyze interface and edge states in one-dimensional (1D) periodic chains. The impedances are defined analytically from the Bloch eigen-modes of the periodic chains. At interface between two periodic structures, interface states arise at the frequencies where the impedances of the two structures become the same. Likewise, edge states occur when the impedance of the structure match the boundary impedance. This approach is universal for studying trivial and topological interface and edge states in 1D chain with different types of boundary conditions. We demonstrate this point with three representative examples: a chain comprising two periodic lattices, a chain anchored to ground springs at both ends, and a symmetric chain with interfacial defects. The analysis of topological interface states offers a vivid physical perspective, revealing that the topological interface states are either symmetric or anti-symmetric modes. Furthermore, we show that the frequency of the symmetric topological sate can be tuned via a single spring at the interface. This finding can be used to design tunable topological devices.

In two-dimensional van der Waals magnetic materials, the interplay between magnetism and electron correlation can give rise to new ground states and lead to novel transport and optical properties. A fundamental question in these materials is how the electron correlation manifests and interacts with the magnetic orders. In this study, we demonstrate that the recently discovered 2D antiferromagnetic material, CrSBr is a Mott insulator, through the combined use of resonant and temperature-dependent angle-resolved photoemission spectroscopy techniques, supplemented by dynamical mean-field theory analysis. Intriguingly, we found that as the system transitions from the antiferromagnetic to the paramagnetic phases, its Mott bands undergo a reconfiguration, and a coherent-incoherent crossover, driven by the dissolution of the magnetic order. Our findings reveal a distinctive evolution of band structure associated with magnetic phase transitions, shedding light on the investigation of the intricate interplay between correlation and magnetic orders in strongly correlated van der Waals magnetic materials.

Abstract Over the past 3 decades, phononic crystals experienced revolutionary development for understanding and utilizing mechanical waves by exploring interaction between mechanical waves and structures. With the significant advances in manufacture technologies from nanoscale to macroscale, phononic crystals attract researchers from diverse disciplines to study abundant directions such as bandgaps, dispersion engineering, novel modes, reconfigurable control, efficient design algorithms and so on. The aim of this roadmap is to present the current state of the art, an overview of properties, functions and applications of phononic crystals, opinions on the challenges and opportunities. The various perspectives cover wide topics on basic property, homogenization, machine learning assisted design, topological, non-Hermitian, nonreciprocal, nanoscale, chiral, nonlocal, active, spatiotemporal, hyperuniform properties of phononic crystals, and applications in underwater acoustics, seismic wave protection, vibration and noise control, thermal transport, sensing, acoustic tweezers, written by over 40 renown experts. It is also intended to guide researchers, funding agencies and industry in identifying new prospects for phononic crystals in the upcoming years.

Beams are fundamental objects in solid mechanics, displaying flexural and torsional modes in three dimensions, and support important applications across all fields of engineering. Here, we introduce Maxwell lattice topological mechanics to beams and present a Maxwell beam model that supports topological floppy flexural modes, localized exclusively at one of its ends. We introduce a modified topological index for this Maxwell beam which lacks a complete band gap, and establish a relation between Maxwell topological polarization and frozen evanescent phonons, shedding new light on the bulk origin of the topological localization. The floppy eigenmodes and their exceptional robustness against defects are experimentally validated through vibration measurements on 3D laser-printed samples at kHz frequencies. This study opens new avenues in fields from mechanical and civil engineering to robotics by introducing topologically polarized mechanics in slender structures.

