Optical Absorption and Emission Mechanisms of Single Defects in Hexagonal Boron Nitride

Room Temperature Dynamics of an Optically Addressable Single Spin in Hexagonal Boron Nitride

Hexagonal boron nitride (h-BN) hosts pure single-photon emitters that have shown evidence of optically detected electronic spin dynamics. However, the electrical and chemical structures of these optically addressable spins are unknown, and the nature of their spin-optical interactions remains mysterious. Here, we use time-domain optical and microwave experiments to characterize a single emitter in h-BN exhibiting room temperature optically detected magnetic resonance. Using dynamical simulations, we constrain and quantify transition rates in the model, and we design optical control protocols that optimize the signal-to-noise ratio for spin readout. This constitutes a necessary step toward quantum control of spin states in h-BN.

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.

Cryogenic Thermal Shock Effects on Optical Properties of Quantum Emitters in Hexagonal Boron Nitride

Solid-state quantum emitters are vital building blocks for quantum information science and quantum technology. Among various types of solid-state emitters discovered to date, color centers in hexagonal boron nitride have garnered tremendous traction in recent years, thanks to their environmental robustness, high brightness, and room-temperature operation. Most recently, these quantum emitters have been employed for satellite-based quantum key distribution. One of the most important requirements to qualify these emitters for space-based applications is their optical stability against cryogenic thermal shock. Such an understanding has, however, remained elusive to date. Here, we report on the effects caused by such thermal shock that induces random, irreversible changes in the spectral characteristics of the quantum emitters. By employing a combination of structural characterizations and density functional calculations, we attribute the observed changes to lattice strain caused by cryogenic temperature shock. Our study sheds light on the stability of the quantum emitters under extreme conditions─similar to those countered in outer space.

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.

Carbon-Related Quantum Emitter in Hexagonal Boron Nitride with Homogeneous Energy and 3-Fold Polarization

Most hexagonal boron nitride (hBN) single-photon emitters (SPEs) studied to date suffer from variable emission energy and unpredictable polarization, two crucial obstacles to their application in quantum technologies. Here, we report an SPE in hBN with an energy of 2.2444 ± 0.0013 eV created via carbon implantation that exhibits a small inhomogeneity of the emission energy. Polarization-resolved measurements reveal aligned absorption and emission dipole orientations with a 3-fold distribution, which follows the crystal symmetry. Photoluminescence excitation (PLE) spectroscopy results show the predictability of polarization is associated with a reproducible PLE band, in contrast with the non-reproducible bands found in previous hBN SPE species. Photon correlation measurements are consistent with a three-level model with weak coupling to a shelving state. Our ab initio excited-state calculations shed light on the atomic origin of this SPE defect, which consists of a pair of substitutional carbon atoms located at boron and nitrogen sites separated by a hexagonal unit cell.

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.

Comprehensive Scheme for Identifying Defects in Solid-State Quantum Systems

A solid-state quantum emitter is a crucial component for optical quantum technologies, ideally with a compatible wavelength for efficient coupling to other components in a quantum network. It is essential to understand fluorescent defects that lead to specific emitters. In this Letter, we employ density functional theory (DFT) to demonstrate the calculations of the complete optical fingerprints of quantum emitters in hexagonal boron nitride. Our results suggest that instead of comparing a single optical property, like the zero-phonon line energy, multiple properties should be used when comparing simulations to the experiment. Moreover, we apply this approach to predict the suitability of using the emitters in specific quantum applications. We therefore apply DFT calculations to identify quantum emitters with a lower risk of misassignments and a way to design optical quantum systems. Hence, we provide a recipe for classification and generation of universal quantum emitters in future hybrid quantum networks.

