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Exciton band structures analysis provides a powerful tool to identify the exciton character of materials, from bulk to isolated systems, and goes beyond the mere analysis of the optical spectra. In this work, we focus on the exciton properties of molybdenum sisulfide (MoS2) by solving the ab initio many-body Bethe–Salpeter equation, as a function of momentum, to obtain the excitation spectra of both monolayer and bulk MoS2. We analyse the spectrum and the exciton dispersion on the basis of a model excitonic Hamiltonian capable of providing an efficient description of the excitations in the bulk crystal, starting from the knowledge of the excitons of a single layer. In this way, we obtain a general characterization of both bright and darks excitons in terms of the interplay between the electronic band dispersion (i.e. interlayer hopping) and the electron–hole exchange interaction. We identify for both the 2D and the 3D limiting cases the character of the lowest-energy excitons in MoS2, we explain the effects and relative weights of both band dispersion and electron–hole exchange interaction and finally we interpret the differences observed when changing the dimensionality of the system.

We present a novel derivation of resonant inelastic x-ray scattering (RIXS) which yields an expression for the RIXS cross section in terms of emission pathways between intermediate and final many-body states. Thereby electron-hole interactions are accounted for, as obtained from full diagonalization of the Bethe-Salpeter equation within an all-electron first-principles framework. We demonstrate our approach with the emission spectra of the fluorine K edge in LiF, and provide an in-depth analysis of the pathways that determine the spectral shape. Excitoninc effects are shown to play a crucial role in both the valence and core regime.

International audience; A promising route towards nanodevice applications relies on the association of graphene and transition metal dichalcogenides with hexagonal boron nitride (h-BN). Due to its insulating nature, h-BN has emerged as a natural substrate and gate dielectric for graphene-based electronic devices. However, some fundamental properties of bulk h-BN remain obscure. For example, the band structure and the position of the Fermi level have not been experimentally resolved. Here, we report a direct observation of parabolic dispersions of h-BN crystals using high-resolution angle-resolved photoemission spectroscopy (ARPES). We find that h-BN exfoliation on epitaxial graphene enables overcoming the technical difficulties of using ARPES with insulating materials. We show trigonal warping of the intensity maps at constant energy. The valence-band maxima are located around the K points, 2.5 eV below the Fermi level, thus confirming the residual p-type character of typical h-BN.

We present a general picture of the exciton properties of layered materials in terms of the excitations of their single-layer building blocks. To this end, we derive a model excitonic hamiltonian by drawing an analogy with molecular crystals, which are other prototypical van der Waals materials. We employ this simplified model to analyse in detail the excitation spectrum of hexagonal boron nitride (hBN) that we have obtained from the {\it ab initio} solution of the many-body Bethe-Salpeter equation as a function of momentum. In this way we identify the character of the lowest-energy excitons in hBN, discuss the effects of the interlayer hopping and the electron-hole exchange interaction on the exciton dispersion, and illustrate the relation between exciton and plasmon excitations in layered materials., Accepted for Phys. Rev. B

International audience; We present the valence electron energy-loss spectrum and the dielectric function of monoclinic hafnia (m-HfO$_2$) obtained from time-dependent density-functional theory (TDDFT) predictions and compared to energy-filtered spectroscopic imaging measurements in a high-resolution transmission-electron microscope. Fermi's Golden Rule density-functional theory (DFT) calculations can capture the qualitative features of the energy-loss spectrum, but we find that TDDFT, which accounts for local-field effects, provides nearly quantitative agreement with experiment. Using the DFT density of states and TDDFT dielectric functions, we characterize the excitations that result in the m-HfO$_2$ energy loss spectrum. The sole plasmon occurs between 13-16 eV, although the peaks $\sim$28 and above 40 eV are also due to collective excitations. We furthermore elaborate on the first-principles techniques used, their accuracy, and remaining discrepancies among spectra. More specifically, we assess the influence of Hf semicore electrons (5$p$ and 4$f$) on the energy-loss spectrum, and find that the inclusion of transitions from the 4$f$ band damps the energy-loss intensity in the region above 13 eV. We study the impact of many-body effects in a DFT framework using the adiabatic local-density approximation (ALDA) exchange-correlation kernel, as well as from a many-body perspective using a $GW$-derived electronic structure to account for self-energy corrections. These results demonstrate some cancellation of errors between self-energy and excitonic effects, even for excitations from the Hf $4f$ shell. We also simulate the dispersion with increasing momentum transfer for plasmon and collective excitation peaks.

