Direct observation of highly confined phonon polaritons in suspended monolayer hexagonal boron nitride

Monolithically Structured van der Waals Materials for Volume-Polariton Refraction and Focusing

Polaritons, hybrid light and matter waves, offer a platform for subwavelength on-chip light manipulation. Recent works on planar refraction and focusing of polaritons all rely on heterogeneous components with different refractive indices. A fundamental question, thus, arises whether it is possible to configure two-dimensional monolithic polariton lenses based on a single medium. Here, we design and fabricate a type of monolithic polariton lens by directly sculpting an individual hyperbolic van der Waals crystal. The in-plane polariton focusing through sculptured step-terraces is triggered by geometry-induced symmetry breaking of momentum matching in polariton refractions. We show that the monolithic polariton lenses can be robustly tuned by the rise of van der Waals terraces and their curvatures, achieving a subwavelength focusing resolution down to 10% of the free-space light wavelength. Fusing with transformation optics, monolithic polariton lenses with gradient effective refractive indices, such as Luneburg lenses and Maxwell's fisheye lenses, are expected by sculpting polaritonic structures with gradually varied depths. Our results bear potential in planar subwavelength lenses, integrated optical circuits, and photonic chips.

Quantum effects in the interaction of low-energy electrons with light

The interaction between free electrons and optical fields constitutes a unique platform to investigate ultrafast processes in matter and explore fundamental quantum phenomena. Specifically, optically modulated electrons in ultrafast electron microscopy act as noninvasive probes that push space-time-energy resolution to the picometer-attosecond-microelectronvolt range. Electron energies well above the involved photon energies are commonly used, rendering a low electron-light coupling and, thus, only providing limited access to the wealth of quantum nonlinear phenomena underlying the dynamical response of nanostructures. Here, we theoretically investigate electron-light interactions between photons and electrons of comparable energies, revealing quantum and recoil effects that include a nonvanishing coupling of surface-scattered electrons to light plane waves, inelastic electron backscattering from confined optical fields, and strong electron-light coupling under grazing electron diffraction by an illuminated crystal surface. Our exploration of electron-light-matter interactions holds potential for applications in ultrafast electron microscopy.

Toward Optimum Coupling between Free Electrons and Confined Optical Modes

Free electrons are excellent tools to probe and manipulate nanoscale optical fields with emerging applications in ultrafast spectromicroscopy and quantum metrology. However, advances in this field are hindered by the small probability associated with the excitation of single optical modes by individual free electrons. Here, we theoretically investigate the scaling properties of the electron-driven excitation probability for a wide variety of optical modes including plasmons in metallic nanostructures and Mie resonances in dielectric cavities, spanning a broad spectral range that extends from the ultraviolet to the infrared region. The highest probabilities for the direct generation of three-dimensionally confined modes are observed at low electron and mode energies in small structures, with order-unity (∼100%) coupling demanding the use of <100 eV electrons interacting with eV polaritons confined down to tens of nanometers in space. Electronic transitions in artificial atoms also emerge as practical systems to realize strong coupling to few-eV free electrons. In contrast, conventional dielectric cavities reach a maximum probability in the few-percent range. In addition, we show that waveguide modes can be generated with higher-than-unity efficiency by phase-matched interaction with grazing electrons, suggesting a practical method to create multiple excitations of a localized optical mode by an individual electron through funneling the so-generated propagating photons into a confining cavity─an alternative approach to direct electron-cavity interaction. Our work provides a roadmap to optimize electron-photon coupling with potential applications in electron spectromicroscopy as well as nonlinear and quantum optics at the nanoscale.

Degree of disorder-regulated ion transport through amorphous monolayer carbon

Nanopore technology, re-fueled by two-dimensional (2D) materials such as graphene and MoS2, controls mass transport by allowing certain species while denying others at the nanoscale and has a wide application range in DNA sequencing, nano-power generation, and others. With their low transmembrane transport resistance and high permeability stemming from their ultrathin nature, crystalline 2D materials do not possess nanoscale holes naturally, thus requiring additional fabrication to create nanopores. Herein, we demonstrate that nanopores exist in amorphous monolayer carbon (AMC) grown at low temperatures. The size and density of nanopores can be tuned by the growth temperature, which was experimentally verified by atomic images and further corroborated by kinetic Monte Carlo simulation. Furthermore, AMC films with varied degrees of disorder (DOD) exhibit tunable transmembrane ionic conductance over two orders of magnitude when serving as nanopore membranes. This work demonstrates the DOD-tuned property in amorphous monolayer carbon and provides a new candidate for modern membrane science and technology.

Atomic-force-microscopy-based time-domain two-dimensional infrared nanospectroscopy

For decades, infrared (IR) spectroscopy has advanced on two distinct frontiers: enhancing spatial resolution and broadening spectroscopic information. Although atomic force microscopy (AFM)-based IR microscopy overcomes Abbe's diffraction limit and reaches sub-10 nm spatial resolutions, time-domain two-dimensional IR spectroscopy (2DIR) provides insights into molecular structures, mode coupling and energy transfers. Here we bridge the boundary between these two techniques and develop AFM-2DIR nanospectroscopy. Our method offers the spatial precision of AFM in combination with the rich spectroscopic information provided by 2DIR. This approach mechanically detects the sample's photothermal responses to a tip-enhanced femtosecond IR pulse sequence and extracts spatially resolved spectroscopic information via FFTs. In a proof-of-principle experiment, we elucidate the anharmonicity of a carbonyl vibrational mode. Further, leveraging the near-field photons' high momenta from the tip enhancement for phase matching, we photothermally probe hyperbolic phonon polaritons in isotope-enriched h10BN. Our measurements unveil an energy transfer between phonon polaritons and phonons, as well as among different polariton modes, possibly aided by scattering at interfaces. The AFM-2DIR nanospectroscopy enables the in situ investigations of vibrational anharmonicity, coupling and energy transfers in heterogeneous materials and nanostructures, especially suitable for unravelling the relaxation process in two-dimensional materials at IR frequencies.

Probing Hyperbolic Shear Polaritons in β-Ga2O3 Nanostructures Using STEM-EELS

Phonon polaritons, quasiparticles arising from strong coupling between electromagnetic waves and optical phonons, have potential for applications in subdiffraction imaging, sensing, thermal conduction enhancement, and spectroscopy signal enhancement. A new class of phonon polaritons in low-symmetry monoclinic crystals, hyperbolic shear polaritons (HShPs), have been verified recently in β-Ga2O3 by free electron laser (FEL) measurements. However, detailed behaviors of HShPs in β-Ga2O3 nanostructures still remain unknown. Here, by using monochromatic electron energy loss spectroscopy in conjunction with scanning transmission electron microscopy, the experimental observation of multiple HShPs in β-Ga2O3 in the mid-infrared (MIR) and far-infrared (FIR) ranges is reported. HShPs in various β-Ga2O3 nanorods and a β-Ga2O3 nanodisk are excited. The frequency-dependent rotation and shear effect of HShPs reflect on the distribution of EELS signals. The propagation and reflection of HShPs in nanostructures are clarified by simulations of electric field distribution. These findings suggest that, with its tunable broad spectral HShPs, β-Ga2O3 is an excellent candidate for nanophotonic applications.