Discretized hexagonal boron nitride quantum emitters and their chemical interconversion

Quantum emitters in two-dimensional hexagonal boron nitride (hBN) are of significant interest because of their unique photophysical properties, such as single-photon emission at room temperature, and promising applications in quantum computing and communications. The photoemission from hBN defects covers a wide range of emission energies but identifying and modulating the properties of specific emitters remain challenging due to uncontrolled formation of hBN defects. In this study, more than 2000 spectra are collected consisting of single, isolated zero-phonon lines (ZPLs) between 1.59 and 2.25 eV from diverse sample types. Most of ZPLs are organized into seven discretized emission energies. All emitters exhibit a range of lifetimes from 1 to 6 ns, and phonon sidebands offset by the dominant lattice phonon in hBN near 1370 cm^-1. Two chemical processing schemes are developed based on water and boric acid etching that generate or preferentially interconvert specific emitters, respectively. The identification and chemical interconversion of these discretized emitters should significantly advance the understanding of solid-state chemistry and photophysics of hBN quantum emission.

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.

Nonlinear absorption and integrated photonics applications of MoSSe

This study explores the wavelength-dependent and pulse-width-dependent nonlinear optical properties of liquid-phase exfoliated molybdenum sulfide selenide (MoSSe) nanosheets. The saturable absorption response of MoSSe nanosheets in the visible region is better than that in the near-infrared region, and the response under 6-ns pulse excitation is better than that of a 380-fs pulse. Furthermore, based on the first-principles calculations, we designed a phase modulator and optimized its structure by integrating a monolayer MoSSe into a silicon slot waveguide. The simulation results revealed that the phase shift could achieve a high optical extinction. Consequently, MoSSe exhibits satisfactory nonlinear optical properties and an excellent potential for applications in optoelectronic devices.

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.

Excited-state spin-resonance spectroscopy of V[Formula: see text] defect centers in hexagonal boron nitride

The recently discovered spin-active boron vacancy (V[Formula: see text]) defect center in hexagonal boron nitride (hBN) has high contrast optically-detected magnetic resonance (ODMR) at room-temperature, with a spin-triplet ground-state that shows promise as a quantum sensor. Here we report temperature-dependent ODMR spectroscopy to probe spin within the orbital excited-state. Our experiments determine the excited-state spin Hamiltonian, including a room-temperature zero-field splitting of 2.1 GHz and a g-factor similar to that of the ground-state. We confirm that the resonance is associated with spin rotation in the excited-state using pulsed ODMR measurements, and we observe Zeeman-mediated level anti-crossings in both the orbital ground- and excited-state. Our observation of a single set of excited-state spin-triplet resonance from 10 to 300 K is suggestive of symmetry-lowering of the defect system from D3h to C2v. Additionally, the excited-state ODMR has strong temperature dependence of both contrast and transverse anisotropy splitting, enabling promising avenues for quantum sensing.

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.

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.

Coupling Spin Defects in Hexagonal Boron Nitride to Monolithic Bullseye Cavities

Color centers in hexagonal boron nitride (hBN) are becoming an increasingly important building block for quantum photonic applications. Herein, we demonstrate the efficient coupling of recently discovered spin defects in hBN to purposely designed bullseye cavities. We show that boron vacancy spin defects couple to the monolithic hBN cavity system and exhibit a 6.5-fold enhancement. In addition, by comparative finite-difference time-domain modeling, we shed light on the emission dipole orientation, which has not been experimentally demonstrated at this point. Beyond that, the coupled spin system exhibits an enhanced contrast in optically detected magnetic resonance readout and improved signal-to-noise ratio. Thus, our experimental results, supported by simulations, constitute a first step toward integration of hBN spin defects with photonic resonators for a scalable spin-photon interface.

Spin-induced linear polarization of photoluminescence in antiferromagnetic van der Waals crystals

Antiferromagnets are promising components for spintronics due to their terahertz resonance, multilevel states and absence of stray fields. However, the zero net magnetic moment of antiferromagnets makes the detection of the antiferromagnetic order and the investigation of fundamental spin properties notoriously difficult. Here, we report an optical detection of Néel vector orientation through an ultra-sharp photoluminescence in the van der Waals antiferromagnet NiPS₃ from bulk to atomically thin flakes. The strong correlation between spin flipping and electric dipole oscillator results in a linear polarization of the sharp emission, which aligns perpendicular to the spin orientation in the crystal. By applying an in-plane magnetic field, we achieve manipulation of the photoluminescence polarization. This correlation between emitted photons and spins in layered magnets provides routes for investigating magneto-optics in two-dimensional materials, and hence opens a path for developing opto-spintronic devices and antiferromagnet-based quantum information technologies.

