We review a theoretical framework for the cuprate superconductors, rooted in a fractionalized Fermi liquid (FL*) description of the intermediate-temperature pseudogap phase at low doping. The FL* theory predicted hole pockets each of fractional areap/8at hole dopingp, in contrast to the areap/4in spin density wave theory. Magnetotransport measurements, including observation of the Yamaji angle, show clear evidence of hole pocket quasiparticles which can tunnel coherently between square lattice layers, and are consistent with the FL* description. The FL* phase of a single-band model is described using a layer construction with a pair of ancilla qubits on each site: the Ancilla layer model (ALM). Its mean field theory yields hole pockets of areap/8, and matches the gapped photoemission spectrum in the anti-nodal region of the Brillouin zone. Fluctuations are described by the SU(2) gauge theory of a background spin liquid with critical Dirac spinons. A Monte Carlo study of the thermal SU(2) gauge theory transforms the hole pockets into Fermi arcs in photoemission. One route to confinement of FL* upon lowering temperature yields ad-wave superconductor via a Kosterlitz-Thouless transition ofh/(2e)vortices, with nodal Bogoliubov quasiparticles featuring anisotropic velocities and vortices surrounded by charge order halos. An alternative route yields a charge-ordered metallic state that has quantum oscillations consistent with observations. These confinement transitions are driven by the condensation of a SU(2) fundamental Higgs field, which also provides a fractionalized description of intertwined orders. Increasing doping from the FL* phase in the ALM drives a transition to a conventional FL at large doping, passing through an intermediate strange metal regime. We formulate a theory of the FL*-FL metal-metal transition without a symmetry-breaking order parameter, using a critical quantum 'charge' liquid of mobile electrons in the presence of disorder, developed via an extension of the Sachdev-Ye-Kitaev model to two spatial dimensions. At low temperatures, and across optimal and over doping, we address the regimes of extended non-FL behavior by Griffiths effects near quantum phase transitions in disordered metals.Partly based on lectures by S S atBoulder School 2025, Dynamics of Strongly Correlated Electrons, 14-18 July.Lecture videos.Joint ICTP-WE Heraeus School and Workshop on Advances in Quantum Matter: Pushing the Boundaries, ICTP, Trieste, 4, 6 August 2025.Lecture videos.School on Quantum Dynamics of Matter, Light and Information, ICTP, Trieste, 18, 19 August 2025.Lecture videos.Croucher Advanced Study Institute for Fractional Chern Insulators, University of Hong Kong, 4, 5 September 2025.Lecture slides.Advanced School and Conference on Quantum Matter, ICTP Trieste, 1-12 December 2025.Lecture Notes.Lecture videos.
Auger photoelectron coincidence spectroscopy (APECS) has emerged as a powerful tool for probing electron-electron correlation in solids. When a photoexcited core hole decays via a core-valence-valence Auger transition, two valence holes are created in the final state. Consequently, the line shape of the Auger electron spectrum is influenced by both Coulomb and exchange interactions between the two holes. By simultaneously detecting the photoelectron and Auger electron emitted from a single photoionization event, APECS measurements place constraints on the two final state holes, enabling one to independently measure Coulomb and exchange correlation energies. This review highlights the key advantages of APECS over other electron spectroscopic techniques including separating overlapping spectral features, removing the background signal from inelastically scattered electrons, enhanced surface sensitivity and site specificity. It also cites examples of how these attributes can be used to investigate the properties of solids in an unprecedented manner. To aid in understanding APECS data and assist in experimental design, a phenomenological model for the probability of electron pair emission as a function of the photo- and Auger electron kinetic energies and emission angles ispresented. The model is applied to a hypotheticalsolid, demonstrating how the contribution to APECS spectrum of final states with different spin configurations depends on these experimental parameters. A summary of results obtained by performing one-dimensional (as a function of Auger [EA]orphotoelectron [EP] kinetic energy), two-dimensional (parallel detection ofEAandEP) and angle-resolved (AR) (as a function ofEAat specific photo- and Auger electron emission angles) APECS measurements is presented. In particular, measurements of ferromagnetic metals and antiferromagnetic transition metal oxides demonstrate how AR-APECS is a powerful tool for independently measuring Coulomb and exchange correlation energies. Finally, potential future applications of APECS and further developments of this experimental technique are discussed.
