First-principles investigation of quantum emission from hBN defects

Probing Correlation of Optical Emission and Defect Sites in Hexagonal Boron Nitride by High-Resolution STEM-EELS

Optically bright emitters in hexagonal boron nitride (hBN) often acting as a source of a single-photon are mostly attributed to point-defect centers, featuring localized intra-bandgap electronic states. Although vacancies, anti-sites, and impurities have been proposed as candidates, the exact physical and chemical nature of most hBN single-photon emitters (SPEs) within the visible region are still up for debate. Combining site-specific high-angle annular dark-field imaging (HAADF) with electron energy loss spectroscopy (EELS), we resolve and identify a few carbon substitutions among neighboring hBN hexagons, all within the same sample region, from which typical defect emission is observed. Our experimental results are further supported by first-principles calculations, through which the stability and possible optical transitions of the proposed carbon-defect complex are assessed. The presented correlation between optical emission and defects provides valuable information toward the controlled creation of emitters in hBN, highlighting carbon complexes as another probable cause of its visible SPEs.

Tunable electronic and magnetic properties of defective g-ZnO monolayer doping with non-metallic elements

CONTEXT

The electronic and magnetic properties of non-metallic (NM) elements doping defective graphene-like ZnO (g-ZnO) monolayer including O vacancy (VO) and Zn vacancy (VZn) are studied. The results show that VO-g-ZnO is a semiconductor and VZn-g-ZnO is a magnetic semiconductor. B, C, N, Si, P, 2S, and 2Si doping VO-g-ZnO systems present half-metal and magnetic semiconductors, and the magnetism mainly originates from the spin polarization of doping atoms. For single or double NM elements doping VZn-g-ZnO, 2P doping system presents a semiconductor, while other systems present ferromagnetic metal, half-metal, and magnetic semiconductor. The magnetism of single NM elements doping VZn-g-ZnO mainly comes from the spin polarization of O atoms near the defect point. For double NM elements doping VZn-g-ZnO, spin splitting occurs mainly in p orbitals of O atoms, dopant atoms, and d orbitals of Zn atoms. NM elements doping defect g-ZnO can effectively regulate the electronic and magnetic properties of the system.

METHODS

The software package VASP 5.4.1 (Vienna ab initio Simulation Package) is used for calculations in this paper. The local density approximation (LDA) is adopted as an exchange and correlation function to perform the structural optimization and analysis of electronic structure and magnetic properties.

Single-Photon Emission from Point Defects in Hexagonal Boron Nitride Induced by Plasma Treatment

Solid-state quantum emitters are gaining significant attention for many quantum information applications. Hexagonal boron nitride (h-BN) is an emerging host material for generating bright, stable, and tunable single-photon emission with narrow line widths at room temperature. In this work, we present a facile and efficient approach to generate high-density single-photon emitters (SPEs) in mechanically exfoliated h-BN through H- or Ar-plasma treatment followed by high-temperature annealing in air. It is notable that the postannealing is essential to suppress the fluorescence background in photoluminescence spectra and enhance emitter stability. These quantum emitters exhibit excellent optical properties, including high purity, brightness, stability, polarization degree, monochromaticity, and saturation intensity. The effects of process parameters on the quality of quantum emitters were systematic investigated. We find that there exists an optimal plasma power and h-BN thickness to achieve a high SPE density. This work offers a practical avenue for generating SPEs in h-BN and holds promise for future research and applications in quantum photonics.

Elementary excitations of single-photon emitters in hexagonal boron nitride

Single-photon emitters serve as building blocks for many emerging concepts in quantum photonics. The recent identification of bright, tunable and stable emitters in hexagonal boron nitride (hBN) has opened the door to quantum platforms operating across the infrared to ultraviolet spectrum. Although it is widely acknowledged that defects are responsible for single-photon emitters in hBN, crucial details regarding their origin, electronic levels and orbital involvement remain unknown. Here we employ a combination of resonant inelastic X-ray scattering and photoluminescence spectroscopy in defective hBN, unveiling an elementary excitation at 285 meV that gives rise to a plethora of harmonics correlated with single-photon emitters. We discuss the importance of N π* anti-bonding orbitals in shaping the electronic states of the emitters. The discovery of elementary excitations in hBN provides fundamental insights into quantum emission in low-dimensional materials, paving the way for future investigations in other platforms.

The Case for a Defect Genome Initiative

The Materials Genome Initiative (MGI) has streamlined the materials discovery effort by leveraging generic traits of materials, with focus largely on perfect solids. Defects such as impurities and perturbations, however, drive many attractive functional properties of materials. The rich tapestry of charge, spin, and bonding states hosted by defects are not accessible to elements and perfect crystals, and defects can thus be viewed as another class of "elements" that lie beyond the periodic table. Accordingly, a Defect Genome Initiative (DGI) to accelerate functional defect discovery for energy, quantum information, and other applications is proposed. First, major advances made under the MGI are highlighted, followed by a delineation of pathways for accelerating the discovery and design of functional defects under the DGI. Near-term goals for the DGI are suggested. The construction of open defect platforms and design of data-driven functional defects, along with approaches for fabrication and characterization of defects, are discussed. The associated challenges and opportunities are considered and recent advances towards controlled introduction of functional defects at the atomic scale are reviewed. It is hoped this perspective will spur a community-wide interest in undertaking a DGI effort in recognition of the importance of defects in enabling unique functionalities in materials.