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.

Photoluminescence upconversion of 2D materials and applications

Photoluminescence (PL) upconversion is a phenomenon involving light-matter interactions, where the energy of emitted photons is higher than that of the incident photons. PL upconversion is an intriguing process in two-dimensional materials and specifically designed 2D heterostructures, which have potential upconversion applications in optoelectronic devices, bioimaging, and semiconductor cooling. In this review, we focus on the recent advances in photoluminescence upconversion in two-dimensional materials and their heterostructures. We discuss the upconversion mechanisms, applications, and future outlook of upconversion in two-dimensional materials.

Cubic-Scaling All-Electron GW Calculations with a Separable Density-Fitting Space-Time Approach

We present an implementation of the GW space-time approach that allows cubic-scaling all-electron calculations with standard Gaussian basis sets without exploiting any localization or sparsity considerations. The independent-electron susceptibility is constructed in a time representation over a nonuniform distribution of real-space locations {r_k} optimized within a separable resolution-of-the-identity framework to reproduce standard Coulomb-fitting calculations with meV accuracy. The compactness of the obtained {r_k} distribution leads to a crossover with the standard Coulomb-fitting scheme for system sizes below a few hundred electrons. The needed analytic continuation follows a recent approach that requires the continuation of the screened Coulomb potential rather than the much more structured self-energy. The present scheme is benchmarked over large molecular sets, and scaling properties are demonstrated on a family of defected hexagonal boron-nitride flakes containing up to 6000 electrons.

Identifying carbon as the source of visible single-photon emission from hexagonal boron nitride

Single-photon emitters (SPEs) in hexagonal boron nitride (hBN) have garnered increasing attention over the last few years due to their superior optical properties. However, despite the vast range of experimental results and theoretical calculations, the defect structure responsible for the observed emission has remained elusive. Here, by controlling the incorporation of impurities into hBN via various bottom-up synthesis methods and directly through ion implantation, we provide direct evidence that the visible SPEs are carbon related. Room-temperature optically detected magnetic resonance is demonstrated on ensembles of these defects. We perform ion-implantation experiments and confirm that only carbon implantation creates SPEs in the visible spectral range. Computational analysis of the simplest 12 carbon-containing defect species suggest the negatively charged [Formula: see text] defect as a viable candidate and predict that out-of-plane deformations make the defect environmentally sensitive. Our results resolve a long-standing debate about the origin of single emitters at the visible range in hBN and will be key to the deterministic engineering of these defects for quantum photonic devices.

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.

Turn of the decade: versatility of 2D hexagonal boron nitride

The era of two-dimensional (2D) materials, in its current form, truly began at the time that graphene was first isolated just over 15 years ago. Shortly thereafter, the use of 2D hexagonal boron nitride (h-BN) had expanded in popularity, with use of the thin isolator permeating a significant number of fields in condensed matter and beyond. Due to the impractical nature of cataloguing every use or research pursuit, this review will cover ground in the following three subtopics relevant to this versatile material: growth, electrical measurements, and applications in optics and photonics. Through understanding how the material has been utilized, one may anticipate some of the exciting directions made possible by the research conducted up through the turn of this decade.

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.

Coupling Hexagonal Boron Nitride Quantum Emitters to Photonic Crystal Cavities

Quantum photonics technologies require a scalable approach for the integration of nonclassical light sources with photonic resonators to achieve strong light confinement and enhancement of quantum light emission. Point defects from hexagonal boron nitride (hBN) are among the front runners for single photon sources due to their ultra-bright emission; however, the coupling of hBN defects to photonic crystal cavities has so far remained elusive. Here we demonstrate on-chip integration of hBN quantum emitters with photonic crystal cavities from silicon nitride (Si₃N₄) and achieve an experimentally measured quality factor (Q-factor) of 3300 for hBN/Si₃N₄ hybrid cavities. We observed 6-fold photoluminescence enhancement of an hBN single photon emission at room temperature. Our work will be useful for further development of cavity quantum electrodynamic experiments and on-chip integration of two-dimensional (2D) materials.