The primary focus of spintronics is the investigation of novel spin splitting effects and related spin-polarized quantum materials, which have been extensively pursued for their potential applications. The structural inversion asymmetric Rashba splitting, bulk inversion asymmetric Dresselhaus splitting, and ferromagnetic spin polarization derived from Zeeman splitting constitute the foundation of traditional spintronics. From a symmetry perspective, ferromagnets achieve spin splitting through the breaking of time-reversal symmetry. However, in time-reversal symmetric and inversion symmetric materials with spin-orbit coupling, unexpected forms of spin-splitting can also arise by breaking local inversion symmetry, known as hidden spin-momentum locking (SML), bringing infinite vitality to fundamental research and future applications. This review first highlights notable advancements in spin-splitting within centrosymmetric systems, then examines the influence of hidden SM locking on superconducting and topological behaviors, concluding with a discussion on prospective opportunities in this emerging field. Given the rapid progress in non-relativistic spin splittings-particularly within altermagnetism-we develop appropriately scaled extensions to advance this emerging field. This review seeks to enhance our understanding of the 'hidden effect' in fundamental research while uncovering additional quantum phenomena that emerge from introducing extra degrees of freedom-an aspect that underscores the unique appeal of quantum materials capable of continuously demonstrating novel effects.
Photon condensation in semiconductor microcavities is a transformative technique for engineering quantum states of light at room temperature by tailoring strong but incoherent light-matter inter- actions. While continuous-wave and electrical pumping offer exceptional prospects for miniaturized quantum photonic technologies,harnessing these requires conceptual advances in understanding non- equilibrium light-matter dynamics in semiconductors. We resolve this challenge through an ab initio quantum kinetic theory capturing how Coulomb interactions of optically excited carriers and phonon scattering mediate photon thermalization and condensation in semiconductors. Our microscopic model shows that at high carrier densities, thermalization is dominated by carrier-carrier Coulomb scattering, in clear contrast to the rovibrational relaxation that governs dye-based photon conden- sates. The theory predicts a rich nonequilibrium phase diagram with thermal, Bose-condensed, multimode, and lasing phases, quantitatively in agreement with recent experiments. Crucially, we identify how cavity detuning controls transitions between equilibrium and gain-dominated regimes, enabling tailored design of coherent light sources. This work thus provides the foundation for semiconductor-based quantum photonic devices operating beyond conventional laser paradigms.
In solution, electrically like-charged particles can experience a strong and long-ranged attraction that leads to the formation of stable, slowly reorganizing clusters. The attractive force underpinning this spontaneous organization process has been shown to depend on both the sign of charge of the particle and the nature of the solvent medium. The origin of the attraction has been ascribed to the preferential orientation of solvent molecules at the object-electrolyte interface. Here, we use optical imaging to directly measure the spatial profile of the potential of mean force between isolated pairs of charged microspheres. Working with particles carrying a variety of surface chemistries we find that the range of the electrosolvation attraction is substantially longer than previously held. In particular we show that particles carrying strongly anionic surface coatings composed of DNA or phospholipid bilayers display long-range attraction. We further find that the length scale governing the decay of the attractive force can depend on the properties of the interacting particles. This contrasts with the canonical expectation that the screening length governing the interaction of charged particles in solution depends exclusively on the properties of the intervening electrolyte medium. The observations point to significant departures from current thinking, and the likely need for a model of interactions that accounts for the molecular nature of the solvent, its interfacial behaviour, and spatial correlations. Finally, a strong and long-ranged attraction mediated by anionic matter constituting lipid membranes and chromatin could carry far-reaching implications for organization and structure formation in biology.