Polarization Dynamics of Solid-State Quantum Emitters

Quantum emitters in solid-state crystals have recently attracted a great deal of attention due to their simple applicability in optical quantum technologies. The polarization of single photons generated by quantum emitters is one of the key parameters that plays a crucial role in various applications, such as quantum computation, which uses the indistinguishability of photons. However, the degree of single-photon polarization is typically quantified using the time-averaged photoluminescence intensity of single emitters, which provides limited information about the dipole properties in solids. In this work, we use single defects in hexagonal boron nitride and nanodiamond as efficient room-temperature single-photon sources to reveal the origin and temporal evolution of the dipole orientation in solid-state quantum emitters. The angles of the excitation and emission dipoles relative to the crystal axes were determined experimentally and then calculated using density functional theory, which resulted in characteristic angles for every specific defect that can be used as an efficient tool for defect identification and understanding their atomic structure. Moreover, the temporal polarization dynamics revealed a strongly modified linear polarization visibility that depends on the excited-state decay time of the individual excitation. This effect can potentially be traced back to the excitation of excess charges in the local crystal environment. Understanding such hidden time-dependent mechanisms can further improve the performance of polarization-sensitive experiments, particularly that for quantum communication with single-photon emitters.

Combining experiments on luminescent centres in hexagonal boron nitride with the polaron model and ab initio methods towards the identification of their microscopic origin

The two-dimensional material hexagonal boron nitride (hBN) hosts luminescent centres with emission energies of ∼2 eV which exhibit pronounced phonon sidebands. We investigate the microscopic origin of these luminescent centres by combining ab initio calculations with non-perturbative open quantum system theory to study the emission and absorption properties of 26 defect transitions. Comparing the calculated line shapes with experiments we narrow down the microscopic origin to three carbon-based defects: C2CB, C2CN, and VNCB. The theoretical method developed enables us to calculate so-called photoluminescence excitation (PLE) maps, which show excellent agreement with our experiments. The latter resolves higher-order phonon transitions, thereby confirming both the vibronic structure of the optical transition and the phonon-assisted excitation mechanism with a phonon energy ∼170 meV. We believe that the presented experiments and polaron-based method accurately describe luminescent centres in hBN and will help to identify their microscopic origin.

Layered materials as a platform for quantum technologies

Layered materials are taking centre stage in the ever-increasing research effort to develop material platforms for quantum technologies. We are at the dawn of the era of layered quantum materials. Their optical, electronic, magnetic, thermal and mechanical properties make them attractive for most aspects of this global pursuit. Layered materials have already shown potential as scalable components, including quantum light sources, photon detectors and nanoscale sensors, and have enabled research of new phases of matter within the broader field of quantum simulations. In this Review we discuss opportunities and challenges faced by layered materials within the landscape of material platforms for quantum technologies. In particular, we focus on applications that rely on light-matter interfaces.

Organic Molecules as Origin of Visible-Range Single Photon Emission from Hexagonal Boron Nitride and Mica

The discovery of room-temperature single-photon emitters (SPEs) hosted by two-dimensional hexagonal boron nitride (2D hBN) has sparked intense research interest. Although emitters in the vicinity of 2 eV have been studied extensively, their microscopic identity has remained elusive. The discussion of this class of SPEs has centered on point defects in the hBN crystal lattice, but none of the candidate defect structures have been able to capture the great heterogeneity in emitter properties that is observed experimentally. Employing a widely used sample preparation protocol but disentangling several confounding factors, we demonstrate conclusively that heterogeneous single-photon emission at ∼2 eV associated with hBN originates from organic molecules, presumably aromatic fluorophores. The appearance of those SPEs depends critically on the presence of organic processing residues during sample preparation, and emitters formed during heat treatment are not located within the hBN crystal as previously thought, but at the hBN/substrate interface. We further demonstrate that the same class of SPEs can be observed in a different 2D insulator, fluorophlogopite mica.

Hexagonal Boron Nitride for Next-Generation Photonics and Electronics

Hexagonal boron nitride (h-BN), an insulating 2D layered material, has recently attracted tremendous interest motivated by the extraordinary properties it shows across the fields of optoelectronics, quantum optics, and electronics, being exotic material platforms for various applications. At an early stage of h-BN research, it is explored as an ideal substrate and insulating layers for other 2D materials due to its atomically flat surface that is free of dangling bonds and charged impurities, and its high thermal conductivity. Recent discoveries of structural and optical properties of h-BN have expanded potential applications into emerging electronics and photonics fields. h-BN shows a very efficient deep-ultraviolet band-edge emission despite its indirect-bandgap nature, as well as stable room-temperature single-photon emission over a wide wavelength range, showing a great potential for next-generation photonics. In addition, h-BN is extensively being adopted as active media for low-energy electronics, including nonvolatile resistive switching memory, radio-frequency devices, and low-dielectric-constant materials for next-generation electronics.

Photodynamics of Bright Subnanosecond Emission from Pure Single-Photon Sources in Hexagonal Boron Nitride

Bright and stable emitters of single indistinguishable photons are crucial for quantum technologies. The origin of the promising bright emitters recently observed in hexagonal boron nitride (hBN) still remains unclear. This study reports pure single-photon sources in multi-layered hBN at room temperature that demonstrate high emission rates. The quantum emitters are introduced with argon beam treatment and air annealing of mechanically exfoliated hBN flakes with thicknesses of 5-100 nm. Spectral and time-resolved measurements reveal the emitters have more than 1 GHz of excited-to-ground state transition rate. The observed photoswitching between dark and bright states indicates the strong sensitivity of the emitter to the electrostatic environment and the importance of the indirect excitation for the photodynamics.