Optical Gating of Photoluminescence from Color Centers in Hexagonal Boron Nitride

We report on multicolor excitation experiments with color centers in hexagonal boron nitride at cryogenic temperatures. We demonstrate controllable optical switching between bright and dark states of color centers emitting around 2 eV. Resonant, or quasi-resonant, excitation of photoluminescence also pumps the color center, via a two-photon process, into a dark state, where it becomes trapped. Repumping back into the bright state has a step-like spectrum with a defect-dependent threshold between 2.25 and 2.6 eV. This behavior is consistent with photoionization and charging between optically bright and dark states of the defect. Furthermore, a second zero phonon line, detuned by +0.4 eV, is observed in absorption with orthogonal polarization to the emission, evidencing an additional energy level in the color center.

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.

Revealing multiple classes of stable quantum emitters in hexagonal boron nitride with correlated optical and electron microscopy

Defects in hexagonal boron nitride (hBN) exhibit high-brightness, room-temperature quantum emission, but their large spectral variability and unknown local structure challenge their technological utility. Here, we directly correlate hBN quantum emission with local strain using a combination of photoluminescence (PL), cathodoluminescence (CL) and nanobeam electron diffraction. Across 40 emitters, we observe zero phonon lines (ZPLs) in PL and CL ranging from 540 to 720 nm. CL mapping reveals that multiple defects and distinct defect species located within an optically diffraction-limited region can each contribute to the observed PL spectra. Local strain maps indicate that strain is not required to activate the emitters and is not solely responsible for the observed ZPL spectral range. Instead, at least four distinct defect classes are responsible for the observed emission range, and all four classes are stable upon both optical and electron illumination. Our results provide a foundation for future atomic-scale optical characterization of colour centres.

Single-photon emitters in hexagonal boron nitride: a review of progress

This report summarizes progress made in understanding properties such as zero-phonon-line energies, emission and absorption polarizations, electron-phonon couplings, strain tuning and hyperfine coupling of single photon emitters in hexagonal boron nitride. The primary aims of this research are to discover the chemical nature of the emitting centres and to facilitate deployment in device applications. Critical analyses of the experimental literature and data interpretation, as well as theoretical approaches used to predict properties, are made. In particular, computational and theoretical limitations and challenges are discussed, with a range of suggestions made to overcome these limitations, striving to achieve realistic predictions concerning the nature of emitting centers. A symbiotic relationship is required in which calculations focus on properties that can easily be measured, whilst experiments deliver results in a form facilitating mass-produced calculations.

Photophysics of quantum emitters in hexagonal boron-nitride nano-flakes

Quantum emitters in hexagonal boron nitride (hBN) have attracted significant interest due to their bright and narrowband photon emission even at room temperature. The wide-bandgap two-dimensional material incorporates crystal defects of yet-unknown configuration, introducing discrete energy levels with radiative transition frequencies in the visible spectral range. The commonly observed high brightness together with the moderate fluorescence lifetime indicates a high quantum efficiency, but the exact dynamics and the underlying energy level structure remain elusive. In this study we present a systematic and detailed analysis of the photon statistics recorded for several individual emitters. We extract the individual decay rates by modeling the second-order correlation functions using a set of rate equations based on an energy level scheme involving long-lived states. Our analysis clearly indicates excitation-power-dependent non-radiative couplings to at least two metastable levels and confirms a near unity quantum efficiency.

Vapor-liquid-solid growth of large-area multilayer hexagonal boron nitride on dielectric substrates

Multilayer hexagonal boron nitride (h-BN) is highly desirable as a dielectric substrate for the fabrication of two-dimensional (2D) electronic and optoelectronic devices. However, the controllable synthesis of multilayer h-BN in large areas is still limited in terms of crystallinity, thickness and stacking order. Here, we report a vapor–liquid–solid growth (VLSG) method to achieve uniform multilayer h-BN by using a molten Fe₈₂B₁₈ alloy and N₂ as reactants. Liquid Fe₈₂B₁₈ not only supplies boron but also continuously dissociates nitrogen atoms from the N₂ vapor to support direct h-BN growth on a sapphire substrate; therefore, the VLSG method delivers high-quality h-BN multilayers with a controllable thickness. Further investigation of the phase evolution of the Fe-B-N system reveals that isothermal segregation dominates the growth of the h-BN. The approach herein demonstrates the feasibility for large-area fabrication of van der Waals 2D materials and heterostructures.