Piezoelectric β-glycine is a promising molecular crystal, yet its controlled preparation remains challenging. Current nanoconfinement strategies, which rely primarily on rigid templates or simulations, cannot reliably capture the intrinsic confinement regime that leads to β-phase formation. Here, we propose electric-field-driven nanoconfinement as a one-step, continuous, and interface-free approach to investigate glycine crystallization and to define the confinement regime that yields the β-phase. We produced glycine nanoparticles via electrohydrodynamic spraying under a direct current field, automatically varying the spraying height to modulate nanoconfinement during nucleation and growth. Structural, morphological, and piezoelectric characterizations reveal that pure β-glycine forms within a crystal radius range of 5-120 nm. By integrating these findings with thermodynamic and kinetic analysis, we elucidate the mechanism of β-phase formation and construct a crystallization phase map that delineates the confinement conditions necessary for its stabilization. This work identifies the critical nanoconfinement parameters for accessing piezoelectric β-glycine and provides fundamental insights into polymorph control in molecular crystalline materials.
We present a generalization of linear response theory(LRT) for mixed jump-diffusion models-which combine both Gaussian and Lévy noise forcings that interact with the nonlinear dynamics-by deriving a comprehensive response formulas that accounts for perturbations to both the drift term and the jumps law. This class of models is particularly relevant for parameterizing the effects of unresolved scales in complex systems. Our formulas help thus quantifying uncertainties in either what needs to be parameterized (e.g. the jumps law), or measuring dynamical changes due to perturbations of the drift term (e.g. parameter variations). By generalizing the concepts of Kolmogorov operators and Green's functions, we obtain new forms of fluctuation-dissipation relations. The resulting response is decomposed into contributions from the eigenmodes of the Kolmogorov operator, providing a fresh look into the intimate relationship between a system's natural and forced variability. We demonstrate the theory's predictive power with two distinct climate-centric applications. First, we apply our framework to a paradigmatic El Niño-Southern Oscillation model subject to state-dependent jumps and additive white noise, showing how the theory accurately predicts the system's response to perturbations and how Kolmogorov modes can be used to diagnose its complex time variability. In a second, more challenging application, we use our LRT to perform accurate climate change projections in the Ghil-Sellers energy balance climate model, which is a spatially-extended model forced here by a spatio-temporalα-stable process. This work provides a comprehensive approach to climate modeling and prediction that enriches Hasselmann's program, with implications for understanding climate sensitivity, detection and attribution of climate change, and assessing the risk of climate tipping points. Our results may find applications beyond the realm of climate, and seem of relevance for epidemiology, biology, finance, and quantitative social sciences, among others.
Manipulating the nonlinear Hall effect (NLHE) through non-volatile approach is of great significance for device applications, yet effective gating control remains elusive. In this Letter, using first-principles calculations and symmetry analysis, we propose a universal design principle for gate-field control of the NLHE in bilayer systems. Using bilayer SnSe and SnTe, the well-known ferroelectric and thermoelectric materials, as examples, it reveals that the inherent hidden polarization can activate a layer-locked hidden Berry curvature dipole (BCD) under an applied gate field, thereby inducing a giant nonlinear Hall current. The hidden polarization locked to BCD in a gate field, experiences a pseudospin Zeeman field as a spin in magnetic field. Therefore, reversing the direction of the gate-field can switch the preferred pseudospin orientation, enabling the switchable second-order NLHE. The gate field strengthens the spin-orbit coupling, leading to energy-band splitting that further enhances the BCD contribution. This mechanism does not require intrinsic magnetism and provides a binary ON/OFF switching control method, greatly expanding the application potential of layered systems in nonlinear Hall transport. Our findings not only demonstrate the universal design principle of the switchable second-order NLHE but also can be extended to other gate-field-controllable nonlinear transport and nonlinear optics.