The aim of rationally designed composites called metamaterials or metasurfaces is to achieve effective properties that go beyond those of their constituent parts. For periodic architectures, the design can draw on concepts from solid-state physics, such as crystal symmetries, reciprocal space, band structures and Floquet–Bloch eigenfunctions. Recently, nonlocality has emerged as a design paradigm, enabling both static and dynamic properties that are unattainable with a local design. In principle, all material properties described by linear response functions can be nonlocal, but for ordinary solids, local descriptions are mostly good approximations, leaving nonlocal effects as corrections. However, metamaterials and metasurfaces can be designed to go far beyond local behaviour. This Review covers these anomalous behaviours in elasticity, acoustics, electromagnetism, optics and diffusion. In the dynamic regime, nonlocal interactions enable versatile band structure and refraction engineering. In the static regime, they result in large decay lengths of ‘frozen’ evanescent Bloch modes, leading to strong size effects. For zero modes, the decay length diverges. Nonlocality has gained increasing attention in metamaterial and metasurface design. This Review discusses recent advances, focusing on the physical mechanisms of nonlocality that lead to intriguing properties and functions.

Interface states and edge states in periodic structures have been extensively investigated in the context of topological dynamics over the past decades. In this study, we propose an impedance method based on surface impedance to analyze interface and edge states in one-dimensional (1D) periodic chains. The impedances are defined analytically from the Bloch eigen-modes of the periodic chains. At the interface between two periodic structures, interface states arise at the frequencies where the impedances of the two structures become the same. Likewise, edge states occur when the impedance of the structure matches the boundary impedance. This approach is universal for studying trivial and topological interface and edge states in 1D chain with different types of boundary conditions. We demonstrate this point with three representative examples: a chain comprising two periodic lattices, a chain anchored to ground springs at both ends, and a symmetric chain with interfacial defects. The analysis of topological interface states offers a vivid physical perspective, revealing that the topological interface states are either symmetric or antisymmetric modes. Furthermore, we show that the frequency of the symmetric topological state can be tuned via a single spring at the interface. This finding can be used to design tunable topological devices.

Recent advances in additive manufacturing have opened up new possibilities to print almost arbitrary structures with submicrometer resolution. An intriguing application is the fabrication of metamaterial-based scaffolds with unprecedented precision and with defined effective elastic properties for mechanobiological research. This field of study has already led to promising results but remains wide open. The vast possibilities, together with the high interdisciplinary character and current lack of established protocols or literature on the subject, are intriguing on the one hand but might discourage researchers who are new to this field. In this review, we aim to provide insights into the work with such microstructured biometamaterials, mainly based on our own experience with 2D systems, hoping to encourage further mechanobiological studies. Finally, we present some considerations for expanding to the third dimension to more closely resemble the in vivo situation.

We observe maxon-like dispersion of ultrasonic guided waves in elastic metamaterials consisting of a rectangular beam and an array of cylindrical resonators. The pillars act as asymmetric resonators that induce a strong modal hybridization. We experimentally observe the strongly localized maxon mode with zero group velocity. Our study also demonstrates a unique feature of the maxon with a down-shifting peak frequency in space. To reveal the fundamental mechanism, we conduct comprehensive numerical studies on all frieze group symmetries and key geometric parameters.

A theoretical paper based on chiral micropolar effective-medium theory suggested the possibility of unusual roton-like acoustical-phonon dispersion relations in 3D elastic materials. Here, as a first novelty, the corresponding inverse problem is solved, that is, a specific 3D chiral elastic metamaterial structure is designed, the behavior of which follows this effective-medium description. The metamaterial structure is based on a simple-cubic lattice of cubes, each of which not only has three translational but also three rotational degrees of freedom. The additional rotational degrees of freedom are crucial within micropolar elasticity. The cubes and their degrees of freedom are coupled by a chiral network of slender rods. As a second novelty, this complex metamaterial is manufactured in polymer form by 3D laser printing and its behavior is characterized experimentally by phonon-band-structure measurements. The results of these measurements, microstructure finite-element calculations, and solutions of micropolar effective-medium theory are in good agreement. The roton-like dispersion behavior of the lowest phonon branch results from two aspects. First, chirality splits the transverse acoustical branches as well as the transverse optical branches. Second, chirality leads to an ultrastrong coupling and hybridization of chiral acoustical and optical phonons at finite wavevectors.