Strain tunable quantum emission from atomic defects in hexagonal boron nitride for telecom-bands

This study presents extending the tunability of 2D hBN Quantum emitters towards telecom (C-band - 1530 to 1560 nm) and UV-C (solar blind - 100 to 280 nm) optical bands using external strain inducements, for long- and short-range quantum communication (Quantum key distribution (QKD)) applications, respectively. Quantum emitters are the basic building blocks of this QKD (quantum communication or information) technologies, which need to emit single photons over room temperature and capable of tuning the emission wavelength to the above necessary range. Recent literature revealed that quantum emitters in 2D hBN only has the ability to withstand at elevated temperatures and aggressive annealing treatments, but density functional theory (DFT) predictions stated that hBN can only emit the single photons from around 290 to 900 nm (UV to near-IR regions) range. So, there is a need to engineer and further tune the emission wavelength of hBN quantum emitters to the above said bands (necessary for efficient QKD implementation). One of the solutions to tune the emission wavelength is by inducing external strain. In this work, we examine the tunability of quantum emission in hBN with point defects by inducing three different normal strains using DFT computations. We obtained the tunability range up to 255 nm and 1589.5 nm, for the point defects viz boron mono vacancies (V_B) and boron mono vacancies with oxygen atoms (V_BO₂) respectively, which can enhance the successful implementation of the efficient QKD. We also examine the tunability of the other defects viz. nitrogen mono vacancies, nitrogen mono vacancy with self-interstitials, nitrogen mono vacancy with carbon interstitials, carbon dimers and boron dangling bonds, which revealed the tunable quantum emission in the visible, other UV and IR spectrum ranges and such customized quantum emission can enhance the birth of other quantum photonic devices.

Identification of an Oxygen Defect in Hexagonal Boron Nitride

Paramagnetic fluorescent defects in two-dimensional hexagonal boron nitride (hBN) are promising building blocks for quantum information processing. Although numerous defect-related single-photon sources and a few quantum bits have been found, except for the boron vacancy, their identification is still elusive. Here, we demonstrate that the comparison of experimental and first-principles simulated electron paramagnetic resonance (EPR) spectra is a powerful tool for defect identification in hBN, and first-principles modeling is inevitable in this process as a result of the dense nuclear spin environment of hBN. In particular, a recently observed EPR center is associated with the negatively charged oxygen vacancy complex by means of the many-body perturbation theory method on top of hybrid density functional calculations. To our surprise, the negatively charged oxygen vacancy complex produces a coherent emission around 2 eV with a well-reproducing previously recorded photoluminescence spectrum of some quantum emitters, according to our calculations.

Lifetime-Limited and Tunable Quantum Light Emission in h-BN via Electric Field Modulation

Color-center-based single-photon emitters in hexagonal boron nitride (h-BN) have shown promising photophysical properties as sources for quantum light emission. Despite significant advances toward such a goal, achieving lifetime-limited quantum light emission in h-BN has proven to be challenging, primarily due to various broadening mechanisms, including spectral diffusion. Here, we propose and experimentally demonstrate suppression of spectral diffusion by applying an electrostatic field. We observe both Stark shift tuning of the resonant emission wavelength and emission line width reduction (down to 89 MHz) nearly to the homogeneously broadened lifetime limit. Finally, we find a cubic dependence of the line width with respect to temperature at the homogeneous broadening regime. Our results suggest that field tuning in electrostatically gated heterostructures is promising as an approach to control the emission characteristics of h-BN color centers, removing spectral diffusion and providing the energy tunability necessary for integrate of quantum light emission in nanophotonic architectures.

Large-Scale, High-Yield Laser Fabrication of Bright and Pure Single-Photon Emitters at Room Temperature in Hexagonal Boron Nitride

Single-photon emitters (SPEs) play an important role in many optical quantum technologies. However, an efficient large-scale approach to the generation of high-quality SPE arrays remains an elusive goal at room temperature. Here, we demonstrate a scalable method of generating SPE arrays in hexagonal boron nitride (hBN) with high yield, brightness, and purity using single-pulse irradiation by a femtosecond laser. Our use of a single pulse per defect pattern minimized heat-related damages and improved the purity of SPEs compared with the previous laser-based approaches. Under the optimized fabrication and post-treatment conditions, SPE arrays were successfully generated from the 3.0 μm defect patterns with 43% yield, the highest among the 2D-based top-down approaches. Importantly, we found that 100% of the bright defect patterns are SPEs with g²(0) < 0.5 under such conditions, with the lowest g²(0) = 0.06 ± 0.03. Our SPEs also exhibit the highest brightness with the saturation SPE rate at 7.15 million counts per second. We believe that our overall high-quality and large-scale approach will help a wide range of applications of SPEs in on-chip quantum technologies.

Dehydrogenation of ammonia on free-standing and epitaxial hexagonal boron nitride

We report a thermodynamically feasible mechanism for producing H₂ from NH₃ using hBN as a catalyst. 2D catalysts have exceptional surface areas with unique thermal and electronic properties suited for catalysis. Metal-free, 2D catalysts, are highly desirable materials that can be more sustainable than the ubiquitously employed precious and transition metal-based catalysts. Here, using density functional theory (DFT) calculations, we demonstrate that metal-free hexagonal boron nitride (hBN) is a valid alternative to precious metal catalysts for producing H₂via reaction of ammonia with a boron and nitrogen divacancy (V_BN). Our results show that the decomposition of ammonia proceeds on monolayer hBN with an activation energy barrier of 0.52 eV. Furthermore, the reaction of ammonia with epitaxially grown hBN on a Ru(0001) substrate was investigated, and we observed similar NH₃ decomposition energy barriers (0.61 eV), but a much more facile H₂ associative desorption barrier (0.69 eV vs 5.89 eV). H₂ generation from the free-standing monolayer would instead occur through a diffusion process with an energy barrier of 3.36 eV. A detailed analysis of the electron density and charge distribution along the reaction pathways was carried out to rationalise the substrate effects on the catalytic reaction.

Tuning colour centres at a twisted hexagonal boron nitride interface

The colour centre platform holds promise for quantum technologies, and hexagonal boron nitride has attracted attention due to the high brightness and stability, optically addressable spin states and wide wavelength coverage discovered in its emitters. However, its application is hindered by the typically random defect distribution and complex mesoscopic environment. Here, employing cathodoluminescence, we demonstrate on-demand activation and control of colour centre emission at the twisted interface of two hexagonal boron nitride flakes. Further, we show that colour centre emission brightness can be enhanced by two orders of magnitude by tuning the twist angle. Additionally, by applying an external voltage, nearly 100% brightness modulation is achieved. Our ab initio GW and GW plus Bethe-Salpeter equation calculations suggest that the emission is correlated to nitrogen vacancies and that a twist-induced moiré potential facilitates electron-hole recombination. This mechanism is further exploited to draw nanoscale colour centre patterns using electron beams.