High-quality nanocavities through multimodal confinement of hyperbolic polaritons in hexagonal boron nitride

Compressing light into nanocavities substantially enhances light-matter interactions, which has been a major driver for nanostructured materials research. However, extreme confinement generally comes at the cost of absorption and low resonator quality factors. Here we suggest an alternative optical multimodal confinement mechanism, unlocking the potential of hyperbolic phonon polaritons in isotopically pure hexagonal boron nitride. We produce deep-subwavelength cavities and demonstrate several orders of magnitude improvement in confinement, with estimated Purcell factors exceeding 108 and quality factors in the 50-480 range, values approaching the intrinsic quality factor of hexagonal boron nitride polaritons. Intriguingly, the quality factors we obtain exceed the maximum predicted by impedance-mismatch considerations, indicating that confinement is boosted by higher-order modes. We expect that our multimodal approach to nanoscale polariton manipulation will have far-reaching implications for ultrastrong light-matter interactions, mid-infrared nonlinear optics and nanoscale sensors.

Compensating losses in polariton propagation with synthesized complex frequency excitation

Surface plasmon polaritons and phonon polaritons offer a means of surpassing the diffraction limit of conventional optics and facilitate efficient energy storage, local field enhancement and highsensitivity sensing, benefiting from their subwavelength confinement of light. Unfortunately, losses severely limit the propagation decay length, thus restricting the practical use of polaritons. While optimizing the fabrication technique can help circumvent the scattering loss of imperfect structures, the intrinsic absorption channel leading to heat production cannot be eliminated. Here, we utilize synthetic optical excitation of complex frequency with virtual gain, synthesized by combining the measurements made at multiple real frequencies, to compensate losses in the propagations of phonon polaritons with dramatically enhanced propagation distance. The concept of synthetic complex frequency excitation represents a viable solution to the loss problem for various applications including photonic circuits, waveguiding and plasmonic/phononic structured illumination microscopy.

Observation of the nonanalytic behavior of optical phonons in monolayer hexagonal boron nitride

Phonon splitting of the longitudinal and transverse optical modes (LO-TO splitting), a ubiquitous phenomenon in three-dimensional polar materials, will break down in two-dimensional (2D) polar systems. Theoretical predictions propose that the LO phonon in 2D polar monolayers becomes degenerate with the TO phonon, displaying a distinctive "V-shaped" nonanalytic behavior near the center of the Brillouin zone. However, the full experimental verification of these nonanalytic behaviors has been lacking. Here, using monolayer hexagonal boron nitride (h-BN) as a prototypical example, we report the comprehensive and direct experimental verification of the nonanalytic behavior of LO phonons by inelastic electron scattering spectroscopy. Interestingly, the slope of the LO phonon in our measurements is lower than the theoretically predicted value for a freestanding monolayer due to the screening of the Cu foil substrate. This enables the phonon polaritons in monolayer h-BN/Cu foil to exhibit ultra-slow group velocity (~5 × 10-6 c, c is the speed of light) and ultra-high confinement (~ 4000 times smaller wavelength than that of light). These exotic behaviors of the optical phonons in h-BN presents promising prospects for future optoelectronic applications.

Accelerating Quantum Materials Development with Advances in Transmission Electron Microscopy

Quantum materials are driving a technology revolution in sensing, communication, and computing, while simultaneously testing many core theories of the past century. Materials such as topological insulators, complex oxides, superconductors, quantum dots, color center-hosting semiconductors, and other types of strongly correlated materials can exhibit exotic properties such as edge conductivity, multiferroicity, magnetoresistance, superconductivity, single photon emission, and optical-spin locking. These emergent properties arise and depend strongly on the material's detailed atomic-scale structure, including atomic defects, dopants, and lattice stacking. In this review, we describe how progress in the field of electron microscopy (EM), including in situ and in operando EM, can accelerate advances in quantum materials and quantum excitations. We begin by describing fundamental EM principles and operation modes. We then discuss various EM methods such as (i) EM spectroscopies, including electron energy loss spectroscopy (EELS), cathodoluminescence (CL), and electron energy gain spectroscopy (EEGS); (ii) four-dimensional scanning transmission electron microscopy (4D-STEM); (iii) dynamic and ultrafast EM (UEM); (iv) complementary ultrafast spectroscopies (UED, XFEL); and (v) atomic electron tomography (AET). We describe how these methods could inform structure-function relations in quantum materials down to the picometer scale and femtosecond time resolution, and how they enable precision positioning of atomic defects and high-resolution manipulation of quantum materials. For each method, we also describe existing limitations to solve open quantum mechanical questions, and how they might be addressed to accelerate progress. Among numerous notable results, our review highlights how EM is enabling identification of the 3D structure of quantum defects; measuring reversible and metastable dynamics of quantum excitations; mapping exciton states and single photon emission; measuring nanoscale thermal transport and coupled excitation dynamics; and measuring the internal electric field and charge density distribution of quantum heterointerfaces- all at the quantum materials' intrinsic atomic and near atomic-length scale. We conclude by describing open challenges for the future, including achieving stable sample holders for ultralow temperature (below 10K) atomic-scale spatial resolution, stable spectrometers that enable meV energy resolution, and high-resolution, dynamic mapping of magnetic and spin fields. With atomic manipulation and ultrafast characterization enabled by EM, quantum materials will be poised to integrate into many of the sustainable and energy-efficient technologies needed for the 21st century.

Four-dimensional electron energy-loss spectroscopy

Recent advances in scanning transmission electron microscopy have enabled atomic-scale focused, coherent, and monochromatic electron probes, achieving nanoscale spatial resolution, meV energy resolution, sufficient momentum resolution, and a wide energy detection range in electron energy-loss spectroscopy (EELS). A four-dimensional EELS (4D-EELS) dataset can be recorded with a slot aperture selecting the specific momentum direction in the diffraction plane and the beam scanning in two spatial dimensions. In this paper, the basic principle of the 4D-EELS technique and a few examples of its application are presented. In addition to parallelly acquired dispersion with energy down to a lattice vibration scale, it can map the real space variation of any EELS spectrum features with a specific momentum transfer and energy loss to study various locally inhomogeneous scattering processes. Furthermore, simple mathematical combinations associating the spectra at different momenta are feasible from the 4D dataset, e.g., the efficient acquisition of a reliable electron magnetic circular dichroism (EMCD) signal is demonstrated. This 4D-EELS technique provides new opportunities to probe the local dispersion and related physical properties at the nanoscale.

