Papers by Francesco Sottile
Physical Review B, 2015
Understanding and controlling the way excitons propagate in solids is a key for tailoring materia... more Understanding and controlling the way excitons propagate in solids is a key for tailoring materials with improved optoelectronic properties. A fundamental step in this direction is the determination of the exciton energy-momentum dispersion. Here, thanks to the solution of the parameter-free Bethe-Salpeter equation (BSE), we draw and explain the exciton energy-momentum map of hexagonal boron nitride (h-BN) in the first three Brillouin zones. We show that h-BN displays strong excitonic effects not only in the optical spectra at vanishing momentum q, as previously reported, but also at large q. We validate our theoretical predictions by assessing the calculated exciton map by means of an inelastic x-ray scattering (IXS) experiment. Moreover, we solve the discrepancies between previous experimental data and calculations, proving then that the BSE is highly accurate through the whole momentum range. Therefore, these results put forward the combination BSE and IXS as the tool of choice for addressing the exciton dynamics in complex materials.
Valence and ionic lowest-lying electronic states of ethyl formate as studied by high-resolution v... more Valence and ionic lowest-lying electronic states of ethyl formate as studied by high-resolution vacuum ultraviolet photoabsorption, He(I) photoelectron spectroscopy, and ab initio calculations
The investigation of the exciton dispersion (i.e. the exciton energy dependence as a function of ... more The investigation of the exciton dispersion (i.e. the exciton energy dependence as a function of the momentum carried by the electron-hole pair) is a powerful approach to identify the exciton character, ranging from the strongly localised Frenkel to the delocalised Wannier-Mott limiting cases. We illustrate this possibility at the example of four prototypical molecular solids (picene, pentacene, tetracene and coronene) on the basis of the parameter-free solution of the many-body Bethe-Salpeter equation. We discuss the mixing between Frenkel and charge-transfer excitons and the origin of their Davydov splitting in the framework of many-body perturbation theory and establish a link with model approaches based on molecular states. Finally, we show how the interplay between the electronic band dispersion and the exchange electron-hole interaction plays a fundamental role in setting the nature of the exciton. This analysis has a general validity holding also for other systems in which the electron wavefunctions are strongly localized, as in strongly correlated insulators.
A major obstacle for computing optical spectra of solids is the lack of reliable approximations f... more 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 accurate 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 formulas 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.
We present a screened exact-exchange (SXX) method for the efficient and accurate calculation of t... more We present a screened exact-exchange (SXX) method for the efficient and accurate calculation of the optical properties of solids, where the screening is achieved through the zero-wave-vector limit of the inverse dielectric function. The SXX approach can be viewed as a simplification of the Bethe-Salpeter equation (BSE) or, in the context of time-dependent density-functional theory, as a first step towards a new class of hybrid functionals for the optical properties of solids. SXX performs well for bound excitons and continuum spectra in both small-gap semiconductors and large-gap insulators, with a computational cost much lower than that of the BSE.
We present ab initio quasiparticle calculations for electronic excitations and the fundamental ba... more 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.
Correlated materials have been studied extensively using photoemission spectroscopy. Their optica... more Correlated materials have been studied extensively using photoemission spectroscopy. Their optical properties are instead much less explored. Here we present calculations of the optical absorption spectrum of vanadium dioxide (VO 2 ) in the framework of the Bethe-Salpeter equation (BSE) of many-body perturbation theory. In order to deal with localized electrons we go beyond the standard BSE implementation and extend it to correlated insulators. We show that it is not enough to describe the spectra on the basis of independent electron-hole pairs, even when the electron and hole are separately well described by state-of-the-art one-body Green's functions. Crystal local-field effects are crucial to explain the experimental findings, even qualitatively, and excitonic effects strongly modify the spectra, especially at their onset. In this context, as highighted by the analysis of the BSE results, the quasi-one-dimensional nature of the vanadium-dimer chains plays a prominent role.
The photoemission spectrum of graphite is still debated. To help resolve this issue, we present p... more 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 π + σ plasmon of graphite, whereas the π 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... more 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.
We present a scheme to calculate exciton dispersions in real materials that is based on the first... more 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.
Strontium titanate SrTiO 3 is an extensively studied material. Of particular interest are its ele... more Strontium titanate SrTiO 3 is an extensively studied material. Of particular interest are its electronic properties.
We present experimental data and theoretical results for valence-band satellites in semiconductor... more We present experimental data and theoretical results for valence-band satellites in semiconductors, using the prototypical example of bulk silicon. In a previous publication we introduced a new approach that allows us to describe satellites in valence photoemission spectroscopy, in good agreement with experiment. Here we give more details; we show how the the spectra change with photon energy, and how the theory explains this behaviour. We also describe how we include several effects which are important to obtain a correct comparison between theory and experiment, such as secondary electrons and photon cross sections. In particular the inclusion of extrinsic losses and their dependence on the photon energy are key to the description of the energy dependence of spectra.