International audience; 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.

A major obstacle for computing optical spectra of solids is the lack of reliable approximations for capturing excitonic effects within time-dependent density-functional theory. We show that the trustful prediction of strongly bound electron-hole pairs within this framework using simple approximations is still a challenge and that available promising results have to be revisited. Deriving a set of analytical formula we analyze and explain the difficulties. We deduce an alternative approximation from an iterative scheme guided by previously available knowledge, significantly improving the description of exciton binding energies. Finally, we show how one can "read" exciton binding energies from spectra determined in the random phase approximation, without any further calculation., Comment: 5 pages, 2 figures plus supplemental material

International audience; We present ab initio quasiparticle calculations for electronic excitations and the fundamental band gap of the strongly correlated transition-metal oxide CuO using the GW approximation of many-body perturbation theory. Problems related to the suitability of the method for strongly correlated materials and issues of self-consistency are addressed. We explain why quasiparticle self-consistent GW strongly overestimates the band gap of CuO. Apart from the band gap, electron addition and removal spectra in the quasiparticle approximation including lifetime and matrix-element effects are found to be in excellent agreement with the quasiparticle excitations in direct and inverse photoemission data.

The photoemission spectrum of graphite is still debated. To help resolve this issue, we present photoemission measurements at high photon energy and analyze the results using a Green's function approach that takes into account the full complexity of the loss spectrum. Our measured data show multiple satellite replicas. We demonstrate that these satellites are of intrinsic origin, enhanced by extrinsic losses. The dominating satellite is due to the $\ensuremath{\pi}+\ensuremath{\sigma}$ plasmon of graphite, whereas the $\ensuremath{\pi}$ plasmon creates a tail on the high-binding energy side of the quasiparticle peak. The interplay between the two plasmons leads to energy shifts, broadening, and additional peaks in the satellite spectrum. We also predict the spectral changes in the transition from graphite towards graphene.

By solving the many-body Bethe-Salpeter equation at finite momentum transfer, we characterize the exciton dispersion in two prototypical molecular crystals, picene and pentacene, in which localized Frenkel excitons compete with delocalized charge-transfer excitons. We explain the exciton dispersion on the basis of the interplay between electron and hole hopping and electron-hole exchange interaction, unraveling a simple microscopic description to distinguish Frenkel and charge-transfer excitons. This analysis is general and can be applied to other systems in which the electron wave functions are strongly localized, as in strongly correlated insulators., The authors acknowledge financial support from the European Research Council Advanced Grant DYNamo (ERC-2010-AdG-267374), Spanish grants (2010-21282-C02-01 and PIB2010US-00652), Grupos Consolidados UPV/EHU del Gobierno Vasco (IT578-13), European Commission projects CRONOS (Grant No. 280879-2 CRONOS CP-FP7), and the Maison de la simulation for technical support. Computational time was granted by GENCI (Project No. 544) and by the CNANO-SIMULEE-2009 project. This work was carried out under the HPC-EUROPA2 project, with the support of the European Community–Research Infrastructure Action of the FP7