Multilayer hexagonal boron nitride (hBN) is a desirable dielectric substrate for 2D electronics but its controllable synthesis is challenging. Here, the authors report a vapor–liquid–solid growth method to achieve uniform multilayer hBN by using a molten Fe₈₂B₁₈ alloy and N₂ as reactants.

Light Scattering from Solid-State Quantum Emitters: Beyond the Atomic Picture

Coherent scattering of light by a single quantum emitter is a fundamental process at the heart of many proposed quantum technologies. Unlike atomic systems, solid-state emitters couple to their host lattice by phonons. Using a quantum dot in an optical nanocavity, we resolve these interactions in both time and frequency domains, going beyond the atomic picture to develop a comprehensive model of light scattering from solid-state emitters. We find that even in the presence of a low-Q cavity with high Purcell enhancement, phonon coupling leads to a sideband that is completely insensitive to excitation conditions and to a nonmonotonic relationship between laser detuning and coherent fraction, both of which are major deviations from atomlike behavior.

Dangling Bonds in Hexagonal Boron Nitride as Single-Photon Emitters

Hexagonal boron nitride has been found to host color centers that exhibit single-photon emission, but the microscopic origin of these emitters is unknown. We propose boron dangling bonds as the likely source of the observed single-photon emission around 2 eV. An optical transition where an electron is excited from a doubly occupied boron dangling bond to a localized B p_{z} state gives rise to a zero-phonon line of 2.06 eV and emission with a Huang-Rhys factor of 2.3. This transition is linearly polarized with the absorptive and emissive dipole aligned. Because of the energetic position of the states within the band gap, indirect excitation through the conduction band will occur for sufficiently large excitation energies, leading to the misalignment of the absorptive and emissive dipoles seen in experiment. Our calculations predict a singlet ground state and the existence of a metastable triplet state, in agreement with experiment.

Single Photon Sources in Atomically Thin Materials

Layered materials are very attractive for studies of light-matter interactions at the nanoscale. In particular, isolated quantum systems such as color centers and quantum dots embedded in these materials are gaining interest due to their potential use in a variety of quantum technologies and nanophotonics. Here, we review the field of nonclassical light emission from van der Waals crystals and atomically thin two-dimensional materials. We focus on transition metal dichalcogenides and hexagonal boron nitride and discuss the fabrication and properties of quantum emitters in these systems and proof-of-concept experiments that provide a foundation for their integration in on-chip nanophotonic circuits. These experiments include tuning of the emission wavelength, electrical excitation, and coupling of the emitters to waveguides, dielectric cavities, and plasmonic resonators. Finally, we discuss current challenges in the field and provide an outlook to further stimulate scientific discussion.

Magnetic-field-dependent quantum emission in hexagonal boron nitride at room temperature

Optically addressable spins associated with defects in wide-bandgap semiconductors are versatile platforms for quantum information processing and nanoscale sensing, where spin-dependent inter-system crossing transitions facilitate optical spin initialization and readout. Recently, the van der Waals material hexagonal boron nitride (h-BN) has emerged as a robust host for quantum emitters, promising efficient photon extraction and atom-scale engineering, but observations of spin-related effects have remained thus far elusive. Here, we report room-temperature observations of strongly anisotropic photoluminescence patterns as a function of applied magnetic field for select quantum emitters in h-BN. Field-dependent variations in the steady-state photoluminescence and photon emission statistics are consistent with an electronic model featuring a spin-dependent inter-system crossing between triplet and singlet manifolds, indicating that optically-addressable spin defects are present in h-BN.

