Phonon Polaritonics in Two-Dimensional Materials

Ultra-Confined Phonon Polaritons and Strongly Coupled Microcavity Exciton Polaritons in Monolayer MoSi2N4 and WSi2N4

The 2D semiconductors are an ideal platform for exploration of bosonic fluids composed of coupled photons and collective excitations of atoms or excitons, primarily due to large excitonic binding energies and strong light-matter interaction. Based on first-principles calculations, it is demonstrated that the phonon polaritons formed by two infrared-active phonon modes in monolayer MoSi2N4 and WSi2N4 possess ultra-high confinement factors of around ≈105 and 103, surpassing those of conventional polaritonic thin-film materials by two orders of magnitude. It is observed that the first bright exciton possesses a substantial binding energies of 750 and 740 meV in these two monolayers, with the radiative recombination lifetimes as long as 25 and 188 ns, and the Rabi splitting of the formed cavity-exciton polaritons reaching 373 and 321 meV, respectively. The effective masses of the cavity exciton polaritons are approximately 10-5me, providing the potential for high-temperature quantum condensation. The ultra-confined and ultra-low-loss phonon polaritons, as well as strongly-coupled cavity exciton polaritons with ultra-small polaritonic effective masses in these two monolayers, offering the flexible control of light at the nanoscale, probably leading to practical applications in nanophotonics, meta-optics, and quantum materials.

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.

Infrared-active phonons in one-dimensional materials and their spectroscopic signatures

Dimensionality provides a clear fingerprint on the dispersion of infrared-active, polar-optical phonons. For these phonons, the local dipoles parametrized by the Born effective charges drive the LO-TO splitting of bulk materials; this splitting actually breaks down in two-dimensional materials. Here, we develop the theory for one-dimensional (1D) systems-nanowires, nanotubes, and atomic and polymeric chains. Combining an analytical model with the implementation of density-functional perturbation theory in 1D boundary conditions, we show that the dielectric splitting in the dispersion relations collapses as x 2 log ( x ) at the zone center. The dielectric properties and the radius of the 1D materials are linked by the present work to these red shifts, opening infrared and Raman characterization avenues.

Low-Velocity-Favored Transition Radiation

When a charged particle penetrates through an optical interface, photon emissions emerge-a phenomenon known as transition radiation. Being paramount to fundamental physics, transition radiation has enabled many applications from high-energy particle identification to novel light sources. A rule of thumb in transition radiation is that the radiation intensity generally decreases with the decrease of particle velocity v; as a result, low-energy particles are not favored in practice. Here, we find that there exist situations where transition radiation from particles with extremely low velocities (e.g., v/c<10^{-3}) exhibits comparable intensity as that from high-energy particles (e.g., v/c=0.999), where c is the light speed in free space. The comparable radiation intensity implies an extremely high photon extraction efficiency from low-energy particles, up to 8 orders of magnitude larger than that from high-energy particles. This exotic phenomenon of low-velocity-favored transition radiation originates from the interference of the excited Ferrell-Berreman modes in an ultrathin epsilon-near-zero slab. Our findings may provide a promising route toward the design of integrated light sources based on low-energy electrons and specialized detectors for beyond-standard-model particles.

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.

Transverse Hypercrystals Formed by Periodically Modulated Phonon Polaritons

Photonic crystals and metamaterials are two overarching paradigms for manipulating light. By combining these approaches, hypercrystals can be created, which are hyperbolic dispersion metamaterials that undergo periodic modulation and mix photonic-crystal-like aspects with hyperbolic dispersion physics. Despite several attempts, there has been limited experimental realization of hypercrystals due to technical and design constraints. In this work, hypercrystals with nanoscale lattice constants ranging from 25 to 160 nm were created. The Bloch modes of these crystals were then measured directly using scattering near-field microscopy. The dispersion of the Bloch modes was extracted from the frequency dependence of the Bloch modes, revealing a clear switch from positive to negative group velocity. Furthermore, spectral features specific to hypercrystals were observed in the form of sharp density of states peaks, which are a result of intermodal coupling and should not appear in ordinary polaritonic crystals with an equivalent geometry. These findings are in agreement with theoretical predictions that even simple lattices can exhibit a rich hypercrystal bandstructure. This work is of both fundamental and practical interest, providing insight into nanoscale light-matter interactions and the potential to manipulate the optical density of states.

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.

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.