Tailoring the Emission Wavelength of Color Centers in Hexagonal Boron Nitride for Quantum Applications

Optical quantum technologies promise to revolutionize today’s information processing and sensors. Crucial to many quantum applications are efficient sources of pure single photons. For a quantum emitter to be used in such application, or for different quantum systems to be coupled to each other, the optical emission wavelength of the quantum emitter needs to be tailored. Here, we use density functional theory to calculate and manipulate the transition energy of fluorescent defects in the two-dimensional material hexagonal boron nitride. Our calculations feature the HSE06 functional which allows us to accurately predict the electronic band structures of 267 different defects. Moreover, using strain-tuning we can tailor the optical transition energy of suitable quantum emitters to match precisely that of quantum technology applications. We therefore not only provide a guide to make emitters for a specific application, but also have a promising pathway of tailoring quantum emitters that can couple to other solid-state qubit systems such as color centers in diamond.

Spin-Resolved Visible Optical Spectra and Electronic Characteristics of Defect-Mediated Hexagonal Boron Nitride Monolayer

Defect-mediated hexagonal boron nitride (hBN) supercells display visible optical spectra and electronic characteristics. The defects in the hBN supercells included atomic vacancy, antisite, antisite vacancy, and the substitution of a foreign atom for boron or nitrogen. The hBN supercells with VB, CB, and NB-VN were characterized by a high electron density of states across the Fermi level, which indicated high conductive electronic characteristics. The hBNs with defects including atomic vacancy, antisite at atomic vacancy, and substitution of a foreign atom for boron or nitride exhibited distinct spin-resolved optical and electronic characteristics, while defects of boron and nitrogen antisite did not display the spin-resolved optical characteristics. The hBNs with positively charged defects exhibited dominant optical and electronic characteristics in the longer spectral region. Acknowledgment: This work at HU is supported by ARO W911NF-15-1-0535, NSF HRD-1137747, and NASA NNX15AQ03A.

Reconstruction of Nuclear Ensemble Approach Electronic Spectra Using Probabilistic Machine Learning

The theoretical prediction of molecular electronic spectra by means of quantum mechanical (QM) computations is fundamental to gain a deep insight into many photophysical and photochemical processes. A computational strategy that is attracting significant attention is the so-called Nuclear Ensemble Approach (NEA), that relies on generating a representative ensemble of nuclear geometries around the equilibrium structure and computing the vertical excitation energies (ΔE) and oscillator strengths (f) and phenomenologically broadening each transition with a line-shaped function with empirical full-width δ. Frequently, the choice of δ is carried out by visually finding the trade-off between artificial vibronic features (small δ) and over-smoothing of electronic signatures (large δ). Nevertheless, this approach is not satisfactory, as it relies on a subjective perception and may lead to spectral inaccuracies overall when the number of sampled configurations is limited due to an excessive computational burden (high-level QM methods, complex systems, solvent effects, etc.). In this work, we have developed and tested a new approach to reconstruct NEA spectra, dubbed GMM-NEA, based on the use of Gaussian Mixture Models (GMMs), a probabilistic machine learning algorithm, that circumvents the phenomenological broadening assumption and, in turn, the use of δ altogether. We show that GMM-NEA systematically outperforms other data-driven models to automatically select δ overall for small datasets. In addition, we report the use of an algorithm to detect anomalous QM computations (outliers) that can affect the overall shape and uncertainty of the NEA spectra. Finally, we apply GMM-NEA to predict the photolysis rate for HgBrOOH, a compound involved in Earth's atmospheric chemistry.

Quantum emitters and detectors based on 2D van der Waals materials

Light plays an essential role in our world, with several technologies relying on it. Photons will also play an important role in the emerging quantum technologies, which are primed to have a transformative effect on our society. The development of single-photon sources and ultra-sensitive photon detectors is crucial. Solid-state emitters are being heavily pursued for developing truly single-photon sources for scalable technology. On the detectors' side, the main challenge lies in inventing sensitive detectors operating at sub-optical frequencies. This review highlights the promising research being conducted for the development of quantum emitters and detectors based on two-dimensional van der Waals (2D-vdW) materials. Several 2D-vdW materials, from canonical graphene to transition metal dichalcogenides and their heterostructures, have generated a lot of excitement due to their tunable emission and detection properties. The recent developments in the creation, fabrication and control of quantum emitters hosted by 2D-vdW materials and their potential applications in integrated photonic devices are discussed. Furthermore, the progress in enhancing the photon-counting potential of 2D material-based detectors, viz. 2D photodetectors, bolometers and superconducting single-photon detectors functioning at various wavelengths is also reported.

Donor-Acceptor Pair Quantum Emitters in Hexagonal Boron Nitride

Quantum emitters are needed for a myriad of applications ranging from quantum sensing to quantum computing. Hexagonal boron nitride (hBN) quantum emitters are one of the most promising solid-state platforms to date due to their high brightness and stability and the possibility of a spin-photon interface. However, the understanding of the physical origins of the single-photon emitters (SPEs) is still limited. Here we report dense SPEs in hBN across the entire visible spectrum and present evidence that most of these SPEs can be well explained by donor-acceptor pairs (DAPs). On the basis of the DAP transition generation mechanism, we calculated their wavelength fingerprint, matching well with the experimentally observed photoluminescence spectrum. Our work serves as a step forward for the physical understanding of SPEs in hBN and their applications in quantum technologies.