In twisted bilayer graphene (TBG) devices, local strain frequently coexists with the twist-angle-dependent moiré superlattice and strongly influences the electronic properties, yet their combined effects remain incompletely understood. Here, using low-temperature scanning tunneling microscopy, we study a TBG device exhibiting both a continuous twist-angle gradient from 0.35° to 1.30° and spatially varying strain fields, spanning the first (1.1°), second (0.5°), and third (0.3°) magic angles. We directly visualize the evolution of flat and remote bands in both energy and real space with atomic resolution. By comparing regions dominated by shear, uniaxial, and mixed strain, we find that shear strain plays a decisive role in controlling flat-band separation, linewidth, and spectral-weight redistribution. Near the first magic angle, this manifests as an anomalous transfer of spectral weight between the two flat-band peaks, accompanied by an unusual spatial dispersion of flat-band states within a moiré unit cell. In contrast, the energy of the remote bands provides a robust, strain-insensitive indicator of the local twist angle. Structural analysis reveals that shear strain dominates over large regions of the sample, consistent with its lower elastic energy cost. All observations are quantitatively reproduced by a continuum model incorporating heterostrain and electron-electron interactions, establishing shear strain as a central ingredient in shaping the low-energy electronic landscape of TBG.
This study delves into the concept of quantum phases in open quantum systems, examining the shortcomings of existing approaches that focus on steady states of Lindbladians and highlighting their limitations in capturing key phase transitions. In contrast to these methods, we introduce the concept of imaginary-time Lindbladian evolution as an alternative framework. This new approach defines gapped quantum phases in open systems through the spectrum properties of the imaginary-Liouville superoperator. We find that, in addition to all pure gapped ground states, the Gibbs state of a stabilizer Hamiltonian at any finite temperature can also be characterized by our scheme, demonstrated through explicit construction. Moreover, the closing of the imaginary Liouville gap is associated with the divergence of the Markov length, which has recently been proposed as an indicator of phase transitions in open quantum systems. To illustrate the effectiveness of this framework, we apply it to investigate the phase diagram for open systems withZ2σ×Z2τsymmetry, including cases with nontrivial average symmetry protected topological order or spontaneous symmetry breaking order. Our findings demonstrate universal properties at quantum criticality, such as nonanalytic behaviors of steady-state observables, divergence of correlation lengths, and closing of the imaginary-Liouville gap. These results advance our understanding of quantum phase transitions in open quantum systems. In contrast, we find that the steady states of real-time Lindbladians do not provide an effective framework for characterizing phase transitions in open systems.
We develop a unified framework for open quantum systems composed of many mutually interacting quantum spins, or any isomorphic systems like qubits and qudits, surrounded by one or more independent bosonic baths. Our framework, based on Schwinger-Keldysh field theory (SKFT), can handle arbitrary spin valueS, dimensionality of space, and geometry, while being applicable to a large parameter space for system and bath. It can probe regimes in whichnon-Markovian dynamicsand nonperturbative effects pose formidable challenges for other state-of-the-art theoretical methods. This is achieved by working with the two-particle irreducible (2PI) effective action, which resums classes of Feynman diagrams of SKFT to an infinite order. Furthermore, such diagrams are generated via an expansion in1/N, whereNis the number of Schwinger bosons we employ to map spin operators onto canonically commuting ones, rather than via conventional expansion in system-bath coupling constant. We carefully benchmark our SKFT+2PI-computed results vs. numerically (quasi)exact ones from tensor network calculations applied to the archetypical spin-boson model where both methodologies are applicable. Additionally, we demonstrate the capability of SKFT+2PI to handle a much more complex spin-chain-boson model with multiple baths interacting with each spin where no benchmark from other methods is available at present. The favorable numerical cost of solving integro-differential equations produced by the SKFT+2PI framework with an increasing number of spins and time steps makes it a promising route for simulating driven-dissipative systems in quantum computing, quantum magnonics, and quantum spintronics.