Functionalizing nanophotonic structures with 2D van der Waals materials

The integration of two-dimensional (2D) van der Waals materials with nanostructures has triggered a wide spectrum of optical and optoelectronic applications. Photonic structures of conventional materials typically lack efficient reconfigurability or multifunctionality. Atomically thin 2D materials can thus generate new functionality and reconfigurability for a well-established library of photonic structures such as integrated waveguides, optical fibers, photonic crystals, and metasurfaces, to name a few. Meanwhile, the interaction between light and van der Waals materials can be drastically enhanced as well by leveraging micro-cavities or resonators with high optical confinement. The unique van der Waals surfaces of the 2D materials enable handiness in transfer and mixing with various prefabricated photonic templates with high degrees of freedom, functionalizing as the optical gain, modulation, sensing, or plasmonic media for diverse applications. Here, we review recent advances in synergizing 2D materials to nanophotonic structures for prototyping novel functionality or performance enhancements. Challenges in scalable 2D materials preparations and transfer, as well as emerging opportunities in integrating van der Waals building blocks beyond 2D materials are also discussed.

Applications of Transmission Electron Microscopy in Phase Engineering of Nanomaterials

Phase engineering of nanomaterials (PEN) is an emerging field that aims to tailor the physicochemical properties of nanomaterials by precisely manipulating their crystal phases. To advance PEN effectively, it is vital to possess the capability of characterizing the structures and compositions of nanomaterials with precision. Transmission electron microscopy (TEM) is a versatile tool that combines reciprocal-space diffraction, real-space imaging, and spectroscopic techniques, allowing for comprehensive characterization with exceptional resolution in the domains of time, space, momentum, and, increasingly, even energy. In this Review, we first introduce the fundamental mechanisms behind various TEM-related techniques, along with their respective application scopes and limitations. Subsequently, we review notable applications of TEM in PEN research, including applications in fields such as metallic nanostructures, carbon allotropes, low-dimensional materials, and nanoporous materials. Specifically, we underscore its efficacy in phase identification, composition and chemical state analysis, in situ observations of phase evolution, as well as the challenges encountered when dealing with beam-sensitive materials. Furthermore, we discuss the potential generation of artifacts during TEM imaging, particularly in scanning modes, and propose methods to minimize their occurrence. Finally, we offer our insights into the present state and future trends of this field, discussing emerging technologies including four-dimensional scanning TEM, three-dimensional atomic-resolution imaging, and electron microscopy automation while highlighting the significance and feasibility of these advancements.

Research Progress in Surface-Enhanced Infrared Absorption Spectroscopy: From Performance Optimization, Sensing Applications, to System Integration

Infrared absorption spectroscopy is an effective tool for the detection and identification of molecules. However, its application is limited by the low infrared absorption cross-section of the molecule, resulting in low sensitivity and a poor signal-to-noise ratio. Surface-Enhanced Infrared Absorption (SEIRA) spectroscopy is a breakthrough technique that exploits the field-enhancing properties of periodic nanostructures to amplify the vibrational signals of trace molecules. The fascinating properties of SEIRA technology have aroused great interest, driving diverse sensing applications. In this review, we first discuss three ways for SEIRA performance optimization, including material selection, sensitivity enhancement, and bandwidth improvement. Subsequently, we discuss the potential applications of SEIRA technology in fields such as biomedicine and environmental monitoring. In recent years, we have ushered in a new era characterized by the Internet of Things, sensor networks, and wearable devices. These new demands spurred the pursuit of miniaturized and consolidated infrared spectroscopy systems and chips. In addition, the rise of machine learning has injected new vitality into SEIRA, bringing smart device design and data analysis to the foreground. The final section of this review explores the anticipated trajectory that SEIRA technology might take, highlighting future trends and possibilities.

In-plane hyperbolic polariton tuners in terahertz and long-wave infrared regimes

One of the main bottlenecks in the development of terahertz (THz) and long-wave infrared (LWIR) technologies is the limited intrinsic response of traditional materials. Hyperbolic phonon polaritons (HPhPs) of van der Waals semiconductors couple strongly with THz and LWIR radiation. However, the mismatch of photon - polariton momentum makes far-field excitation of HPhPs challenging. Here, we propose an In-Plane Hyperbolic Polariton Tuner that is based on patterning van der Waals semiconductors, here α-MoO₃, into ribbon arrays. We demonstrate that such tuners respond directly to far-field excitation and give rise to LWIR and THz resonances with high quality factors up to 300, which are strongly dependent on in-plane hyperbolic polariton of the patterned α-MoO₃. We further show that with this tuner, intensity regulation of reflected and transmitted electromagnetic waves, as well as their wavelength and polarization selection can be achieved. Our results can help the development of THz and LWIR miniaturized devices.

Mid-infrared analogue polaritonic reversed Cherenkov radiation in natural anisotropic crystals

Cherenkov radiation (CR) excited by fast charges can serve as on-chip light sources with a nanoscale footprint and broad frequency range. The reversed CR, which usually occurs in media with the negative refractive index or negative group-velocity dispersion, is highly desired because it can effectively separate the radiated light from fast charges thanks to the obtuse radiation angle. However, reversed CR at the mid-infrared remains challenging due to the significant loss of conventional artificial structures. Here we observe mid-infrared analogue polaritonic reversed CR in a natural van der Waals (vdW) material (i.e., α-MoO₃), whose hyperbolic phonon polaritons exhibit negative group velocity. Further, the real-space image results of analogue polaritonic reversed CR indicate that the radiation distributions and angles are closely related to the in-plane isofrequency contours of α-MoO₃, which can be further tuned in the heterostructures based on α-MoO₃. This work demonstrates that natural vdW heterostructures can be used as a promising platform of reversed CR to design on-chip mid-infrared nano-light sources.

Hyperbolic whispering-gallery phonon polaritons in boron nitride nanotubes

Light confinement in nanostructures produces an enhanced light-matter interaction that enables a vast range of applications including single-photon sources, nanolasers and nanosensors. In particular, nanocavity-confined polaritons display a strongly enhanced light-matter interaction in the infrared regime. This interaction could be further boosted if polaritonic modes were moulded to form whispering-gallery modes; but scattering losses within nanocavities have so far prevented their observation. Here, we show that hexagonal BN nanotubes act as an atomically smooth nanocavity that can sustain phonon-polariton whispering-gallery modes, owing to their intrinsic hyperbolic dispersion and low scattering losses. Hyperbolic whispering-gallery phonon polaritons on BN nanotubes of ～4 nm radius (sidewall of six atomic layers) are characterized by an ultrasmall nanocavity mode volume (V_m ≈ 10^-10λ₀³ at an optical wavelength λ₀ ≈ 6.4 μm) and a Purcell factor (Q/V_m) as high as 10¹². We posit that BN nanotubes could become an important material platform for the realization of one-dimensional, ultrastrong light-matter interactions, with exciting implications for compact photonic devices.