Density functionals with asymptotic-potential corrections are required for the simulation of spectroscopic properties of materials

Five effects of correction of the asymptotic potential error in density functionals are identified that significantly improve calculated properties of molecular excited states involving charge-transfer character. Newly developed materials-science computational methods are used to demonstrate how these effects manifest in materials spectroscopy. Connection is made considering chlorophyll-a as a paradigm for molecular spectroscopy, 22 iconic materials as paradigms for 3D materials spectroscopy, and the VN - defect in hexagonal boron nitride as an example of the spectroscopy of defects in 2D materials pertaining to nanophotonics. Defects can equally be thought of as being "molecular" and "materials" in nature and hence bridge the relms of molecular and materials spectroscopies. It is concluded that the density functional HSE06, currently considered as the standard for accurate calculations of materials spectroscopy, should be replaced, in most instances, by the computationally similar but asymptotically corrected CAM-B3LYP functional, with some specific functionals for materials-use only providing further improvements.

Room-temperature optically detected magnetic resonance of single defects in hexagonal boron nitride

Optically addressable solid-state spins are important platforms for quantum technologies, such as repeaters and sensors. Spins in two-dimensional materials offer an advantage, as the reduced dimensionality enables feasible on-chip integration into devices. Here, we report room-temperature optically detected magnetic resonance (ODMR) from single carbon-related defects in hexagonal boron nitride with up to 100 times stronger contrast than the ensemble average. We identify two distinct bunching timescales in the second-order intensity-correlation measurements for ODMR-active defects, but only one for those without an ODMR response. We also observe either positive or negative ODMR signal for each defect. Based on kinematic models, we relate this bipolarity to highly tuneable internal optical rates. Finally, we resolve an ODMR fine structure in the form of an angle-dependent doublet resonance, indicative of weak but finite zero-field splitting. Our results offer a promising route towards realising a room-temperature spin-photon quantum interface in hexagonal boron nitride.

Optical Inspection of 2D Materials: From Mechanical Exfoliation to Wafer-Scale Growth and Beyond

Optical inspection is a rapid and non-destructive method for characterizing the properties of two-dimensional (2D) materials. With the aid of optical inspection, in situ and scalable monitoring of the properties of 2D materials can be implemented industrially to advance the development and progress of 2D material-based devices toward mass production. This review discusses the optical inspection techniques that are available to characterize various 2D materials, including graphene, transition metal dichalcogenides (TMDCs), hexagonal boron nitride (h-BN), group-III monochalcogenides, black phosphorus (BP), and group-IV monochalcogenides. First, the authors provide an introduction to these 2D materials and the processes commonly used for their fabrication. Then they review several of the important structural properties of 2D materials, and discuss how to characterize them using appropriate optical inspection tools. The authors also describe the challenges and opportunities faced when applying optical inspection to recently developed 2D materials, from mechanically exfoliated to wafer-scale-grown 2D materials. Most importantly, the authors summarize the techniques available for largely and precisely enhancing the optical signals from 2D materials. This comprehensive review of the current status and perspective of future trends for optical inspection of the structural properties of 2D materials will facilitate the development of next-generation 2D material-based devices.

Strain Engineering of Low-Dimensional Materials for Emerging Quantum Phenomena and Functionalities

Recent discoveries of exotic physical phenomena, such as unconventional superconductivity in magic-angle twisted bilayer graphene, dissipationless Dirac fermions in topological insulators, and quantum spin liquids, have triggered tremendous interest in quantum materials. The macroscopic revelation of quantum mechanical effects in quantum materials is associated with strong electron-electron correlations in the lattice, particularly where materials have reduced dimensionality. Owing to the strong correlations and confined geometry, altering atomic spacing and crystal symmetry via strain has emerged as an effective and versatile pathway for perturbing the subtle equilibrium of quantum states. This review highlights recent advances in strain-tunable quantum phenomena and functionalities, with particular focus on low-dimensional quantum materials. Experimental strategies for strain engineering are first discussed in terms of heterogeneity and elastic reconfigurability of strain distribution. The nontrivial quantum properties of several strain-quantum coupled platforms, including 2D van der Waals materials and heterostructures, topological insulators, superconducting oxides, and metal halide perovskites, are next outlined, with current challenges and future opportunities in quantum straintronics followed. Overall, strain engineering of quantum phenomena and functionalities is a rich field for fundamental research of many-body interactions and holds substantial promise for next-generation electronics capable of ultrafast, dissipationless, and secure information processing and communications.

Nanoscale axial position and orientation measurement of hexagonal boron nitride quantum emitters using a tunable nanophotonic environment

Color centers in hexagonal boron nitride (hBN) have emerged as promising candidates for single-photon emitters (SPEs) due to their bright emission characteristics at room temperature. In contrast to mono- and few-layeredhBN, color centers in multi-layered flakes show superior emission characteristics such as higher saturation counts and spectral stability. Here, we report a method for determining both the axial position and three-dimensional dipole orientation of SPEs in thickhBN flakes by tuning the photonic local density of states using vanadium dioxide (VO₂), a phase change material. Quantum emitters under study exhibit a strong surface-normal dipole orientation, providing some insight on the atomic structure ofhBN SPEs, deeply embedded in thick crystals. Next, we optimized a hot pickup technique to reproducibly transfer thehBN flake from VO₂/sapphire substrate onto SiO₂/Si substrate and relocated the same emitters. Our approach serves as a practical method to systematically characterize SPEs inhBN prior to integration in quantum photonics systems.

Generation of High-Density Quantum Emitters in High-Quality, Exfoliated Hexagonal Boron Nitride

Single-photon emitters in hexagonal boron nitride (hBN) are promising constituents for integrated quantum photonics. Specifically, engineering these emitters in large-area, high-quality, exfoliated hBN is needed for their incorporation into photonic devices and two dimensional heterostructures. Here, we report on two different routes to generate high-density quantum emitters with excellent optical properties-including high brightness and photostability. We study in detail high-temperature annealing and plasma treatments as an efficient means to generate dense emitters. We show that both an optimal oxygen flow rate and annealing temperature are required for the formation of high-density quantum emitters. In parallel, we demonstrate that the plasma treatment in various environments, followed by standard annealing is also an effective route for emission engineering. Our work provides vital information for the fabrication of quantum emitters in high-quality, exfoliated hBN flakes and paves the way toward the integration of the quantum emitters with photonic devices.