In complex oxides, charge carriers often couple strongly with lattice vibrations to form polarons-entangled electron-phonon quasiparticles whose transport properties remain difficult to characterize. Experimental access to intrinsic polaronic transport requires ultraclean samples, while theoretical description demands methods beyond low-order perturbation theory. Here, we show a predictive theory-experiment workflow to study polaron transport in complex oxides. Focusing on a prototypical polaronic oxide, anatase TiO2, we combine growth of high-quality oxygen-vacancy-doped films using hybrid molecular beam epitaxy with a first-principles electron-phonon diagrammatic Monte-Carlo (FEP-DMC) framework recently developed for accurate polaron predictions. Our films exhibit record-high electron mobility for anatase TiO2, in excellent agreement with FEP-DMC calculations conducted prior to experiment, which predict a room-temperature mobility of 45 ± 15 cm-2V-1s-1and a mobility-temperature scaling ofμ∝T-1.9 ± 0.077. Microscopic analysis using scanning transmission electron microscopy and x-ray photoelectron spectroscopy reveals the role of oxygen vacancies in modulating transport at lower temperatures. FEP-DMC further provides quantitative insight into polaron formation energy, phonon cloud distribution, lattice distortion around the polaron, and the polaronic contribution to mobility. Together, these results provide a deeper microscopic understanding of large-polaron transport in a complex oxide and provide the blueprint to characterize other polaronic materials.
To understand the emergence of macroscopic irreversibility from microscopic reversible dynamics, the idea of coarse-graining plays a fundamental role. In this work, we develop a unified inferential framework formacroscopic states, that is, coarse descriptions of microscopic quantum systems that can be inferred from macroscopic measurements. Building on quantum statistical sufficiency and Bayesian retrodiction, we characterize macroscopic states through equivalent abstract (algebraic) and explicit (constructive) formulations. Central to our approach is the notion ofobservational deficit, which quantifies the degree of irretrodictability of a state relative to a prior and a measurement. This leads to a general definition of macroscopic entropy as an inferentially grounded measure of asymmetry under Bayesian inversion. We formalize this structure in terms ofinferential reference frames, defined by the pair consisting of a prior and a measurement, which encapsulate the observer's informational perspective. We then formulate a resource theory of microscopicity, treating macroscopic states as free states and introducing a hierarchy ofmacroscopicity-non-generating operations. This theory unifies and extends existing resource theories of coherence, athermality, and asymmetry. Finally, we apply the framework to study quantum correlations under observational constraints, introducing the notion ofobservational discordand deriving necessary and sufficient conditions for their vanishing in terms of information recoverability. This work is dedicated to Professor Ryszard Horodecki on the occasion of his 80th birthday, in deep admiration and gratitude for his pioneering contributions to quantum information theory.
Strain relaxation at lattice-mismatched interfaces is critical for epitaxial growth and high-quality single-crystal films. While van der Waals (vdW) epitaxy is considered as a promising platform due to its high tolerance to lattice mismatch, its actual response to lattice mismatch remains largely unexplored. Here, we investigate the effect of lattice mismatch on vdW interfaces by epitaxially growing MoS2on WS2or WSe2substrate. annular dark-field scanning transmission electron microscopy reveals that MoS2/WS2with a negligible lattice mismatch of ∼0.22% forms a fully commensurate structure, whereas MoS2/WSe2with a large lattice mismatch of ∼3.96% exhibits non-uniform moiré patterns, characteristic of an incommensurate interface. Detailed analysis shows that the MoS2/WS2hetero-bilayers exhibit perfectly aligned structure through compression of MoS2, whereas the MoS2/WSe2hetero-bilayers show elongation and rotation of moiré orientation driven by tensile strain. Notably, even small twist angles induce significant changes in moiré orientation, resulting in bent fringes that are indicative of local rotational distortions. Large lattice mismatch drives localized lattice distortion, where rotation of the MoS2lattice emerges as an energetically favorable mechanism for strain release, in contrast to commensurate alignment in small-mismatch systems. Our results establish moiré pattern analysis as a powerful framework for directly visualizing spatially varying strain and its relaxation pathways in vdW hetero-bilayers. Our work reveals previously inaccessible interfacial deformation modes in vdW hetero-bilayers and establishes moiré analysis as a powerful platform for strain engineering in 2D electronic and optoelectronic materials.