Hyperbolic shear polaritons in low-symmetry crystals

The lattice symmetry of a crystal is one of the most important factors in determining its physical properties. Particularly, low-symmetry crystals offer powerful opportunities to control light propagation, polarization and phase^1–4. Materials featuring extreme optical anisotropy can support a hyperbolic response, enabling coupled light–matter interactions, also known as polaritons, with highly directional propagation and compression of light to deeply sub-wavelength scales⁵. Here we show that monoclinic crystals can support hyperbolic shear polaritons, a new polariton class arising in the mid-infrared to far-infrared due to shear phenomena in the dielectric response. This feature emerges in materials in which the dielectric tensor cannot be diagonalized, that is, in low-symmetry monoclinic and triclinic crystals in which several oscillators with non-orthogonal relative orientations contribute to the optical response^6,7. Hyperbolic shear polaritons complement previous observations of hyperbolic phonon polaritons in orthorhombic^1,3,4 and hexagonal^8,9 crystal systems, unveiling new features, such as the continuous evolution of their propagation direction with frequency, tilted wavefronts and asymmetric responses. The interplay between diagonal loss and off-diagonal shear phenomena in the dielectric response of these materials has implications for new forms of non-Hermitian and topological photonic states. We anticipate that our results will motivate new directions for polariton physics in low-symmetry materials, which include geological minerals¹⁰, many common oxides¹¹ and organic crystals¹², greatly expanding the material base and extending design opportunities for compact photonic devices.

Shear phenomena in the infrared dielectric response of a monoclinic crystal are shown to unveil a new polariton class termed hyperbolic shear polariton that can emerge in any low-symmetry monoclinic or triclinic system.

Collective Phonon-Polaritonic Modes in Silicon Carbide Subarrays

Localized surface phonon polaritons (LSPhPs) can be implemented to engineer light-matter interactions through nanoscale patterning for a range of midinfrared application spaces. However, the polar material systems studied to date have mainly focused on simple designs featuring a single element in the periodic unit cell. Increasing the complexity of the unit cell can serve to modify the resonant near-fields and intra- and inter-unit-cell coupling as well as to dictate spectral tuning in the far-field. In this work, we exploit more complicated unit-cell structures to realize LSPhP modes with additional degrees of design freedom, which are largely unexplored. Collectively excited LSPhP modes with distinctly symmetric and antisymmetric near-fields are supported in these subarray designs, which are based on nanopillars that are scaled by the number of subarray elements to ensure a constant unit-cell size. Moreover, we observe an anomalous mode-matching of the collective symmetric mode in our fabricated subarrays that is robust to changing numbers of pillars within the subarrays as well as to defects intentionally introduced in the form of missing pillars. This work therefore illustrates the hierarchical design of tailored LSPhP resonances and modal near-field profiles simultaneously for a variety of IR applications such as surface-enhanced spectroscopies and biochemical sensing.

Material strategies for function enhancement in plasmonic architectures

Plasmonic materials are promising for applications in enhanced sensing, energy, and advanced optical communications. These applications, however, often require chemical and physical functionality that is suited and designed for the specific application. In particular, plasmonic materials need to access the wide spectral range from the ultraviolet to the mid-infrared in addition to having the requisite surface characteristics, temperature dependence, or structural features that are not intrinsic to or easily accessed by the noble metals. Herein, we describe current progress and identify promising strategies for further expanding the capabilities of plasmonic materials both across the electromagnetic spectrum and in functional areas that can enable new technology and opportunities.

Nanoscale lattice dynamics in hexagonal boron nitride moiré superlattices

Twisted two-dimensional van der Waals (vdW) heterostructures have unlocked a new means for manipulating the properties of quantum materials. The resulting mesoscopic moiré superlattices are accessible to a wide variety of scanning probes. To date, spatially-resolved techniques have prioritized electronic structure visualization, with lattice response experiments only in their infancy. Here, we therefore investigate lattice dynamics in twisted layers of hexagonal boron nitride (hBN), formed by a minute twist angle between two hBN monolayers assembled on a graphite substrate. Nano-infrared (nano-IR) spectroscopy reveals systematic variations of the in-plane optical phonon frequencies amongst the triangular domains and domain walls in the hBN moiré superlattices. Our first-principles calculations unveil a local and stacking-dependent interaction with the underlying graphite, prompting symmetry-breaking between the otherwise identical neighboring moiré domains of twisted hBN.

Here, the authors investigate the lattice dynamics of twisted hexagonal boron nitride layers via nano-infrared spectroscopy, showing local and stacking-dependent variations of the optical phonon frequencies associated to the interaction with the graphite substrate.

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.

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.