Extrinsic Effects on the Optical Properties of Surface Color Defects Generated in Hexagonal Boron Nitride Nanosheets

Hexagonal boron nitride (hBN) is a wide-band gap van der Waals material able to host light-emitting centers behaving as single photon sources. Here, we report the generation of color defects in hBN nanosheets dispersed on different kinds of substrates by thermal treatment processes. The optical properties of these defects have been studied using microspectroscopy techniques and far-field simulations of their light emission. Using these techniques, we have found that subsequent ozone treatments of the deposited hBN nanosheets improve the optical emission properties of created defects, as revealed by their zero-phonon linewidth narrowing and reduction of background emission. Microlocalized color defects deposited on dielectric substrates show bright (≈1 MHz) and stable room-temperature light emission with zero-phonon line peak energy varying from 1.56 to 2.27 eV, being the most probable value 2.16 eV. In addition to this, we have observed a substrate dependence of the optical performance of the generated color defects. The energy range of the emitters prepared on gold substrates is strongly reduced, as compared to that observed in dielectric substrates or even alumina. We attribute this effect to the quenching of low-energy color defects (these of energies lower than 1.9 eV) when gold substrates are used, which reveals the surface nature of the defects created in hBN nanosheets. Results described here are important for future quantum light experiments and their integration in photonic chips.

Defect Polaritons from First Principles

Control over the optical properties of defects in solid-state materials is necessary for their application in quantum technologies. In this study, we demonstrate, from first principles, how to tune these properties via the formation of defect polaritons in an optical cavity. We show that the polaritonic splitting that shifts the absorption energy of the lower polariton is much higher than can be expected from a Jaynes-Cummings interaction. We also find that the absorption intensity of the lower polariton increases by several orders of magnitude, suggesting a possible route toward overcoming phonon-limited single-photon emission from defect centers. These findings are a result of an effective continuum of electronic transitions near the lowest-lying electronic transition that dramatically enhances the strength of the light-matter interaction. We expect our findings to spur experimental investigations of strong light-matter coupling between defect centers and cavity photons for applications in quantum technologies.

Point Defects in Monolayer h-AlN as Candidates for Single-Photon Emission

A single-photon emission (SPE) system based on a solid state is one of the fundamental branches in quantum information and communication technologies. The traditional bulk semiconductors suffered limitations of difficult photon extraction and long radiative lifetime. Two-dimensional (2D) semiconductors with an entire open structure and low dielectric screening can overcome these shortcomings. In this work, we focus on monolayer h-AlN due to its wide band gap and the successful achievement of SPE compared to its bulk counterpart. We systematically investigate the properties of point defects, including vacancies, antisites, and impurities, in monolayer h-AlN by employing hybrid density functional theory calculations. The -1 charged Al vacancy (V_Al^-) and +1 charged nitrogen antisite (N_Al⁺) are predicted to achieve SPE with the zero-phonon lines of 0.77 and 1.40 eV, respectively. Moreover, the charged point-defect complex C_AlV_N⁺, which is composed of vacancies and carbon substitutions, also can be used for SPE. Our results extend the avenue for realizing SPE in 2D semiconductors.

Polymer transfer technique for strain-activated emission in hexagonal boron nitride

We present a hexagonal boron nitride (hBN) polymer-assisted transfer technique and discuss subtleties about the process. We then demonstrate localized emission from strained regions of the film draped over features on a prepatterned substrate. Notably, we provide insight into the brightness distribution of these emitters and show that the brightest emission is clearly localized to the underlyin-g substrate features rather than unintentional wrinkles present in the hBN film. Our results aide in the current discussion surrounding scalability of single photon emitter arrays.

Optical quantum technologies with hexagonal boron nitride single photon sources

Single photon quantum emitters are important building blocks of optical quantum technologies. Hexagonal boron nitride (hBN), an atomically thin wide band gap two dimensional material, hosts robust, optically active luminescent point defects, which are known to reduce phonon lifetimes, promises as a stable single-photon source at room temperature. In this Review, we present the recent advances in hBN quantum light emission, comparisons with other 2D material based quantum sources and analyze the performance of hBN quantum emitters. We also discuss state-of-the-art stable single photon emitter's fabrication in UV, visible and near IR regions, their activation, characterization techniques, photostability towards a wide range of operating temperatures and harsh environments, Density-functional theory predictions of possible hBN defect structures for single photon emission in UV to IR regions and applications of single photon sources in quantum communication and quantum photonic circuits with associated potential obstacles.

Accurate prediction of the properties of materials using the CAM-B3LYP density functional

Density functionals with asymptotic corrections to the long-range potential provide entry-level methods for calculations on molecules that can sustain charge transfer, but similar applications in materials science are rare. We describe an implementation of the CAM-B3LYP range-separated functional within the Vienna Ab-initio Simulation Package (VASP) framework, together with its analytical functional derivatives. Results obtained for eight representative materials: aluminum, diamond, graphene, silicon, NaCl, MgO, 2D h-BN, and 3D h-BN, indicate that CAM-B3LYP predictions embody mean-absolute deviations (MAD) compared to HSE06 that are reduced by a factor of six for lattice parameters, four for quasiparticle band gaps, three for the lowest optical excitation energies, and six for exciton binding energies. Further, CAM-B3LYP appears competitive compared to ab initio G₀ W₀ and Bethe-Salpeter equation approaches. The CAM-B3LYP implementation in VASP was verified by comparison of optimized geometries and reaction energies for isolated molecules taken from the ACCDB database, evaluated in large periodic unit cells, to analogous results obtained using Gaussian basis sets. Using standard GW pseudopotentials and energy cutoffs for the plane-wave calculations and the aug-cc-pV5Z basis set for the atomic-basis ones, the MAD in energy for 1738 chemical reactions was 0.34 kcal mol^-1 , while for 480 unique bond lengths this was 0.0036 Å; these values reduced to 0.28 kcal mol^-1 (largest error 0.94 kcal mol^-1 ) and 0.0009 Å by increasing the plane-wave cutoff energy to 850 eV.