Single-atom vibrational spectroscopy with chemical-bonding sensitivity

Correlation of lattice vibrational properties with local atomic configurations in materials is essential for elucidating functionalities that involve phonon transport in solids. Recent developments in vibrational spectroscopy in a scanning transmission electron microscope have enabled direct measurements of local phonon modes at defects and interfaces by combining high spatial and energy resolution. However, pushing the ultimate limit of vibrational spectroscopy in a scanning transmission electron microscope to reveal the impact of chemical bonding on local phonon modes requires extreme sensitivity of the experiment at the chemical-bond level. Here we demonstrate that, with improved instrument stability and sensitivity, the specific vibrational signals of the same substitutional impurity and the neighbouring carbon atoms in monolayer graphene with different chemical-bonding configurations are clearly resolved, complementary with density functional theory calculations. The present work opens the door to the direct observation of local phonon modes with chemical-bonding sensitivity, and provides more insights into the defect-induced physics in graphene.

Phonon transition across an isotopic interface

Isotopic mixtures result in distinct properties of materials such as thermal conductivity and nuclear process. However, the knowledge of isotopic interface remains largely unexplored mainly due to the challenges in atomic-scale isotopic identification. Here, using electron energy-loss spectroscopy in a scanning transmission electron microscope, we reveal momentum-transfer-dependent phonon behavior at the h-¹⁰BN/h-¹¹BN isotope heterostructure with sub-unit-cell resolution. We find the phonons' energy changes gradually across the interface, featuring a wide transition regime. Phonons near the Brillouin zone center have a transition regime of ~3.34 nm, whereas phonons at the Brillouin zone boundary have a transition regime of ~1.66 nm. We propose that the isotope-induced charge effect at the interface accounts for the distinct delocalization behavior. Moreover, the variation of phonon energy between atom layers near the interface depends on both of momentum transfer and mass change. This study provides new insights into the isotopic effects in natural materials.

Fano Resonance in Near-Field Thermal Radiation of Two-Dimensional Van der Waals Heterostructures

Two-dimensional (2D) materials and their vertically stacked heterostructures have attracted much attention due to their novel optical properties and strong light-matter interactions in the infrared. Here, we present a theoretical study of the near-field thermal radiation of 2D vdW heterostructures vertically stacked of graphene and monolayer polar material (2D hBN as an example). An asymmetric Fano line shape is observed in its near-field thermal radiation spectrum, which is attributed to the interference between the narrowband discrete state (the phonon polaritons in 2D hBN) and a broadband continuum state (the plasmons in graphene), as verified by the coupled oscillator model. In addition, we show that 2D van der Waals heterostructures can achieve nearly the same high radiative heat flux as graphene but with markedly different spectral distributions, especially at high chemical potentials. By tuning the chemical potential of graphene, we can actively control the radiative heat flux of 2D van der Waals heterostructures and manipulate the radiative spectrum, such as the transition from Fano resonance to electromagnetic-induced transparency (EIT). Our results reveal the rich physics and demonstrate the potential of 2D vdW heterostructures for applications in nanoscale thermal management and energy conversion.

Polaritons in Van der Waals Heterostructures

2D monolayers supporting a wide variety of highly confined plasmons, phonon polaritons, and exciton polaritons can be vertically stacked in van der Waals heterostructures (vdWHs) with controlled constituent layers, stacking sequence, and even twist angles. vdWHs combine advantages of 2D material polaritons, rich optical structure design, and atomic scale integration, which have greatly extended the performance and functions of polaritons, such as wide frequency range, long lifetime, ultrafast all-optical modulation, and photonic crystals for nanoscale light. Here, the state of the art of 2D material polaritons in vdWHs from the perspective of design principles and potential applications is reviewed. Some fundamental properties of polaritons in vdWHs are initially discussed, followed by recent discoveries of plasmons, phonon polaritons, exciton polaritons, and their hybrid modes in vdWHs. The review concludes with a perspective discussion on potential applications of these polaritons such as nanophotonic integrated circuits, which will benefit from the intersection between nanophotonics and materials science.

Curvature-Induced One-Dimensional Phonon Polaritons at Edges of Folded Boron Nitride Sheets

Generation and manipulation of phonon polaritons are of paramount importance for understanding the interaction between an electromagnetic field and dielectric materials and furthering their application in mid-infrared optical communication. However, the formation of tunable one-dimensional phonon polaritons has been rarely realized in van der Waals layered structures. Here we report the discovery of curvature-induced phonon polaritons localized at the crease of folded hexagonal boron nitrides (h-BNs) with a few atomic layers using monochromated electron energy-loss spectroscopy. Compared to bulk regions, the creased-localized signals undergo an abnormal blue-shift of 1.4 meV. First-principles calculations reveal that the energy shift arises from the optical phonon hardening in the curled region. Interestingly, the curvature-induced phonon polariton can also be controllably achieved via an electron-beam etching approach. This work opens an avenue of tailoring local electromagnetic response and creating unique phonon polariton modes in van der Waals layered materials for diverse applications.

Entangling free electrons and optical excitations

The inelastic interaction between flying particles and optical nanocavities gives rise to entangled states in which some excitations of the latter are paired with momentum changes in the former. Specifically, free-electron entanglement with nanocavity modes opens appealing opportunities associated with the strong interaction capabilities of the electrons. However, the achievable degree of entanglement is currently limited by the lack of control over the resulting state mixtures. Here, we propose a scheme to generate pure entanglement between designated optical-cavity excitations and separable free-electron states. We shape the electron wave function profile to select the accessible cavity modes and simultaneously associate them with targeted electron scattering directions. This concept is exemplified through theoretical calculations of free-electron entanglement with degenerate and nondegenerate plasmon modes in silver nanoparticles and atomic vibrations in an inorganic molecule. The generated entanglement can be further propagated through its electron component to extend quantum interactions beyond existing protocols.

Complete Excitation of Discrete Quantum Systems by Single Free Electrons

We reveal a wealth of nonlinear and recoil effects in the interaction between individual low-energy electrons (≲100  eV) and samples comprising a discrete number of states. Adopting a quantum theoretical description of combined free-electron and two-level systems, we find a maximum achievable excitation probability of 100%, which requires specific conditions relating to the coupling strength and the transition symmetry, as we illustrate through calculations for dipolar and quadrupolar modes. Strong recoil effects are observed when the kinetic energy of the probe lies close to the transition threshold, although the associated probability remains independent of the electron wave function even when fully accounting for nonlinear interactions with arbitrarily complex multilevel samples. Our work reveals the potential of free electrons to control localized excitations and delineates the boundaries of such control.

