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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.

Black phosphorus (BP), a 2D semiconducting material of interest in electronics and photonics, exhibits physical properties characterized by strong anisotropy and band gap energy that scales with reducing layer number. However, the investigation of its intrinsic properties is challenging because thin-layer BP is photo-oxidized under ambient conditions and the energy of its electronic states shifts in different dielectric environments. We prepared free-standing samples of few-layer BP under glovebox conditions and probed the dielectric response in a vacuum using scanning transmission electron microscopy and electron energy loss spectroscopy (STEM-EELS). Thresholds of the excitation energy are measured at 1.9, 1.4, and 1.1 eV for the mono-, bi-, and trilayer BP, respectively, and these values are used to estimate the corresponding optical band gaps. A comparison of our results with electronic structure calculations indicates that the variation of the quasi-particle gap is larger than that of the exciton binding energy. The dispersion of the plasmons versus momentum for one- to three-layer BP and bulk BP highlights a deviation from parabolic to linear dispersion and strong anisotropic fingerprints.

A quantitative analysis of the excitonic luminescence efficiency in hexagonal boron nitride (h-BN) 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 h-BN at 10 K comparable to that of direct band-gap semiconductors. This bright luminescence at 215 nm remains stable up to room temperature, evidencing the strongly bound character of excitons in bulk h-BN. Ab initio calculations of the exciton dispersion confirm the indirect nature of the lowest-energy exciton whose binding energy is found equal to 300±50  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 h-BN.

Low-dimensional materials differ from their bulk counterparts in many respects. In particular, the screening of the Coulomb interaction is strongly reduced, which can have important consequences such as the significant increase of exciton binding energies. In bulk materials the binding energy is used as an indicator in optical spectra to distinguish different kinds of excitons, but this is not possible in low-dimensional materials, where the binding energy is large and comparable in size for excitons of very different localization. Here we demonstrate that the exciton band structure, which can be accessed experimentally, instead provides a powerful way to identify the exciton character. By comparing the ab initio solution of the many-body Bethe-Salpeter equation for graphane and single-layer hexagonal boron nitride, we draw a general picture of the exciton dispersion in two-dimensional materials, highlighting the different role played by the exchange electron-hole interaction and by the electronic band structure. Our interpretation is substantiated by a prediction for phosphorene.

One of the big challenges of theoretical condensed-matter physics is the description, understanding, and prediction of the effects of the Coulomb interaction on materials properties. In electronic spectra, the Coulomb interaction causes a renormalization of energies and change of spectral weight. Most importantly, it can lead to new structures, often called satellites. These can be linked to the coupling of excitations, also termed dynamical effects. State-of-the-art methods in the framework of many-body perturbation theory, in particular, the widely used GW approximation, often fail to describe satellite spectra. Instead, approaches based on a picture of electron-boson coupling such as the cumulant expansion are promising for the description of plasmon satellites. In this work, we give a unified derivation of the GW approximation and the cumulant expansion for the one-body Green's function. Using the example of bulk sodium, we compare the resulting spectral functions both in the valence and in the core region, and we discuss the dispersion of quasi-particles and satellites. We show that self-consistency is crucial to obtain meaningful results, in particular, at large binding energies. Very good agreement with experiment is obtained when the intrinsic spectral function is corrected for extrinsic and interference effects. Finally, we sketch how one can approach the problem in the case of the two-body Green's function, and we discuss the cancellation of various dynamical effects that occur in that case.