Atomistic Simulations of Defect Production in Monolayer and Bulk Hexagonal Boron Nitride under Low- and High-Fluence Ion Irradiation

Controlled production of defects in hexagonal boron nitride (h-BN) through ion irradiation has recently been demonstrated to be an effective tool for adding new functionalities to this material, such as single-photon generation, and for developing optical quantum applications. Using analytical potential molecular dynamics, we study the mechanisms of vacancy creation in single- and multi-layer h-BN under low- and high-fluence ion irradiation. Our results quantify the densities of defects produced by noble gas ions in a wide range of ion energies and elucidate the types and distribution of defects in the target. The simulation data can directly be used to guide the experiment aimed at the creation of defects of particular types in h-BN targets for single-photon emission, spin-selective optical transitions and other applications by using beams of energetic ions.

Stimulated Emission Depletion Spectroscopy of Color Centers in Hexagonal Boron Nitride

We demonstrate the use of Stimulated Emission Depletion (STED) spectroscopy to map the electron-optical-phonon sideband of the ground state of the radiative transition of color centers in hexagonal boron nitride emitting at 2.0-2.2 eV, with in-plane linear polarization. The measurements are compared to photoluminescence of excitation (PLE) spectra that maps the electron-optical-phonon sideband of the excited state. The main qualitative difference is a red-shift in the longitudinal optical phonon peak associated with E _1u symmetry at the zone center. We compare our results to theoretical work on different defect species in hBN and find they are consistent with a carbon-based defect.

Stimulated Emission Depletion Spectroscopy of Color Centers in Hexagonal Boron Nitride

We demonstrate the use of Stimulated Emission Depletion (STED) spectroscopy to map the electron-optical-phonon sideband of the ground state of the radiative transition of color centers in hexagonal boron nitride emitting at 2.0-2.2 eV, with in-plane linear polarization. The measurements are compared to photoluminescence of excitation (PLE) spectra that maps the electron-optical-phonon sideband of the excited state. The main qualitative difference is a red-shift in the longitudinal optical phonon peak associated with E _1u symmetry at the zone center. We compare our results to theoretical work on different defect species in hBN and find they are consistent with a carbon-based defect.

Hybridized Defects in Solid-State Materials as Artificial Molecules

Two-dimensional materials can be crafted with structural precision approaching the atomic scale, enabling quantum defects-by-design. These defects are frequently described as "artificial atoms" and are emerging optically addressable spin qubits. However, interactions and coupling of such artificial atoms with each other, in the presence of the lattice, warrants further investigation. Here we present the formation of "artificial molecules" in solids, introducing a chemical degree of freedom in control of quantum optoelectronic materials. Specifically, in monolayer hexagonal boron nitride as our model system, we observe configuration- and distance-dependent dissociation curves and hybridization of defect orbitals within the bandgap into bonding and antibonding orbitals, with splitting energies ranging from ∼10 meV to nearly 1 eV. We calculate the energetics of cis and trans out-of-plane defect pairs CH_B-CH_B against an in-plane defect pair C_B-C_B and find that in-plane defect pair interacts more strongly than out-of-plane pairs. We demonstrate an application of this chemical degree of freedom by varying the distance between C_B and V_N of C_BV_N and observe changes in the predicted peak absorption wavelength from the visible to the near-infrared spectral band. We envision leveraging this chemical degree of freedom of defect complexes to precisely control and tune defect properties toward engineering robust quantum memories and quantum emitters for quantum information science.

First-Principles Identification of Single Photon Emitters Based on Carbon Clusters in Hexagonal Boron Nitride

A recent study associates carbon with single photon emitters (SPEs) in hexagonal boron nitride (h-BN). This observation, together with the high mobility of carbon in h-BN, suggests the existence of SPEs based on carbon clusters. Here, by means of density functional theory calculations, we studied clusters of substitutional carbon atoms up to tetramers in h-BN. Two different conformations of neutral carbon trimers have zero-point line energies and shifts of the phonon sideband compatible with typical photoluminescence spectra. Moreover, some conformations of two small C clusters next to each other result in photoluminescence spectra similar to those found in the experiments. We also showed that vacancies are unable to reproduce the typical features of the phonon sideband observed in most measurements because of the large spectral weight of low-energy breathing modes, ubiquitous in such defects.

DMRG on Top of Plane-Wave Kohn-Sham Orbitals: A Case Study of Defected Boron Nitride

In this paper, we analyze the numerical aspects of the inherent multireference density matrix renormalization group (DMRG) calculations on top of the periodic Kohn-Sham density functional theory using the complete active space approach. The potential of the framework is illustrated by studying hexagonal boron nitride nanoflakes embedding a charged single boron vacancy point defect by revealing a vertical energy spectrum with a prominent multireference character. We investigate the consistency of the DMRG energy spectrum from the perspective of sample size, basis size, and active space selection protocol. Results obtained from standard quantum chemical atom-centered basis calculations and plane-wave based counterparts show excellent agreement. Furthermore, we also discuss the spectrum of the periodic sheet which is in good agreement with extrapolated data of finite clusters. These results pave the way toward applying the DMRG method in extended correlated solid-state systems, such as point defect qubit in wide band gap semiconductors.