Recent Progress in Fabrication and Application of BN Nanostructures and BN-Based Nanohybrids

Due to its unique physical, chemical, and mechanical properties, such as a low specific density, large specific surface area, excellent thermal stability, oxidation resistance, low friction, good dispersion stability, enhanced adsorbing capacity, large interlayer shear force, and wide bandgap, hexagonal boron nitride (h-BN) nanostructures are of great interest in many fields. These include, but are not limited to, (i) heterogeneous catalysts, (ii) promising nanocarriers for targeted drug delivery to tumor cells and nanoparticles containing therapeutic agents to fight bacterial and fungal infections, (iii) reinforcing phases in metal, ceramics, and polymer matrix composites, (iv) additives to liquid lubricants, (v) substrates for surface enhanced Raman spectroscopy, (vi) agents for boron neutron capture therapy, (vii) water purifiers, (viii) gas and biological sensors, and (ix) quantum dots, single photon emitters, and heterostructures for electronic, plasmonic, optical, optoelectronic, semiconductor, and magnetic devices. All of these areas are developing rapidly. Thus, the goal of this review is to analyze the critical mass of knowledge and the current state-of-the-art in the field of BN-based nanomaterial fabrication and application based on their amazing properties.

Electron Microscopy Probing Electron-Photon Interactions in SiC Nanowires with Ultrawide Energy and Momentum Match

Light-matter interactions are commonly probed by optical spectroscopy, which, however, has some fundamental limitations such as diffraction-limited spatial resolution, tiny momentum transfer, and noncontinuous excitation/detection. In this work, through the use of scanning transmission electron microscopy-electron energy loss spectroscopy (STEM-EELS) with ultrawide energy and momentum match and subnanometer spatial resolution, the longitudinal Fabry-Perot (FP) resonating modes and the transverse whispering-gallery modes (WGMs) in individual SiC nanowires are simultaneously excited and detected, which span from near-infrared (∼1.2 μm) to ultraviolet (∼0.2 μm) spectral regime, and the momentum transfer can range up to 10⁸ cm^-1. The size effects on the resonant spectra of nanowires are also revealed. This work provides an alternative technique to optical resonating spectroscopy and light-matter interactions in dielectric nanostructures, which is promising for modulating free electrons via photonic structures.

Studying Plasmon Dispersion of MXene for Enhanced Electromagnetic Absorption

2D metal carbides and nitrides (MXene) are promising candidates for electromagnetic (EM) shielding, saturable absorption, thermal therapy, and photocatalysis owing to their excellent EM absorption. The plasmon resonances in metallic MXene micro/nanostructures may play an important role in enhancing the EM absorption; however, their contribution has not been determined due to the lack of a precise understanding of its plasmon behavior. Here, the use of high-spatial-resolution electron energy-loss spectroscopy to measure the plasmon dispersion of MXene films with different thicknesses is reported, enabling accurate analysis of the EM absorption of complex MXene structures in a wide frequency range via a theoretical model. The EM absorption of MXene can be excited at the desired frequency by controlling the momentum (e.g., the sizes of the nanoflakes for EM excitation) as the strength can be enhanced by increasing the layer number and the interlayer distance in MXene. For example, a 3 nm interlayer distance can nearly double the plasmon-enhanced EM absorption in MXene nanostructures. These findings can guide the design of advanced ultrathin EM absorption materials for a broad range of applications.

On-chip photonics and optoelectronics with a van der Waals material dielectric platform

During the last few decades, photonic integrated circuits have increased dramatically, facilitating many high-performance applications, such as on-chip sensing, data processing, and inter-chip communications. The currently dominating material platforms (i.e., silicon, silicon nitride, lithium niobate, and indium phosphide), which have exhibited great application successes, however, suffer from their own disadvantages, such as the indirect bandgap of silicon for efficient light emission, and the compatibility challenges of indium phosphide with the silicon industry. Here, we report a new dielectric platform using nanostructured bulk van der Waals materials. On-chip light propagation, emission, and detection are demonstrated by taking advantage of different van der Waals materials. Low-loss passive waveguides with MoS2 and on-chip light sources and photodetectors with InSe have been realised. Our proof-of-concept demonstration of passive and active on-chip photonic components endorses van der Waals materials for offering a new dielectric platform with a large material-selection degree of freedom and unique properties toward close-to-atomic scale manufacture of on-chip photonic and optoelectronic devices.

Probing phonon dynamics with multidimensional high harmonic carrier-envelope-phase spectroscopy

High harmonic generation (HHG) has recently been established as a powerful method for probing ultrafast electron dynamics in solids. However, it remains unknown if HHG can be similarly applied for probing lattice distortions such as phonons. Specifically, it is unclear if the extreme nonlinearity of HHG can contribute to enhanced temporal resolution or sensitivity for probing lattice dynamics (compared to other, perturbative, methods). Here, we theoretically explore HHG in solids with active phonons. We present a pump-probe and multidimensional spectroscopy approach that relies on carrier-envelope-phase-sensitivity, in which HHG is highly sensitive for phonon dynamics. Strikingly, the predicted temporal resolution is ∼1 femtosecond, much below the probe pulse duration, owing to the subcycle nature of the approach.

We explore pump-probe high harmonic generation (HHG) from monolayer hexagonal-boron-nitride, where a terahertz pump excites coherent optical phonons that are subsequently probed by an intense infrared pulse that drives HHG. We find, through state-of-the-art ab initio calculations, that the structure of the emission spectrum is attenuated by the presence of coherent phonons and no longer comprises discrete harmonic orders, but rather a continuous emission in the plateau region. The HHG yield strongly oscillates as a function of the pump-probe delay, corresponding to ultrafast changes in the lattice such as specific bond compression or stretching dynamics. We further show that in the regime where the excited phonon period and the pulse duration are of the same order of magnitude, the HHG process becomes sensitive to the carrier-envelope phase (CEP) of the driving field, even though the pulse duration is so long that no such sensitivity is observed in the absence of coherent phonons. The degree of CEP sensitivity versus pump-probe delay is shown to be a highly selective measure for instantaneous structural changes in the lattice, providing an approach for ultrafast multidimensional HHG spectroscopy. Remarkably, the obtained temporal resolution for phonon dynamics is ∼1 femtosecond, which is much shorter than the probe pulse duration because of the inherent subcycle contrast mechanism. Our work paves the way toward routes of probing phonons and ultrafast material structural changes with subcycle temporal resolution and provides a mechanism for controlling the HHG spectrum.