Band structure analysis is central to understanding wave propagation in periodic media; however, it becomes challenging in open systems owing to energy leakage. Photonic crystal (PhC) slabs exemplify such systems, featuring periodicity in thex-yplane and finite extent in thez-direction, and supporting diverse guided-mode resonances whose interactions give rise to phenomena such as bound states in the continuum (BICs), exceptional points (EPs), and circular polarisation states. Although numerical simulations can reveal these effects, effective non-Hermitian Hamiltonians are often employed to elucidate the underlying physical mechanisms. This approach, however, relies on manually selected resonant modes and may suffer from basis incompleteness. Here, a systematic first-principles approach is presented to derive the complex band structure. The minimal channels in the scattering matrix, either open or closed, are determined by the number of propagating bulk Bloch waves. The interactions between these waves fully reveal the complex band structure. For instance, two Bloch waves predict the leading-order imaginary frequencyω''and identify accidental BICs, each associated with a dual Fabry-Pérot mode, whereas three waves reveal robust Friedrich-Wintgen and symmetry-protected BICs together with the associated linewidth behaviours. Orthogonally polarised waves are further incorporated to characterise far-field polarisation and EPs. When extended to a two-dimensional periodic structure, this framework accurately predictsω'', encompasses all known BICs, and tracks their evolution with system parameters. Overall, this first-principles approach provides a unified foundation for studying complex band structure and facilitates the exploration of light confinement in periodic media.
The possibility that evolutionary forces-together with a few fundamental factors such as thermodynamic constraints, specific computational features enabling information processing, and ecological processes-might constrain the logic of living systems is tantalizing. However, it is often overlooked that any practical implementation of such a logic requires complementary circuitry that, in biological systems, happens through complex networks of genetic regulation, metabolic reactions, cellular signaling, communication, social and eusocial non-trivial organization. Here, we review and discuss how circuitries are not merely passive structures, but active agents of change that, by means of hierarchical and modular organization, are able to enhance and catalyze the evolution of evolvability. By analyzing the role of non-trivial topologies in major evolutionary transitions under the lens of statistical physics and nonlinear dynamics, we show that biological innovations are strictly related to circuitry and its deviation from trivial structures and (thermo)dynamic equilibria. We argue that sparse heterogeneous networks such as hierarchical modular, which are ubiquitously observed in nature, are favored in terms of the trade-off between energetic costs for redundancy, error-correction and maintenance. We identify three main features-namely, interconnectivity, plasticity and interdependency-pointing towards a unifying framework for modeling the phenomenology, discussing them in terms of dynamical systems theory, non-equilibrium thermodynamics and evolutionary dynamics. Within this unified picture, we also show that 'slow' evolutionary dynamics is an emergent phenomenon governed by the replicator-mutator equation as the direct consequence of a constrained variational nonequilibrium process. Overall, this work highlights how dynamical systems theory and nonequilibrium thermodynamics provide powerful analytical techniques to study biological complexity.
Physical reservoir computing (RC) systems have emerged as a prominent research frontier due to their exceptional efficiency in temporal information processing. However, existing implementations, predominantly utilizing resistive devices, face challenges pertaining to power efficiency and dynamic richness. Here, we propose a ferroelectric capacitor-linear capacitor (FC-LC) series device for RC implementation. By leveraging nonlinear polarization switching and back-switching, the FC-LC series device realizes two essential reservoir properties: nonlinearity and fading memory. In addition, the device exhibits an ultralow power consumption, which, along with its direct voltage readout capability, marks a significant advance over resistive reservoir devices. Moreover, the device features bidirectional operation and widely tunable time constants, thereby enhancing reservoir space dimensionality and state richness. Building upon these FC-LC series devices, a ferroelectric capacitive RC system is developed, which demonstrates superior performance in various benchmark tasks. By exploiting the bidirectional operation of the device, the RC system not only delivers enhanced performance in waveform classification but also enables high-accuracy multimodal digit recognition. Through strategically hybridizing the FC-LC series devices with varying time constants, the RC system achieves remarkable performance in Mackey-Glass time-series prediction. Our study paves the way for power-efficient, dynamic-rich RC systems capable of handling diverse temporal tasks.
