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We present a benchmarking protocol that combines the characterization of boron nitride (BN) crystals and films with the evaluation of the electronic properties of graphene on these substrates. Our study includes hBN crystals grown under different conditions and scalable BN films deposited by either chemical or physical vapor deposition (CVD or PVD). We explore the complete process from boron nitride growth, over its optical characterization by time-resolved cathodoluminescence (TRCL), to the optical and electronic characterization of graphene by Raman spectroscopy after encapsulation and Hall bar processing. Within our benchmarking protocol we achieve a homogeneous electronic performance within each Hall bar device through a fast and reproducible processing routine. We find that a free exciton lifetime of 1 ns measured on as-grown hBN crystals by TRCL is sufficient to achieve high graphene room temperature charge carrier mobilities of 80,000 cm$^2$/(Vs) at a carrier density of |n| = 10$^{12}$ cm$^{-2}$, while respective exciton lifetimes around 100 ps yield mobilities up to 30,000 cm$^2$/(Vs). For scalable PVD-grown BN films, we measure carrier mobilities exceeding 10,000 cm$^2$/(Vs) which correlates with a graphene Raman 2D peak linewidth of 22 cm$^{-1}$. Our work highlights the importance of the Raman 2D linewidth of graphene as a critical metric that effectively assesses the interface quality (i.e. surface roughness) to the BN substrate, which directly affects the charge carrier mobility of graphene. Graphene 2D linewidth analysis is suitable for all BN substrates and is particularly advantageous when TRCL or BN Raman spectroscopy cannot be applied to specific BN materials such as amorphous or thin films. This underlines the superior role of spatially-resolved spectroscopy in the evaluation of BN crystals and films for the use of high-mobility graphene devices., Comment: 18 pages, 11 figures

One of the main interests of 2D materials is their ability to be assembled with many degrees of freedom for tuning and manipulating excitonic properties. There is a need to understand how the structure of the interfaces between atomic layers influences exciton properties. Here we use cathodoluminescence (CL) and time-resolved CL experiments to study how excitons interact with the interface between two twisted hexagonal boron nitride (hBN) crystals with various angles. An efficient capture of free excitons by the interface is demonstrated, which leads to a population of long lived and interface-localized (2D) excitons. Temperature dependent experiments indicate that for high twist angles, these excitons localized at the interface further undergo a self-trapping. It consists in a distortion of the lattice around the exciton on which the exciton traps itself. Our results suggest that this exciton-interface interaction causes a broad optical emission of highly twisted hBN-hBN structures around 300 nm (4 eV). Exciton self-trapping is finally discussed as a common feature of sp2 hybridized boron nitride polytypes and nanostructures due to the ionic nature of the B-N bond and their compact excitons., Comment: 15 pages, 13 figures

We present a novel experimental protocol using Cathodoluminescence measurements as a function of the electron incident energy to study both exciton diffusion in a directional way and surface exciton recombination. Our approach overcomes the challenges of anisotropic diffusion and the limited applicability of existing methods to the bulk counterparts of 2D materials. The protocol is then applied at room and at cryogenic temperatures to four bulk hexagonal boron nitride crystals grown by different synthesis routes. The exciton diffusivity depends on the sample quality but not on the temperature, indicating it is limited by defect scattering even in the best quality crystals. The lower limit for the diffusivity by phonon scattering is 0.2 cm$^{2}$.s$^{-1}$. Diffusion lengths were as much as 570 nm. Finally, the surface recombination velocity exceeds 10$^{5}$ cm$^{2}$.s$^{-1}$, at a level similar to silicon or diamond. This result reveals that surface recombination could strongly limit light-emitting devices based on 2D materials., Comment: Main text : 8 pages, 5 figures. Annexes : 3 pages, 3 figures. Submitted to Physical Review B

Despite its simple crystal structure, layered boron nitride features a surprisingly complex variety of phonon-assisted luminescence peaks. We present a combined experimental and theoretical study on ultraviolet-light emission in hexagonal and rhombohedral bulk boron nitride crystals. Emission spectra of high-quality samples are measured via cathodoluminescence spectroscopy, displaying characteristic differences between the two polytypes. These differences are explained using a fully first-principles computational technique that takes into account radiative emission from ``indirect'', finite-momentum, excitons via coupling to finite-momentum phonons. We show that the differences in peak positions, number of peaks and relative intensities can be qualitatively and quantitatively explained, once a full integration over all relevant momenta of excitons and phonons is performed., Comment: Main: 6 pages and 4 figures, Supplementary: 6 pages and 7 figures

Integrated quantum photonics, with potential applications in quantum information processing, relies on the integration of quantum emitters into on-chip photonic circuits. Hexagonal boron nitride (hBN) is recognized as a material that is compatible with such implementations, owing to its relatively high refractive index and low losses in the visible range, together with advantageous fabrication techniques. Here, we combine hBN waveguide nanofabrication with the recently demonstrated local generation of quantum emitters using electron irradiation to realize a fully top-down elementary quantum photonic circuit in this material, operating at room temperature. This proof of principle constitutes a first step towards deterministic quantum photonic circuits in hBN.