We present a scheme to calculate exciton dispersions in real materials that is based on the first-principles many-body Bethe-Salpeter equation. We assess its high level of accuracy by comparing our results for LiF with recent inelastic x-ray scattering experimental data on a wide range of energy and momentum transfer. We show its great analysis power by investigating the role of the different electron-hole interactions that determine the exciton band structure and the peculiar “exciton revival” at large momentum transfer. Our calculations for solid argon are a prediction and a suggestion for future experiments. These results demonstrate that the first-principles Bethe-Salpeter equation is able to describe the dispersion of localized and delocalized excitons on equal footing and represent a key step for the ab initio study of the exciton mobility., We acknowledge financial support from Triangle de la Physique 2013-0013T IXST, the ERC Advanced Grant DYNamo (No. ERC-2010-AdG-267374), Spanish Grants (No. 2010-21282-C02-01 and No. PIB2010US-00652),Grupos Consolidados UPV/EHU del GobiernoVasco (Grant No. IT578-13) and European Commission projects CRONOS (Grant No. 280879-2 CRONOS CP-FP7). Computational time was granted by GENCI (Project No. 544) and by the CNANO-SIMULEE-2009 project.

PACS numbers: 71.45.Gm, 71.10. w, 71.15.Qe.-- et al., The experimental valence band photoemission spectrum of semiconductors exhibits multiple satellites that cannot be described by the GW approximation for the self-energy in the framework of many-body perturbation theory. Taking silicon as a prototypical example, we compare experimental high energy photoemission spectra with GW calculations and analyze the origin of the GW failure. We then propose an approximation to the functional differential equation that determines the exact one-body Green's function, whose solution has an exponential form. This yields a calculated spectrum, including cross sections, secondary electrons, and an estimate for extrinsic and interference effects, in excellent agreement with experiment. Our result can be recast as a dynamical vertex correction beyond GW, giving hints for further developments. © 2011 American Physical Society., We acknowledge support by ANR (NT09-610745), St Gobain R&D (091986), and Triangle de la Physique (2007-71). J.J.R. and J.J.K. are also supported in part by DOE BES Grant DE-FG03-97ER45623 and DOE CMCSN. Computer time was granted by IDRIS (544).

International audience; We present a method for the evaluation of electronic excitations of advanced materials by reformulating spectral sum-over-states expressions such that only occupied states appear. All empty states are accounted for by one effective energy. Thus we keep the simplicity and precision of the sum-over-states approach while speeding up calculations by more than an order of magnitude. We demonstrate its power by applying it to the GW method, where a huge summation over empty states appears twice (screening and self-energy). The precision is shown for bulk Si and solid and atomic Ar. We then use it to determine the band gap of the technologically important oxide SnO2.

Time-dependent density-functional theory (TDDFT) is widely used in the study of linear response properties of finite systems. However, there are difficulties in properly describing excited states, which have double- and higher-excitation characters, which are particularly important in molecules with an open-shell ground state. These states would be described if the exact TDDFT kernel were used; however, within the adiabatic approximation to the exchange-correlation (xc) kernel, the calculated excitation energies have a strict single-excitation character and are fewer than the real ones. A frequency-dependent xc kernel could create extra poles in the response function, which would describe states with a multiple-excitation character. We introduce a frequency-dependent xc kernel, which can reproduce, within TDDFT, double excitations in finite systems. In order to achieve this, we use the Bethe-Salpeter equation with a dynamically screened Coulomb interaction W(omega), which can describe these excitations, and from this we obtain the xc kernel. Using a two-electron model system, we show that the frequency dependence of W does indeed introduce the double excitations that are instead absent in any static approximation of the electron-hole screening.

International audience; The electron energy-loss function of graphite is studied for momentum transfers q beyond the first Brillouin zone. We find that near Bragg reflections the spectra can change drastically for very small variations in q. The effect is investigated by means of first principle calculations in the random phase approximation and confirmed by inelastic x-ray scattering measurements of the dynamic structure factor S(q,ω). We demonstrate that this effect is governed by crystal local field effects and the stacking of graphite. It is traced back to a strong coupling between excitations at small and large momentum transfers.