Controlled generation of luminescent centers in hexagonal boron nitride by irradiation engineering

Luminescent centers in the two-dimensional material hexagonal boron nitride have the potential to enable quantum applications at room temperature. To be used for applications, it is crucial to generate these centers in a controlled manner and to identify their microscopic nature. Here, we present a method inspired by irradiation engineering with oxygen atoms. We systematically explore the influence of the kinetic energy and the irradiation fluence on the generation of luminescent centers. We find modifications of their density for both parameters, while a fivefold enhancement is observed with increasing fluence. Molecular dynamics simulations clarify the generation mechanism of these centers and their microscopic nature. We infer that V_NC_B and [Formula: see text] are the most likely centers formed. Ab initio calculations of their optical properties show excellent agreement with our experiments. Our methodology generates quantum emitters in a controlled manner and provides insights into their microscopic nature.

Emerging Light-Emitting Materials for Photonic Integration

The arrival of the information explosion era is urging the development of large-bandwidth high-data-rate optical interconnection technology. Up to now, the biggest stumbling block in optical interconnections has been the lack of efficient light sources despite significant progress that has been made in germanium-on-silicon (Ge-on-Si) and III-V-on-silicon (III-V-on-Si) lasers. 2D materials and metal halide perovskites have attracted much attention in recent years, and exhibit distinctive advantages in the application of on-chip light emitters. Herein, this Progress Report reviews the recent progress made in light-emitting materials with a focus on new materials, i.e., 2D materials and metal halide perovskites. The report briefly introduces the current status of Ge-on-Si and III-V-on-Si lasers and discusses the advances of 2D and perovskite light-emitting materials for photonic integration, including their optical properties, preparation methods, as well as the light sources based on these materials. Finally, challenges and perspectives of these emerging materials on the way to the efficient light sources are discussed.

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.

Polarization and Localization of Single-Photon Emitters in Hexagonal Boron Nitride Wrinkles

Color centers in two-dimensional hexagonal boron nitride (h-BN) have recently emerged as stable and bright single-photon emitters (SPEs) operating at room temperature. In this study, we combine theory and experiment to show that vacancy-based SPEs selectively form at nanoscale wrinkles in h-BN with its optical dipole preferentially aligned to the wrinkle direction. By using density functional theory calculations, we find that the wrinkle's curvature plays a crucial role in localizing vacancy-based SPE candidates and aligning the defect's symmetry plane to the wrinkle direction. By performing optical measurements on SPEs created in h-BN single-crystal flakes, we experimentally confirm the wrinkle-induced generation of SPEs and their polarization alignment to the wrinkle direction. Our results not only provide a new route to controlling the atomic position and the optical property of the SPEs but also revealed the possible crystallographic origin of the SPEs in h-BN, greatly enhancing their potential for use in solid-state quantum photonics and quantum information processing.

Bootstrap Embedding For Large Molecular Systems

Recent developments in quantum embedding theories have provided attractive approaches to correlated calculations for large systems. In this work, we extend our previous work [J. Chem. Theory Comput. 2019, 15, 4497-4506; J. Phys. Chem. Lett. 2019, 10, 6368-6374] on bootstrap embedding (BE) to enable correlated ab initio calculations at the coupled cluster with singles and doubles (CCSD) level for large molecules. We introduce several new algorithmic developments that significantly reduce the computational cost of BE, while maintaining its accuracy. The resulting implementation scales as O(N³) for the integral transform and O(N) for the CCSD calculation. Numerical results on a series of conjugated molecules suggest that BE with reasonably sized fragments can recover more than 99.5% of the total correlation energy of a full CCSD calculation, while the required computational resources (time and storage) compare favorably to one popular local correlation scheme: domain localized pair natural orbital (DLPNO). The largest BE calculation in this work involves ∼2900 basis functions and can be performed on a single node with 16 CPU cores and 64 GB of memory in a few days. We anticipate that these developments represent an important step toward the application of BE to solve practical problems.

Midgap radiative centers in carbon-enriched hexagonal boron nitride

When serving as a protection tissue and/or inducing a periodic lateral modulation for/in atomically thin crystals, hexagonal boron nitride (hBN) has revolutionized the research on van der Waals heterostructures. By itself, hBN appears as an emergent wide-bandgap material, which, importantly, can be optically bright in the far-ultraviolet range and which frequently displays midgap defect-related centers of yet-unclear origin, but, interestingly, acting as single-photon emitters. Controlling the hBN doping is of particular interest in view of the possible practical use of this material. Here, we demonstrate that enriching hBN with carbon (C) activates an optical response of this material in the form of a series of well-defined resonances in visible and near-infrared regions, which appear in the luminescence spectra measured under below-bandgap excitation. Two, qualitatively different, C-related radiative centers are identified: One follows the Franck-Condon principle that describes transitions between two defect states with emission/annihilation of optical phonons, and the other shows atomic-like resonances characteristic of intradefect transitions. With a detailed characterization of the energy structure and emission dynamics of these radiative centers, we contribute to the development of controlled doping of hBN with midgap centers.

Hexagonal boron nitride: a review of the emerging material platform for single-photon sources and the spin-photon interface

Single-photon sources and their optical spin readout are at the core of applications in quantum communication, quantum computation, and quantum sensing. Their integration in photonic structures such as photonic crystals, microdisks, microring resonators, and nanopillars is essential for their deployment in quantum technologies. While there are currently only two material platforms (diamond and silicon carbide) with proven single-photon emission from the visible to infrared, a quantum spin-photon interface, and ancilla qubits, it is expected that other material platforms could emerge with similar characteristics in the near future. These two materials also naturally lead to monolithic integrated photonics as both are good photonic materials. While so far the verification of single-photon sources was based on discovery, assignment and then assessment and control of their quantum properties for applications, a better approach could be to identify applications and then search for the material that could address the requirements of the application in terms of quantum properties of the defects. This approach is quite difficult as it is based mostly on the reliability of modeling and predicting of color center properties in various materials, and their experimental verification is challenging. In this paper, we review some recent advances in an emerging material, low-dimensional (2D, 1D, 0D) hexagonal boron nitride (h-BN), which could lead to establishing such a platform. We highlight the recent achievements of the specific material for the expected applications in quantum technologies, indicating complementary outstanding properties compared to the other 3D bulk materials.