The ability to identify and characterize homogeneous and inhomogeneous dephasing processes is crucial in solid-state quantum optics. In particular, spectral diffusion leading to line broadening is difficult to evidence when the associated timescale is shorter than the inverse of the photon detection rate. Here, we show that a combination of resonant laser excitation and second-order photon correlations allows to access such fast dynamics. The resonant laser drive converts spectral diffusion into intensity fluctuations, leaving a signature in the second-order coherence function $g^{(2)}(\tau)$ of the scattered light that can be characterized using two-photon coincidences -- which simultaneously provides the homogeneous dephasing time. We experimentally implement this method to investigate the fast spectral diffusion of a color center generated by an electron beam in the two-dimensional material hexagonal boron nitride. The $g^{(2)}(\tau)$ function of the quantum emitter measured over more than ten orders of magnitude of delay times, at various laser powers, establishes that the color center experiences spectral diffusion at a characteristic timescale of a few tens of microseconds, while emitting Fourier-limited single photons ($T_2/2T_1 \sim 1$) between spectral jumps.

Black phosphorus (BP) stands out from other 2D materials by the wide amplitude of the band-gap energy (Delta(Eg)) that sweeps an optical window from Visible (VIS) to Infrared (IR) wavelengths, depending on the layer thickness. This singularity made the optical and excitonic properties of BP difficult to map. Specifically, the literature lacks in presenting experimental and theoretical data on the optical properties of BP on an extended thickness range. Here we report the study of an ensemble of photoluminescence spectra from 79 passivated BP flakes recorded at 4 K with thicknesses ranging from 4 nm to 700 nm, obtained by mechanical exfoliation. We observe that the exfoliation steps induce additional defects states that compete the radiative recombination from bound excitons observed in the crystal. We also show that the evolution of the photoluminescence energy versus thickness follows a quantum well confinement model appreciable from a thickness predicted and probed at 25 nm. The BP slabs placed in different 2D heterostructures show that the emission energy is not significantly modulated by the dielectric environment. Introduction Confinement effects, Comment: 11 pages, 3 figures - Main text 12 pages, 5 figures - Supporting information

Recently discovered quantum emitters in two-dimensional (2D) materials have opened new perspectives of integrated photonic devices for quantum information. Most of these applications require the emitted photons to be indistinguishable, which has remained elusive in 2D materials. Here, we investigate two-photon interference of a quantum emitter generated in hexagonal boron nitride (hBN) using an electron beam. We measure the correlations of zero-phonon-line photons in a Hong-Ou-Mandel (HOM) interferometer under non-resonant excitation. We find that the emitted photons exhibit a partial indistinguishability of $0.44 \pm 0.11$ in a 3 ns time window, which corresponds to a corrected value of $0.56 \pm 0.11$ after accounting for imperfect emitter purity. The dependence of the HOM visibility on the width of the post-selection time window allows us to estimate the dephasing time of the emitter to be $\sim 1.5$ ns, about half the limit set by spontaneous emission. A visibility above 90 % is under reach using Purcell effect with up-to-date 2D material photonics.

The ability to locally activate or generate quantum emitters in two-dimensional materials is of major interest for the realization of integrated quantum photonic devices. In particular, hexagonal boron nitride (hBN) has recently been shown to allow a variety of techniques for obtaining quantum emitters at desired locations. Here, we use cathodoluminescence (CL) to monitor in situ the local activation of color centers by an electron beam in hBN. We observe that the CL signal saturates at a given surface dose, independently of the electron current density. Based on photoluminescence and photon correlations, we show that the number of photoactive color centers is proportional to the CL signal, and we estimate the maximum density of quantum emitters that can be generated by our technique. Our results provide insights about the activation mechanism and could help to optimize the controlled generation of single photon sources in hexagonal boron nitride.