International audience; We have measured a strictly linear pi-plasmon dispersion along the axis of individualized single wall carbon nanotubes, which is completely different from plasmon dispersions of graphite or bundled single wall carbon nanotubes. Comparative ab initio studies on graphene based systems allow us to reproduce the different dispersions. This suggests that individualized nanotubes provide viable experimental access to collective electronic excitations of graphene, and it validates the use of graphene to understand electronic excitations of carbon nanotubes. In particular, the calculations reveal that local field effects (LFE) cause a mixing of electronic transitions, including the 'Dirac cone', resulting in the observed linear dispersion.

Time-dependent density functional theory faces an important problem when it comes to extended systems: The long-range component of the exchange-correlation kernel ${f}_{\mathrm{xc}}$ is completely absent from local density or generalized gradient approximations, but it is believed to be present in the ``exact'' ${f}_{\mathrm{xc}}$. Several attempts have been made to solve this issue, the simplest of them being the use of a model static long-range kernel of the form $\ensuremath{-}{\ensuremath{\alpha}}^{\mathrm{static}}∕{q}^{2}$. In this paper, we propose and motivate a dynamical extension of this model of the form $\ensuremath{-}(\ensuremath{\alpha}+\ensuremath{\beta}{\ensuremath{\omega}}^{2})∕{q}^{2}$. The dynamical model is then used to calculate the dielectric function of a large variety of semiconductors and insulators. The absorption spectra of large gap insulators are remarkably improved with respect to calculations where the kernel is taken to be static. This approach is valid also for energies in the range of plasmons, and hence it yields, e.g., good electron energy loss spectra. Finally, we present some simple theoretical arguments that relate the parameters of the model to physical quantities, like the dielectric constant and the plasmon frequency.

We propose an alternative formulation of Many-Body Perturbation Theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, that leads to excellent optical absorption and energy loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-dependent density-functional theory. Numerical results for the band gap of bulk silicon and solid argon illustrate corrections beyond the GW approximation for the self-energy., Comment: 4 pages, in press on Phys. Rev. Lett

et al., We discuss the effects of a static long-range contribution -α/q2 to the exchange-correlation kernel fxc(q) of time-dependent density functional theory. We show that the optical absorption spectrum of solids exhibiting a strong continuum excitonic effect is considerably improved with respect to calculations where the adiabatic local-density approximation is used. We discuss the limitations of this simple approach, and in particular that the same improvement cannot be found for the whole spectral range including the valence plasmons and bound excitons. On the other hand, we also show that within the range of validity of the method, the parameter α depends linearly on the inverse of the dielectric constant, and we demonstrate that this fact can be used to predict continuum excitonic effects in semiconductors. Results are shown for the real and imaginary part of the dielectric function of Si, GaAs, AlAs, diamond, MgO, SiC and Ge, and for the loss function of Si., This work was supported in part by the European Community Contract No. HPRN-CT-2000-00167, and by the French ‘‘Ministère de Recherche’’ in the framework of the program ‘‘ACI Nanostructures’’ under the Contract No. N52-01.

178 pages; My thesis fits into the domain of theoretical spectroscopy. This term describes a set of theoretical approaches that go hand-in-hand with several experimental techniques such as optical absorption and reflectivity, inelastic X-ray scattering (IXS), electron energy-loss spectroscopy (EELS) and photoelectron (or photoe- mission) spectroscopy. This set of ab-initio theories is used to simulate, study, predict and understand what is and will be seen in experiment. These spectro- scopies are all connected to the dielectric function ε(ω ) of an electronic system which is, in fact, a fundamental quantity in many modern electronic structure theories. In particular I focused my research on photoemission spectroscopy, where the dielectric function enters as the screening of the hole due to the sys- tem. During my thesis I have worked on the development of new theoretical approaches, the aim of my project being to go beyond state-of-the-art meth- ods used in electronic structure calculations. These methods stem mainly from two larger theoretical frameworks: Time-Dependent Density-Functional The- ory (TDDFT) and Green's function theory -- also known as Many-Body Pertur- bation Theory (MBPT). I carried on the theoretical development in parallel with numerical simulations on real materials and with experimental measurements, performed to verify the reliability of theory.