Scanning Electron Thermal Absorbance Microscopy for Light Element Detection and Atomic Number Analysis

Recent developments in nanoscale thermal metrology using electron microscopy have made impressive advancements in measuring either phononic or thermal transport properties of nanoscale samples. However, its potential in material analysis has never been considered. Here we introduce a direct thermal absorbance measurement platform in scanning electron microscope (SEM) and demonstrate that its signal can be utilized for atomic number (Z) analysis at nanoscales. We prove that the measured absorbance of materials is complementary to signals of backscattering electrons but exhibits a much higher collection efficiency and signal-to-noise ratio. Thus, it not only enables successful detections of light elements/compounds under low acceleration voltages of SEM but also allows quantitative Z analyses in agreement with simulations. The direct thermal absorbance measurement platform would become an ideal tool for SEM, especially for thin films, light elements/compounds, or biological samples at nanoscales.

Atomic-scale probing of heterointerface phonon bridges in nitride semiconductor

Interface phonon modes that are generated by several atomic layers at the heterointerface play a major role in the interface thermal conductance for nanoscale high-power devices such as nitride-based high-electron-mobility transistors and light-emitting diodes. Here we measure the local phonon spectra across AlN/Si and AlN/Al interfaces using atomically resolved vibrational electron energy-loss spectroscopy in a scanning transmission electron microscope. At the AlN/Si interface, we observe various interface phonon modes, of which the extended and localized modes act as bridges to connect the bulk AlN modes and bulk Si modes and are expected to boost the phonon transport, thus substantially contributing to interface thermal conductance. In comparison, no such phonon bridge is observed at the AlN/Al interface, for which partially extended modes dominate the interface thermal conductivity. This work provides valuable insights into understanding the interfacial thermal transport in nitride semiconductors and useful guidance for thermal management via interface engineering.

Hourglass Weyl and Dirac nodal line phonons, and drumhead-like and torus phonon surface states in orthorhombic-type KCuS

In parallel to electronic systems, the concept of topology has been extended to phonons, which has led to the birth of topological phonons. In this Communication, based on symmetry analysis and first-principles calculations, we propose that hourglass Weyl nodal line (HWNL) phonons and Dirac nodal line (DNL) phonons coexist in the phonon dispersion of a single material, KCuS, with a Pnma-type structure. The HWNLs and DNLs are relatively flat in frequency and well separated from other phonon bands. The drumhead-like phonon surface state and the torus phonon surface state appear at the [001] and [100] surfaces, respectively. The reason for this phenomenon is explained based on the Zak phase calculations. The DNL and HWNL phonons are symmetry-related and these phonons can also be observed in other realistic materials, such as BaSi₂, TiB and ZrSi, with a Pnma-type structure. Our Communication, for the first time, proves that phononic nodal lines with different types of degeneracies and different types of phonon surface states can be achieved in one single material. Thus, KCuS with a Pnma-type structure can be viewed as a good platform to investigate the entanglement between HWNL phonons and DNL phonons and to realize the drumhead-like and torus phonon surface states.

Visualization of Charge-Density-Wave Reconstruction and Electronic Superstructure at the Edge of Correlated Insulator 1T-NbSe2

Edges of low-dimensional quantum systems have profound effects on both fundamental research and device functionality. Real-space investigation of the microscopic edge structures and understanding the edge-modulated electronic properties are of great essence. Here we report the nanoscale structural reconstruction at the atomically sharp edge of a charge-density-wave (CDW) correlated insulator 1T-NbSe₂ and the induced electronic properties. We find the CDW unit cells at the edge of single layer (SL) 1T-NbSe₂ evolve from the well-defined CDW order in bulk and spontaneously reconstruct into the quartet along the edge. Moreover, we capture an anomalous electronic superstructure along the edge, the periodicity of which is four times that of ordinary CDW lattice. Our findings provide a way to design the one-dimensional electronic superstructure in 2D quantum materials.

Measuring phonon dispersion at an interface

The breakdown of translational symmetry at heterointerfaces leads to the emergence of new phonon modes localized at the interface¹. These modes have an essential role in thermal and electrical transport properties in devices, especially in miniature ones wherein the interface may dominate the entire response of the device². Although related theoretical work began decades ago^1,3-5, experimental research is totally absent owing to challenges in achieving the combined spatial, momentum and spectral resolutions required to probe localized modes. Here, using the four-dimensional electron energy-loss spectroscopy technique, we directly measure both the local vibrational spectra and the interface phonon dispersion relation for an epitaxial cubic boron nitride/diamond heterointerface. In addition to bulk phonon modes, we observe modes localized at the interface and modes isolated from the interface. These features appear only within approximately one nanometre around the interface. The localized modes observed here are predicted to substantially affect the interface thermal conductance and electron mobility. Our findings provide insights into lattice dynamics at heterointerfaces, and the demonstrated experimental technique should be useful in thermal management, electrical engineering and topological phononics.

Inelastic Scattering of Electron Beams by Nonreciprocal Nanotructures

Probing optical excitations with high resolution is important for understanding their dynamics and controlling their interaction with other photonic elements. This can be done using state-of-the-art electron microscopes, which provide the means to sample optical excitations with combined meV-sub-nm energy-space resolution. For reciprocal photonic systems, electrons traveling in opposite directions produce identical signals, while this symmetry is broken in nonreciprocal structures. Here, we theoretically investigate this phenomenon by analyzing electron energy-loss spectroscopy (EELS) and cathodoluminescence (CL) for structures consisting of magnetically biased InAs as an instance of gyrotropic nonreciprocal material. We find that the spectral features associated with excitations of InAs films depend on the electron propagation direction in both EELS and CL, and can be tuned by varying the applied magnetic field within a relatively modest subtesla regime. The magnetic field modifies the optical field distribution of the sampled resonances, and this in turn produces a direction-dependent coupling to the electron. The present results pave the way to the use of electron microscope spectroscopies to explore the near-field characteristics of nonreciprocal systems with high spatial resolution.

Revealing Nanoscale Confinement Effects on Hyperbolic Phonon Polaritons with an Electron Beam

Hyperbolic phonon polaritons (HPhPs) in hexagonal boron nitride (hBN) enable the direct manipulation of mid-infrared light at nanometer scales, many orders of magnitude below the free-space light wavelength. High-resolution monochromated electron energy-loss spectroscopy (EELS) facilitates measurement of excitations with energies extending into the mid-infrared while maintaining nanoscale spatial resolution, making it ideal for detecting HPhPs. The electron beam is a precise source and probe of HPhPs, which allows the observation of nanoscale confinement in HPhP structures and directly extract hBN polariton dispersions for both modes in the bulk of the flake and modes along the edge. The measurements reveal technologically important nontrivial phenomena, such as localized polaritons induced by environmental heterogeneity, enhanced and suppressed excitation due to 2D interference, and strong modification of high-momenta excitations such as edge-confined polaritons by nanoscale heterogeneity on edge boundaries. The work opens exciting prospects for the design of real-world optical mid-infrared devices based on hyperbolic polaritons.