Enhanced Interaction of Optical Phonons in h-BN with Plasmonic Lattice and Cavity Modes

Hexagonal boron nitride (h-BN) is regarded as a milestone in the investigation of light interaction with phonon polaritons in two-dimensional van der Waals materials, showing significant potential in novel and high-efficient photonics devices in the mid-infrared region. Here, we investigate a structure composed of Au-grating arrays fabricated onto a Fabry-Perot (FP) cavity composed of h-BN, Ge, and Au back-reflector layers. The plasmonic FP cavity reduces the required device thickness by enhancing modal interactions and introduces in-plane polarization sensitivity based on the Au array lattice. Our experiments show multiple absorption peaks of over 90% in the mid-infrared region and the band stop filters with 80% efficiency using only a 15 nm h-BN slab. Moreover, mode interaction with experimental coupling strengths as high as 10.8 meV in the mid-infrared region is investigated. In particular, the interaction and hybridization of optical phonon modes with plasmonic modes including the lattice and cavity modes are studied. Anticrossing splitting ascribed to the coupling of optical phonons to plasmonic modes can be tuned by the designed geometry which can be tailored to efficient response band engineering for infrared photonics. We also show that in practical applications involving wet transfer of h-BN thin films, the contribution of minor optical phonon modes to resonant peaks should not be ignored, which originate from defects and multicrystallinity in the h-BN slab. Our findings provide a favorable complement to manipulation of light-phonon interaction, inspiring a promising design of phonon-based nanophotonic devices in the infrared range.

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

Phonon polaritons enable light confinement at deep subwavelength scales, with potential technological applications, such as subdiffraction imaging, sensing and engineering of spontaneous emission. However, the trade-off between the degree of confinement and the excitation efficiency of phonon polaritons prevents direct observation of these modes in monolayer hexagonal boron nitride (h-BN), where they are expected to reach ultrahigh confinement. Here, we use monochromatic electron energy-loss spectroscopy (about 7.5 meV energy resolution) in a scanning transmission electron microscope to measure phonon polaritons in monolayer h-BN, directly demonstrating the existence of these modes as the phonon Reststrahlen band (RS) disappears. We find phonon polaritons in monolayer h-BN to exhibit high confinement (>487 times smaller wavelength than that of light in free space) and ultraslow group velocity down to about 10^-5c. The large momentum compensation provided by electron beams additionally allows us to excite phonon polaritons over nearly the entire RS band of multilayer h-BN. These results open up a broad range of opportunities for the engineering of metasurfaces and strongly enhanced light-matter interactions.

Quantum Information and Algorithms for Correlated Quantum Matter

Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.

Three-dimensional near-field analysis through peak force scattering-type near-field optical microscopy

Scattering-type scanning near-field optical microscopy (s-SNOM) is instrumental in exploring polaritonic behaviors of two-dimensional (2D) materials at the nanoscale. A sharp s-SNOM tip couples momenta into 2D materials through phase matching to excite phonon polaritons, which manifest as nanoscale interference fringes in raster images. However, s-SNOM lacks the ability to detect the progression of near-field properties along the perpendicular axis to the surface. Here, we perform near-field analysis of a micro-disk and a reflective edge made of isotopically pure hexagonal boron nitride (h-11BN), by using three-dimensional near-field response cubes obtained by peak force scattering-type near-field optical microscopy (PF-SNOM). Momentum quantization of polaritons from the confinement of the circular structure is revealed in situ. Moreover, tip-sample distance is found to be capable of fine-tuning the momentum of polaritons and modifying the superposition of quantized polaritonic modes. The PF-SNOM-based three-dimensional near-field analysis provides detailed characterization capability with a high spatial resolution to fully map three-dimensional near-fields of nano-photonics and polaritonic structures.

Phonon Polaritons in Monolayers of Hexagonal Boron Nitride

Phonon polaritons in van der Waals materials reveal significant confinement accompanied with long propagation length: important virtues for tasks pertaining to the control of light and energy flow at the nanoscale. While previous studies of phonon polaritons have relied on relatively thick samples, here reported is the first observation of surface phonon polaritons in single atomic layers and bilayers of hexagonal boron nitride (hBN). Using antenna-based near-field microscopy, propagating surface phonon polaritons in mono- and bilayer hBN microcrystals are imaged. Phonon polaritons in monolayer hBN are confined in a volume about one million times smaller than the free-space photons. Both the polariton dispersion and their wavelength-thickness scaling law are altered compared to those of hBN bulk counterparts. These changes are attributed to phonon hardening in monolayer-thick crystals. The data reported here have bearing on applications of polaritons in metasurfaces and ultrathin optical elements.