Controlled synthesis of uniform multilayer hexagonal boron nitride films on Fe2B alloy

Two-dimensional (2D) hexagonal boron nitride (h-BN) is highly appreciated for its excellent insulating performance and absence of dangling bonds, which could be employed to maintain the intrinsic properties of 2D materials. However, controllable synthesis of large scale multilayer h-BN is still very challenging. Here, we demonstrate chemical vapor deposition (CVD) growth of multilayer h-BN by using iron boride (Fe₂B) alloy and nitrogen (N₂) as precursors. Different from the self-limited growth mechanism of monolayer h-BN on catalytic metal surfaces, with sufficient B source in the bulk, Fe₂B alloy promotes the controllable isothermal segregation of multilayer h-BN by reacting with active N atoms on the surface of the substrate. Microscopic and spectroscopic characterizations prove the high uniformity and crystalline quality of h-BN with a highly orientated layered lattice structure. The achievement of large scale multilayer h-BN in this work would facilitate its applications in 2D electronics and optoelectronics in the future.

CVD growth of large scale and high quality multilayer h-BN.

Photoluminescence Upconversion by Defects in Hexagonal Boron Nitride

Hexagonal boron nitride (h-BN) was recently reported to display single photon emission from ultraviolet to near-infrared range due to the existence of defects. Single photon emission has potential applications in quantum information processing and optoelectronics. These findings trigger increasing research interests in h-BN defects, such as revealing the nature of the defects. Here, we report another intriguing defect property in h-BN, namely photoluminescence (PL) upconversion (anti-Stokes process). The energy gain by the PL upconversion is about 162 meV. The anomalous PL upconversion is attributed to optical phonon absorption in the one-photon excitation process, based on excitation power, excitation wavelength, and temperature-dependence investigations. Possible constitutions of the defects are discussed from the results of scanning transmission electron microscopy (STEM) studies and theoretical calculations. These findings show that defects in h-BN exhibit strong defect-phonon coupling. The results from STEM and theoretical calculations are beneficial for understanding the constitution of the h-BN defects.

Stark Tuning of Single-Photon Emitters in Hexagonal Boron Nitride

Single-photon emitters play an essential role in quantum technologies, including quantum computing and quantum communications. Atomic defects in hexagonal boron nitride ( h-BN) have recently emerged as new room-temperature single-photon emitters in solid-state systems, but the development of scalable and tunable h-BN single-photon emitters requires external methods that can control the emission energy of individual defects. Here, by fabricating van der Waals heterostructures of h-BN and graphene, we demonstrate the electrical control of single-photon emission from atomic defects in h-BN via the Stark effect. By applying an out-of-plane electric field through graphene gates, we observed Stark shifts as large as 5.4 nm per GV/m. The Stark shift generated upon a vertical electric field suggests the existence of out-of-plane dipole moments associated with atomic defect emitters, which is supported by first-principles theoretical calculations. Furthermore, we found field-induced discrete modification and stabilization of emission intensity, which were reversibly controllable with an external electric field.

Anomalous Pressure Characteristics of Defects in Hexagonal Boron Nitride Flakes

Research on hexagonal boron nitride (hBN) has been intensified recently due to the application of hBN as a promising system of single-photon emitters. To date, the single photon origin remains under debate even though many experiments and theoretical calculations have been performed. We have measured the pressure-dependent photoluminescence (PL) spectra of hBN flakes at low temperatures by using a diamond anvil cell device. The absolute values of the pressure coefficients of discrete PL emission lines are all below 15 meV/GPa, which is much lower than the pressure-induced 36 meV/GPa redshift rate of the hBN bandgap. These PL emission lines originate from atom-like localized defect levels confined within the bandgap of the hBN flakes. Interestingly, the experimental results of the pressure-dependent PL emission lines present three different types of pressure responses corresponding to a redshift (negative pressure coefficient), a blueshift (positive pressure coefficient), or even a sign change from negative to positive. Density functional theory calculations indicate the existence of competition between the intralayer and interlayer interaction contributions, which leads to the different pressure-dependent behaviors of the PL peak shift.