Interface nano-optics with van der Waals polaritons

Polaritons are hybrid excitations of matter and photons. In recent years, polaritons in van der Waals nanomaterials-known as van der Waals polaritons-have shown great promise to guide the flow of light at the nanoscale over spectral regions ranging from the visible to the terahertz. A vibrant research field based on manipulating strong light-matter interactions in the form of polaritons, supported by these atomically thin van der Waals nanomaterials, is emerging for advanced nanophotonic and opto-electronic applications. Here we provide an overview of the state of the art of exploiting interface optics-such as refractive optics, meta-optics and moiré engineering-for the control of van der Waals polaritons. This enhanced control over van der Waals polaritons at the nanoscale has not only unveiled many new phenomena, but has also inspired valuable applications-including new avenues for nano-imaging, sensing, on-chip optical circuitry, and potentially many others in the years to come.

Nonlinear Tunable Vibrational Response in Hexagonal Boron Nitride

Nonlinear light-matter interactions in structured materials are the source of exciting properties and enable vanguard applications in photonics. However, the magnitude of nonlinear effects is generally small, thus requiring high optical intensities for their manifestation at the nanoscale. Here, we reveal a large nonlinear response of monolayer hexagonal boron nitride (hBN) in the mid-infrared phonon-polariton region, triggered by the strongly anharmonic potential associated with atomic vibrations in this material. We present robust first-principles theory predicting a threshold light field ∼24 MV/m to produce order-unity effects in Kerr nonlinearities and harmonic generation, which are made possible by a combination of the long lifetimes exhibited by optical phonons and the strongly asymmetric landscape of the configuration energy in hBN. We further foresee polariton blockade at the few-quanta level in nanometer-sized structures. In addition, by mixing static and optical fields, the strong nonlinear response of monolayer hBN gives rise to substantial frequency shifts of optical phonon modes, exceeding their spectral width for in-plane DC fields that are attainable using lateral gating technology. We therefore predict a practical scheme for electrical tunability of the vibrational modes with potential interest in mid-infrared optoelectronics. The strong nonlinear response, low damping, and robustness of hBN polaritons set the stage for the development of applications in light modulation, sensing, and metrology, while triggering the search for an intense vibrational nonlinear response in other ionic materials.

Anisotropic acoustic phonon polariton-enhanced infrared spectroscopy for single molecule detection

Nanoscale Fourier transform infrared spectroscopy (nano-FTIR) based on scanning probe microscopy enables the identification of the chemical composition and structure of surface species with a high spatial resolution (∼10 nm), which is crucial for exploring catalytic reaction processes, cellular processes, virus detection, etc. However, the characterization of a single molecule with nano-FTIR is still challenging due to the weak coupling between the molecule and infrared light due to a large size mismatch. Here, we propose a novel structure (monolayer α-MoO₃/air nanogap/Au) to excite anisotropic acoustic phonon polaritons (APhPs) with ultra-high field confinement (mode volume, V_APhPs∼ 10^-11V₀) and electromagnetic energy enhancement (>10⁷), which largely enhance the interaction of single molecules with infrared light. In addition, the anisotropic APhP-assisted nano-FTIR can detect single molecular dipoles in directions both along and perpendicular to the probe axis, while pristine nano-FTIR mainly detects molecular dipoles along the probe axis. The proposed structure provides a way to detect a single molecule, which will impact the fields of biology, chemistry, energy, and environment through fundamental research and applications.

Strong coupling regime and bound states in the continuum between a quantum emitter and phonon-polariton modes

We investigate the population dynamics of a two-level quantum emitter (QE) placed near a hexagonal boron nitride (h-BN) layer. The h-BN layer supports two energy phonon-polariton bands. In the case that the transition energy of the QE is resonant to them, its relaxation rate is enhanced several orders of magnitude compared to its free-space value and the population of the QE excited state shows reversible dynamics. We further show that for specific parameters of the QE/h-BN layer system, the QE population can be trapped in the excited state, keeping a constant value over long periods of time, thus demonstrating that the h-BN layer is a platform that can provide the strong light-matter interaction conditions needed for the formation of bound states in the electromagnetic continuum of modes. Semi-analytical methods are employed for determining whether such a bound state can be formed for given coupling conditions, as well as for computing the amount of initial population trapped in it. The bound states in the continuum are important for designing practical future quantum applications.

Efficient and Tunable Reflection of Phonon Polaritons at Built-In Intercalation Interfaces

Phonon polaritons-light coupled to lattice vibrations-in polar van der Waals crystals offer unprecedented opportunities for controlling light at the nanoscale due to their anisotropic and ultralow-loss propagation. While their analog plasmon polaritons-light coupled to electron oscillations-have long been studied and exhibit interesting reflections at geometrical edges and electronic boundaries, whether phonon polaritons can be reflected by such barriers has been elusive. Here, the effective and tunable reflection of phonon polaritons at embedded interfaces formed in hydrogen-intercalated α-MoO₃ flakes is elaborated upon. Without breaking geometrical continuity, such intercalation interfaces can reflect phonon polaritons with low losses, yielding the distinct phase changes of -0.8π and -0.3π associated with polariton propagation, high efficiency of 50%, and potential electrical tunability. The results point to a new approach to construct on-demand polariton reflectors, phase modulators, and retarders, which may be transplanted into building future polaritonic circuits using van der Waals crystals.

Synthesis of centimeter-scale high-quality polycrystalline hexagonal boron nitride films from Fe fluxes

High-quality hexagonal BN (hBN) crystals, owing to their irreplaceable roles in new functional devices such as universal substrates and excellent layered insulators are exceedingly required in the field of two-dimensional (2D) materials. Although large-scale monolayer hBN crystals have been successfully grown on catalytic metals, the synthesis of large-area continuous hBN films with thickness in microns is challenging, hindering their applications at the mesoscopic level. Herein, we report the single-metal flux growth of centimeter-large, micron-thick, and high-quality continuous hBN films by balancing the grain size and coverage. The as-grown films can be readily exfoliated and transferred onto arbitrary substrates. Isotopically engineered hBN crystals can be obtained as well by the method. The narrow Raman line widths of the intralayer E2g mode peak (2.9 cm-1 for h11BN, 3.3 cm-1 for h10BN, and 7.9 cm-1 for hNaBN) and ultrahigh thermal conductivity (830 W m-1 K-1 for 4L h11BN) demonstrate high crystal quality and low defect density. Our results provide the foundation for the cost-efficient and lab-achievable synthesis of high-quality hBN films aimed at its mesoscopic applications.