In a recent Rapid Communication [J. A. Berger, L. Reining, and F. Sottile, Phys. Rev. B 82, 04110... more In a recent Rapid Communication [J. A. Berger, L. Reining, and F. Sottile, Phys. Rev. B 82, 041103(R) (2010)], we presented the effective-energy technique to evaluate, in an accurate and numerically efficient manner, electronic excitations by reformulating spectral sum-over-states expressions such that only occupied states appear. In our approach all the empty states are accounted for by a single effective energy that can be obtained from first principles. In this work we provide further details of the effective-energy technique, in particular, when combined with the GW method, in which a huge summation over empty states appears in the calculation of both the screened Coulomb interaction and the self-energy. We also give further evidence of the numerical accuracy of the effective-energy technique by applying it to the technological important materials SnO 2 and ZnO. Finally, we use this technique to predict the band gap of bulk rubrene, an organic molecular crystal with a 140-atom unit cell.
In a recent publication [J.A. Berger, L. Reining, F. Sottile, Phys. Rev. B 82, 041103(R) (2010)]
The experimental valence band photoemission spectrum of semiconductors exhibits multiple satellit... more 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.
We present a method for the evaluation of electronic excitations of advanced materials by reformu... more 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 Í‘screening and self-energyÍ’. 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 SnO 2 .
We present a detailed investigation of the dynamic structure factor SÍ‘Q , Í’ as well as of the die... more We present a detailed investigation of the dynamic structure factor SÍ‘Q , Í’ as well as of the dielectric function M Í‘Q , Í’ of the prototypical semiconductor silicon for finite momentum transfer, combining inelastic x-ray scattering measurements and ab initio calculations. We show that, in contrast to optical spectra, for finite momentum transfer, time-dependent density-functional theory in adiabatic local-density approximation Í‘TDLDAÍ’ together with the inclusion of lifetime effects in a modified independent-particle polarizability 0,LT describes the physics of valence excitations with high precision. This applies to the dynamic structure factor as well as to the dielectric function, which demonstrates that TDLDA contains the short-range many-body effects that are crucial for a correct description of M Í‘Q , Í’ in silicon at finite momentum transfer. The form of a nonlocal and energy-dependent exchange-correlation kernel is presented which provides the inclusion of the lifetime effects using the true independent-particle polarizability 0 . The description of the silicon L 2,3 absorption edge has been possible by including the outer core electrons 2s and 2p in the valence electrons of the pseudopotential. The energy of the edge is underestimated but a scissor shift of the respective states by the self-energy correction for these states yields good agreement with experiment. Short-range crystal local-field effects and exchange-correlation effects become important with increasing momentum transfer. The inclusion of crystal local-field effects in the random-phase approximation is able to describe the anisotropy of the response well. Our results demonstrate the quantitative predictive power of the first-principles description.
We present a theoretical investigation of electronic and optical properties of free-base porphyri... more We present a theoretical investigation of electronic and optical properties of free-base porphyrins based on density functional theory and many-body perturbation theory. The electronic levels of free-base porphine Í‘H 2 PÍ’ and its phenyl derivative, free-base tetraphenylporphyrin Í‘H 2 TPPÍ’ are calculated using the ab initio GW approximation for the self-energy. The approach is found to yield results that compare favorably with the available photoemission spectra. The excitonic nature of the optical peaks is revealed by solving the Bethe-Salpeter equation, which provides an accurate description of the experimental absorption spectra. The lowest triplet transition energies are in good agreement with the measured values.
Time-dependent density-functional theory Í‘TDDFTÍ’ is widely used in the study of linear response p... more Time-dependent density-functional theory Í‘TDDFTÍ’ 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 Í‘xcÍ’ 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 WÍ‘Í’, 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.
The suitability of the time-dependent density-functional theory (TDDFT) approach for the theoreti... more The suitability of the time-dependent density-functional theory (TDDFT) approach for the theoretical study of the optical properties of biomolecules is demonstrated by several examples. We critically discuss the limitations of available TDDFT implementations to address some of the present open questions in the description of the excited-state dynamics of biological complexes. The key objective of the present work is to address the performance of TDDFT in the linear response regime of the bio-molecular systems to the visible or near UV radiation -measured by, e.g. optical absorption or optical dichroism spectra. Although these spectra are essentially determined by the electronic degrees of freedom of small, optically active regions within the usually large biological systems, they can also be strongly influenced by environment effects (solvent, hosting protein, temperature, etc.). Moreover, many key biological processes consist of photo-induced dynamics (photoisomerisation, etc.), and their description requires a coupled treatment of electronic and nuclear degrees of freedom. We illustrate these aspects with a selection of paradigmatic biomolecular systems: chromophores in fluorescent proteins, porphyrins, DNA basis, the azobenzene dye, etc.
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Papers by Francesco Sottile