Single-Photon Emitters in Boron Nitride Nanococoons

Quantum emitters in two-dimensional hexagonal boron nitride (hBN) are attractive for a variety of quantum and photonic technologies because they combine ultra-bright, room-temperature single-photon emission with an atomically thin crystal. However, the emitter's prominence is hindered by large, strain-induced wavelength shifts. We report the discovery of a visible-wavelength, single-photon emitter (SPE) in a zero-dimensional boron nitride allotrope (the boron nitride nanococoon, BNNC) that retains the excellent optical characteristics of few-layer hBN while possessing an emission line variation that is lower by a factor of 5 than the hBN emitter. We determined the emission source to be the nanometer-size BNNC through the cross-correlation of optical confocal microscopy with high-resolution scanning and transmission electron microscopy. Altogether, this discovery enlivens color centers in BN materials and, because of the BN nanococoon's size, opens new and exciting opportunities in nanophotonics, quantum information, biological imaging, and nanoscale sensing.

Quantum Emitters in Hexagonal Boron Nitride Have Spectrally Tunable Quantum Efficiency

Understanding the properties of novel solid-state quantum emitters is pivotal for a variety of applications in research fields ranging from quantum optics to biology. Recently discovered defects in hexagonal boron nitride are especially interesting, as they offer much desired characteristics such as narrow emission lines and photostability. Here, the dependence of the emission on the excitation wavelength is studied. It is found that, in order to achieve bright single-photon emission with high quantum efficiency, the excitation wavelength has to be matched to the emitter. This is a strong indication that the emitters possess a complex level scheme and cannot be described by a simple two or three-level system. Using this excitation dependence of the emission, further insight to the internal level scheme is gained and it is demonstrated how to distinguish different emitters both spatially as well as in terms of their photon correlations.

All-optical control and super-resolution imaging of quantum emitters in layered materials

Layered van der Waals materials are emerging as compelling two-dimensional platforms for nanophotonics, polaritonics, valleytronics and spintronics, and have the potential to transform applications in sensing, imaging and quantum information processing. Among these, hexagonal boron nitride (hBN) is known to host ultra-bright, room-temperature quantum emitters, whose nature is yet to be fully understood. Here we present a set of measurements that give unique insight into the photophysical properties and level structure of hBN quantum emitters. Specifically, we report the existence of a class of hBN quantum emitters with a fast-decaying intermediate and a long-lived metastable state accessible from the first excited electronic state. Furthermore, by means of a two-laser repumping scheme, we show an enhanced photoluminescence and emission intensity, which can be utilized to realize a new modality of far-field super-resolution imaging. Our findings expand current understanding of quantum emitters in hBN and show new potential ways of harnessing their nonlinear optical properties in sub-diffraction nanoscopy.

Quantum Light in Curved Low Dimensional Hexagonal Boron Nitride Systems

Low-dimensional wide bandgap semiconductors open a new playing field in quantum optics using sub-bandgap excitation. In this field, hexagonal boron nitride (h-BN) has been reported to host single quantum emitters (QEs), linking QE density to perimeters. Furthermore, curvature/perimeters in transition metal dichalcogenides (TMDCs) have demonstrated a key role in QE formation. We investigate a curvature-abundant BN system - quasi one-dimensional BN nanotubes (BNNTs) fabricated via a catalyst-free method. We find that non-treated BNNT is an abundant source of stable QEs and analyze their emission features down to single nanotubes, comparing dispersed/suspended material. Combining high spatial resolution of a scanning electron microscope, we categorize and pin-point emission origin to a scale of less than 20 nm, giving us a one-to-one validation of emission source with dimensions smaller than the laser excitation wavelength, elucidating nano-antenna effects. Two emission origins emerge: hybrid/entwined BNNT. By artificially curving h-BN flakes, similar QE spectral features are observed. The impact on emission of solvents used in commercial products and curved regions is also demonstrated. The 'out of the box' availability of QEs in BNNT, lacking processing contamination, is a milestone for unraveling their atomic features. These findings open possibilities for precision engineering of QEs, puts h-BN under a similar 'umbrella' of TMDC's QEs and provides a model explaining QEs spatial localization/formation using electron/ion irradiation and chemical etching.