In the wide world of 2D materials, hexagonal boron nitride (hBN) holds a special place due to its excellent characteristics. In addition to its thermal, chemical and mechanical stability, hBN demonstrates high thermal conductivity, low compressibility, and wide band gap around 6 eV, making it promising candidate for many groundbreaking applications and more specifically for optoelectronic devices. Millimeters scale hexagonal boron nitride crystals are obtained through a disruptive dual method (PDC/PCS) consisting in a complementary coupling of the Polymer Derived Ceramics route and a Pressure-Controlled Sintering process. In addition to their excellent chemical and crystalline quality, these crystals exhibit a free exciton lifetime of 0.43 ns, as determined by time-resolved cathodoluminescence measurements, confirming their interesting optical properties. To go further in applicative fields, hBN crystals are then exfoliated, and resulting Boron Nitride NanoSheets (BNNSs) are used to encapsulate transition metal dichalcogenides (TMDs). Such van der Waals heterostructures are tested by optical spectroscopy. BNNSs do not luminesce in the emission spectral range of TMDs and the photoluminescence width of the exciton at 4K is in the range 2-3 meV. All these results demonstrate that these BNNSs are relevant for future opto-electronic applications., Comment: 16 pages, 9 figures

Using a new time-resolved cathodoluminescence system dedicated to the UV spectral range, we present a first estimate of the radiative lifetime of free excitons in hBN at room temperature. This is carried out from a single experiment giving both the absolute luminescence intensity under continuous excitation and the decay time of free excitons in the time domain. The radiative lifetime of indirect excitons in hBN is equal to 27 ns, which is much shorter than in other indirect bandgap semiconductors. This is explained by the close proximity of the electron and the hole in the exciton complex, and also by the small energy difference between indirect and direct excitons. The unusually high luminescence efficiency of hBN for an indirect bandgap is therefore semi-quantitatively understood.

Single photon emitters (SPEs) in low-dimensional layered materials have recently gained a large interest owing to the auspicious perspectives of integration and extreme miniaturization offered by this class of materials. However, accurate control of both the spatial location and the emission wavelength of the quantum emitters is essentially lacking to date, thus hindering further technological steps towards scalable quantum photonic devices. Here, we evidence SPEs in high purity synthetic hexagonal boron nitride (hBN) that can be activated by an electron beam at chosen locations. SPE ensembles are generated with a spatial accuracy better than the cubed emission wavelength, thus opening the way to integration in optical microstructures. Stable and bright single photon emission is subsequently observed in the visible range up to room temperature upon non-resonant laser excitation. Moreover, the low-temperature emission wavelength is reproducible, with an ensemble distribution of width 3 meV, a statistical dispersion that is more than one order of magnitude lower than the narrowest wavelength spreads obtained in epitaxial hBN samples. Our findings constitute an essential step towards the realization of top-down integrated devices based on identical quantum emitters in 2D materials., Comment: Main text and supplementary information: 22 pages, 11 figures

Atomic layers of Black Phosphorus (BP) present unique opto-electronic properties dominated by a direct tunable bandgap in a wide spectral range from visible to mid-infrared. In this work, we investigate the infrared photoluminescence of BP single crystals at very low temperature. Near-bandedge recombinations are observed at 2 K, including dominant excitonic transitions at 0.276 eV and a weaker one at 0.278 eV. The free-exciton binding energy is calculated with an anisotropic Wannier-Mott model and found equal to 9.1 meV. On the contrary, the PL intensity quenching of the 0.276 eV peak at high temperature is found with a much smaller activation energy, attributed to the localization of free excitons on a shallow impurity. This analysis leads us to attribute respectively the 0.276 eV and 0.278 eV PL lines to bound excitons and free excitons in BP. As a result, the value of bulk BP bandgap is refined to 0.287 eV at 2K., Comment: 12 pages, 3 figures - Main text 13 pages, 6 figures - Supporting information

Known as a prominent recombination path at high excitation densities, exciton-exciton annihilation (EEA) is evidenced in bulk hexagonal boron nitride (hBN) by cathodoluminescence at low temperature. Thanks to a careful tune of the the exciton density by varying either the current or the focus of the incident electron beam, we could estimate an EEA rate of 2$\times$10$^{-6}$ cm$^{3}$.s$^{-1}$ at $T=10$ K, the highest reported so far for a bulk semiconductor. Expected to be even stronger in nanotubes or atomic layers, EEA probablly contributes to the luminescence quenching observed in low-dimensionality BN materials.

We have quantified substitutional impurity concentrations in synthetic diamond crystals down to sub parts-per-billion levels. The capture lifetimes of electrons and excitons injected by photoexcitation were compared for several samples with different impurity concentrations. Based on the assessed impurity concentrations, we have determined the capture cross section of electrons to boron impurity, sA=1.3x10^-14 cm2, and that of excitons to nitrogen impurity, sD^ex=3.1x10^-14 cm2. The general tendency of the mobility values for different carrier species is successfully reproduced by including carrier scattering by impurities and by excitons.