In addition to topological lattice defects such as dislocations and disclinations, crystals are also accompanied by unavoidable ordinary defects, devoid of any non-trivial geometry or topology, among which vacancies, Schottky defects, substitutions, interstitials, and Frenkel pairs are the most common. In this work, we demonstrate that these ubiquitous ordinary lattice defects, although geometrically trivial, can nonetheless serve as universal probes of the non-trivial topology of electronic Bloch bands, and any change in the local topological environment in an otherwise normal insulator in terms of mid-gap bound states in their vicinity. We theoretically establish these generic findings by implementing a minimal model Hamiltonian describing time-reversal symmetry breaking topological and normal insulators on a square lattice, fostering such point defects. The defect-bound mid-gap modes are also shown to be robust against sufficiently weak random point-like charge impurities. Furthermore, we showcase experimental observation of such bound states by embedding ordinary crystal defects in two-dimensional acoustic Chern lattices, where precision-controlled hopping amplitudes are implemented via active meta-atoms and Green's-function-based spectroscopy is used to reconstruct spectra and eigenstates. Our combined theory-experiment study establishes ordinary lattice defects as probes of topology that should be germane in crystals of any symmetry and dimension, raising the possibility of arresting localized Majorana modes near such defects in the bulk of topological superconductors and to emulate ordinary-defect-engineered topological devices.
Leveraging membrane-dominated deformation modes, plate lattice metamaterials exhibit superior stiffness, strength, and toughness amongst all lattice metamaterials. Beyond mechanical performances, plate lattices are also emerging as versatile platforms for harnessing a broad spectrum of physical properties, including acoustical, thermal, and vibrational functionalities. This review presents a comprehensive overview of the design principles, classification schemes, underlying mechanisms, and multiphysical properties of plate lattice metamaterials. Architecturally, we propose a classification into three categories: (i) pure plates, (ii) perforated plates, and (iii) hybrid plates. In terms of functions, pure plate lattices maximize mechanical efficiency through in-plane stress transfer; perforated plates enable manufacturability and offer acoustic and thermal active geometries via engineered porosity; hybrid plates integrate truss or other elements to enhance vibration attenuation. The key property-governing mechanisms, such as membrane stress, resonance behaviors, Bragg scattering, forced convection, are deeply explained. We further highlight the intrinsic interplay between different physical responses, illustrating how a single geometric design can concurrently harness multiple functionalities. The review concludes with a forward-looking perspective on emerging applications and the integration of advanced physics-informed methods to accelerate the optimization and implementation of multifunctional plate lattices.
Raman spectroscopy is a widely used technique for the analysis of graphene materials within single academic and industry contexts. This technique is characterized by its ease of implementation, rapidity, and non-destructive nature. Spectra resulting from this technique typically consist of two bands (G and 2D), which gives the spectra a seemingly simple appearance. Indeed, as early as 2007, Raman criteria were proposed to determine the number of layers in a stack based solely on the Raman spectrum. However, a multitude of studies published since 2007 have demonstrated that behind this apparent simplicity lie multiple effects that affect the G and 2D bands, thereby rendering interpretation complex and the determination of the number of layers in a stack uncertain. Furthermore, Raman spectroscopy has emerged as a pivotal technique for the analysis of twisted structures and diverse stacking sequences, such as ABA and ABC, which have culminated in significant discoveries, including strongly correlated states such as unconventional superconductivity. In addition to the resonance effects associated with superlattice formation, the shape of the 2D band provides valuable insight into stacking types, although its interpretation remains complex. In this article, we propose a methodology for interpreting the 2D Raman band that is informed by a review of selected references of the extant literature as well as original data. A compendium of recommendations and a series of diagrams are also provided to address other physical effects that can complicate spectral interpretation.