Highly Confined Phonon Polaritons in Monolayers of Perovskite Oxides

Two-dimensional (2D) materials are able to strongly confine light hybridized with collective excitations of atoms, enabling electric-field enhancements and novel spectroscopic applications. Recently, freestanding monolayers of perovskite oxides have been synthesized, which possess highly infrared-active phonon modes and a complex interplay of competing interactions. Here, we show that this new class of 2D materials exhibits highly confined phonon polaritons by evaluating central figures of merit for phonon polaritons in the tetragonal phases of the 2D perovskites SrTiO₃, KTaO₃, and LiNbO₃, using density functional theory calculations. Specifically, we compute the 2D phonon-polariton dispersions, the propagation-quality, confinement, and deceleration factors, and we show that they are comparable to those found in the prototypical 2D dielectric hexagonal boron nitride. Our results suggest that monolayers of perovskite oxides are promising candidates for polaritonic platforms that enable new possibilities in terms of tunability and spectral ranges.

Spatiotemporal imaging of 2D polariton wave packet dynamics using free electrons

Coherent optical excitations in two-dimensional (2D) materials, 2D polaritons, can generate a plethora of optical phenomena that arise from the extraordinary dispersion relations that do not exist in regular materials. Probing of the dynamical phenomena of 2D polaritons requires simultaneous spatial and temporal imaging capabilities and could reveal unknown coherent optical phenomena in 2D materials. Here, we present a spatiotemporal measurement of 2D wave packet dynamics, from its formation to its decay, using an ultrafast transmission electron microscope driven by femtosecond midinfrared pulses. The ability to coherently excite phonon-polariton wave packets and probe their evolution in a nondestructive manner reveals intriguing dispersion-dependent dynamics that includes splitting of multibranch wave packets and, unexpectedly, wave packet deceleration and acceleration. Having access to the full spatiotemporal dynamics of 2D wave packets can be used to illuminate puzzles in topological polaritons and discover exotic nonlinear optical phenomena in 2D materials.

Near-Field Excited Archimedean-like Tiling Patterns in Phonon-Polaritonic Crystals

Phonon-polaritons (PhPs) arise from the strong coupling of photons to optical phonons. They offer light confinement and harnessing below the diffraction limit for applications including sensing, imaging, superlensing, and photonics-based communications. However, structures consisting of both suspended and supported hyperbolic materials on periodic dielectric substrates are yet to be explored. Here we investigate phonon-polaritonic crystals (PPCs) that incorporate hyperbolic hexagonal boron nitride (hBN) to a silicon-based photonic crystal. By using the near-field excitation in scattering-type scanning near-field optical microscopy (s-SNOM), we resolved two types of repetitive local field distribution patterns resembling the Archimedean-like tiling on hBN-based PPCs, i.e., dipolar-like field distributions and highly dispersive PhP interference patterns. We demonstrate the tunability of PPC band structures by varying the thickness of hyperbolic materials, supported by numerical simulations. Lastly, we conducted scattering-type nanoIR spectroscopy to confirm the interaction of hBN with photonic crystals. The introduced PPCs will provide the base for fabricating essential subdiffraction components of advanced optical systems in the mid-IR range.

Design of 2D materials - MSi2CxN4-x (M = Cr, Mo, and W; x = 1 and 2) - with tunable electronic and magnetic properties

Two-dimensional (2D) materials have attracted increasing interest in the past decades due to their unique physical and chemical properties for diverse applications. In this work, we present a first-principles design on a novel 2D family, MSi₂C_xN_4-x (M = Cr, Mo, and W; x = 1 and 2), based on density-functional theory (DFT). We find that all MSi₂C_xN_4-x monolayers are stable by investigating their mechanic, dynamic, and thermodynamic properties. Interestingly, we see that the alignment of magnetic moments can be tuned to achieve non-magnetism (NM), ferromagnetism (FM), anti-ferromagnetism (AFM) or paramagnetism (PM) by arranging the positions of carbon atoms in the 2D systems. Accordingly, their electronic properties can be controlled to obtain semiconductor, half-metal, or metal. The FM states in half-metallic 2D systems are contributed to the hole-mediated double exchange, while the AFM states are induced by super-exchange. Our findings show that the physical properties of 2D systems can be tuned by compositional and structural engineering, especially the layer of C atoms, which may provide guidance on the design and fabrication of novel 2D materials with projected properties for multi-functional applications.

Optical Excitations with Electron Beams: Challenges and Opportunities

Free electron beams such as those employed in electron microscopes have evolved into powerful tools to investigate photonic nanostructures with an unrivaled combination of spatial and spectral precision through the analysis of electron energy losses and cathodoluminescence light emission. In combination with ultrafast optics, the emerging field of ultrafast electron microscopy utilizes synchronized femtosecond electron and light pulses that are aimed at the sampled structures, holding the promise to bring simultaneous sub-Å-sub-fs-sub-meV space-time-energy resolution to the study of material and optical-field dynamics. In addition, these advances enable the manipulation of the wave function of individual free electrons in unprecedented ways, opening sound prospects to probe and control quantum excitations at the nanoscale. Here, we provide an overview of photonics research based on free electrons, supplemented by original theoretical insights and discussion of several stimulating challenges and opportunities. In particular, we show that the excitation probability by a single electron is independent of its wave function, apart from a classical average over the transverse beam density profile, whereas the probability for two or more modulated electrons depends on their relative spatial arrangement, thus reflecting the quantum nature of their interactions. We derive first-principles analytical expressions that embody these results and have general validity for arbitrarily shaped electrons and any type of electron-sample interaction. We conclude with some perspectives on various exciting directions that include disruptive approaches to noninvasive spectroscopy and microscopy, the possibility of sampling the nonlinear optical response at the nanoscale, the manipulation of the density matrices associated with free electrons and optical sample modes, and appealing applications in optical modulation of electron beams, all of which could potentially revolutionize the use of free electrons in photonics.

Computation and data driven discovery of topological phononic materials

The discovery of topological quantum states marks a new chapter in both condensed matter physics and materials sciences. By analogy to spin electronic system, topological concepts have been extended into phonons, boosting the birth of topological phononics (TPs). Here, we present a high-throughput screening and data-driven approach to compute and evaluate TPs among over 10,000 real materials. We have discovered 5014 TP materials and grouped them into two main classes of Weyl and nodal-line (ring) TPs. We have clarified the physical mechanism for the occurrence of single Weyl, high degenerate Weyl, individual nodal-line (ring), nodal-link, nodal-chain, and nodal-net TPs in various materials and their mutual correlations. Among the phononic systems, we have predicted the hourglass nodal net TPs in TeO₃, as well as the clean and single type-I Weyl TPs between the acoustic and optical branches in half-Heusler LiCaAs. In addition, we found that different types of TPs can coexist in many materials (such as ScZn). Their potential applications and experimental detections have been discussed. This work substantially increases the amount of TP materials, which enables an in-depth investigation of their structure-property relations and opens new avenues for future device design related to TPs.

Topological phononic (TP) materials are attracting wide attentions and it is more difficult to seek TP materials compared to electronic materials. Here, the authors present a high-throughput screening and data-driven approach to discover 5014 TP materials and further clarify the mechanism for the occurrence of various TPs.