A quantitative analysis of the excitonic luminescence efficiency in hexagonal boron nitride (hBN) is carried out by cathodoluminescence in the ultraviolet range and compared with zinc oxide and diamond single crystals. A high quantum yield value of ~50% is found for hBN at 10 K comparable to that of direct bandgap semiconductors. This bright luminescence at 215 nm remains stable up to room temperature, evidencing the strongly bound character of excitons in bulk hBN. Ab initio calculations of the exciton dispersion confirm the indirect nature of the lowest-energy exciton whose binding energy is found equal to 300 meV, in agreement with the thermal stability observed in luminescence. The direct exciton is found at a higher energy but very close to the indirect one, which solves the long debated Stokes shift in bulk hBN.

Electron energy loss spectra have been measured on hexagonal boron nitride single crystals employing a novel electron energy loss spectroscopic set-up composed by an electron microscope equipped with a monochromator and an in-column filter. This set-up provides high-quality energy-loss spectra and allows also for the imaging of energy-filtered diffraction patterns. These two acquisition modes provide complementary pieces of information, offering a global view of excitations in reciprocal space. As an example of the capabilities of the method we show how easily the core loss spectra at the $K$ edges of boron and nitrogen can be measured and imaged. Low losses associated to interband and/or plasmon excitations are also measured. This energy range allows us to illustrate that our method provides results of quality comparable to those obtained from non resonant X-ray inelastic scattering, but with advantageous specificities such as an enhanced sensitivity at low q and a much higher simplicity and versatility that makes it well adapted to the study of two-dimensional materials and related heterostructures. Finally, by comparing theoretical calculations against our measures, we are able to relate the range of applicability of ab initio calculations to the anisotropy of the sample and assess the level of approximation required for a proper simulation of our acquisition method.

Hexagonal boron nitride (hBN) regains interest as a strategic component in graphene engineering and in van der Waals heterostructures built with two dimensional materials. It is crucial then, to handle reliable characterization techniques capable to assess the quality of structural and electronic properties of the hBN material used. We present here characterization procedures based on optical spectroscopies, namely cathodoluminescence and Raman, with the additional support of structural analysis conducted by transmission electron microscopy. We show the capability of optical spectroscopies to investigate and benchmark the optical and structural properties of various hBN thin layers sources.

Cathodoluminescence (CL) experiments at low temperature have been undertaken on various bulk and exfoliated hexagonal boron nitride (hBN) samples. Different bulk crystals grown from different synthesis methods have been studied. All of them present the same so-called S series in the 5.6--6 eV range, proving its intrinsic character. Luminescence spectra of flakes containing 100 down to 6 layers have been recorded. Strong modifications in the same UV range are observed and discussed within the general framework of 2D exciton properties in lamellar crystals.

Hexagonal boron nitride (h-BN) and graphite are structurally similar but with very different properties. Their combination in graphene-based devices meets now a huge research focus, and it becomes particularly important to evaluate the role played by crystalline defects in them. In this work, the cathodoluminescence (CL) properties of hexagonal boron nitride crystallites are reported and compared to those of nanosheets mechanically exfoliated from them. First the link between the presence of structural defects and the recombination intensity of bound-excitons, the so-called D series, is confirmed. Low defective h-BN regions are further evidenced by CL spectral mapping (hyperspectral imaging), allowing us to observe new features in the near-band-edge region, tentatively attributed to phonon replica of exciton recombinations. Second the h-BN thickness was reduced down to six atomic layers, using mechanical exfoliation, as evidenced by atomic force microscopy. Even at these low thicknesses, the luminescence remains intense and exciton recombination energies are not strongly modified with respect to the bulk, as expected from theoretical calculations indicating extremely compact excitons in h-BN.

Near band gap photoluminescence (PL) of hBN single crystal has been studied at cryogenic temperatures with synchrotron radiation excitation. The PL signal is dominated by the D-series previously assigned to excitons trapped on structural defects. A much weaker S-series of self-trapped excitons at 5.778 eV and 5.804 eV has been observed using time-window PL technique. The S-series excitation spectrum shows a strong peak at 6.02 eV, assigned to free exciton absorption. Complementary photoconductivity and PL measurements set the band gap transition energy to 6.4 eV and the Frenkel exciton binding energy larger than 380 meV.

The excitonic recombinations in hexagonal boron nitride (hBN) are investigated with spatially resolved cathodoluminescence spectroscopy in the UV range. Cathodoluminescence images of an individual hBN crystallite reveals that the 215 nm free excitonic line is quite homogeneously emitted along the crystallite whereas the 220 nm and 227 nm excitonic emissions are located in specific regions of the crystallite. Transmission electron microscopy images show that these regions contain a high density of crystalline defects. This suggests that both the 220 nm and 227 nm emissions are produced by the recombination of excitons bound to structural defects.

Cathodoluminescence imaging and spectroscopy experiments on a single bamboo-like boron nitride nanotube are reported. Imaging experiments show that the luminescence is located all along the nanotube. Spectroscopy experiments point out the important role of dimensionality in this one dimensional object.