Berry-phase treatment of the homogeneous electric field perturbation in insulators

A perturbation theory of the static response of insulating crystals to homogeneous electric fields, that combines the modern theory of polarization (MTP) with the variation-perturbation framework is developed, at unrestricted order of perturbation. First, we address conceptual issues related to the definition of such a perturbative approach. In particular, in our definition of an electric-field-dependent energy functional for periodic systems, the position operator appearing in the perturbation term is replaced by a Berry-phase expression, along the lines of the MTP. Moreover, due to the unbound nature of the perturbation, a regularization of the Berry-phase expression for the polarization is needed in order to define a numerically-stable variational procedure. Regularization is achieved by means of discretization, which can be performed either before or after the perturbation expansion. We compare the two possibilities and apply them to a model tight-binding Hamiltonian. Lowest-order as well as generic formulas are presented for the derivatives of the total energy, the normalization condition, the eigenequation, and the Lagrange parameters.Comment: 52 pages + 4 figures; accepted for publication in Physical Review

A many-body perturbation theory approach to the electron-phonon interaction with density-functional theory as a starting point

The electron-phonon interaction plays a crucial role in many fields of physics and chemistry. Nevertheless, its actual calculation by means of modern many-body perturbation theory is weakened by the use of model Hamiltonians that are based on parameters difficult to extract from the experiments. Such shortcoming can be bypassed by using density-functional theory to evaluate the electron-phonon scattering amplitudes, phonon frequencies and electronic bare energies. In this work, we discuss how a consistent many-body diagrammatic expansion can be constructed on top of density-functional theory. In that context, the role played by screening and self-consistency when all the components of the electron-nucleus and nucleus-nucleus interactions are taken into account is paramount. A way to avoid over-screening is notably presented. Finally, we derive cancellations rules as well as internal consistency constraints in order to draw a clear, sound and practical scheme to merge many-body perturbation and density-functional theory.Comment: 25 pages, 13 figure

Ab initio Study of Luminescence in Ce-doped Lu2_2SiO5_5: The Role of Oxygen Vacancies on Emission Color and Thermal Quenching Behavior

We study from first principles the luminescence of Lu$_2$SiO$_5$:Ce$^{3+}$ (LSO:Ce), a scintillator widely used in medical imaging applications, and establish the crucial role of oxygen vacancies (V$_O$) in the generated spectrum. The excitation energy, emission energy and Stokes shift of its luminescent centers are simulated through a constrained density-functional theory method coupled with a ${\Delta}$SCF analysis of total energies, and compared with experimental spectra. We show that the high-energy emission band comes from a single Ce-based luminescent center, while the large experimental spread of the low-energy emission band originates from a whole set of different Ce-V$_O$ complexes together with the other Ce-based luminescent center. Further, the luminescence thermal quenching behavior is analyzed. The $4f-5d$ crossover mechanism is found to be very unlikely, with a large crossing energy barrier (E$_{fd}$) in the one-dimensional model. The alternative mechanism usually considered, namely the electron auto-ionization, is also shown to be unlikely. In this respect, we introduce a new methodology in which the time-consuming accurate computation of the band gap for such models is bypassed. We emphasize the usually overlooked role of the differing geometry relaxation in the excited neutral electronic state Ce$^{3+,*}$ and in the ionized electronic state Ce$^{4+}$. The results indicate that such electron auto-ionization cannot explain the thermal stability difference between the high- and low-energy emission bands. Finally, a hole auto-ionization process is proposed as a plausible alternative. With the already well-established excited state characterization methodology, the approach to color center identification and thermal quenching analysis proposed here can be applied to other luminescent materials in the presence of intrinsic defects.Comment: 13 pages, 8 figures, accepted by Phys. Rev. Material

Convergence and pitfalls of density functional perturbation theory phonons calculations from a high-throughput perspective

The diffusion of large databases collecting different kind of material properties from high-throughput density functional theory calculations has opened new paths in the study of materials science thanks to data mining and machine learning techniques. Phonon calculations have already been employed successfully to predict materials properties and interpret experimental data, e.g. phase stability, ferroelectricity and Raman spectra, so their availability for a large set of materials will further increase the analytical and predictive power at hand. Moving to a larger scale with density functional perturbation calculations, however, requires the presence of a robust framework to handle this challenging task. In light of this, we automatized the phonon calculation and applied the result to the analysis of the convergence trends for several materials. This allowed to identify and tackle some common problems emerging in this kind of simulations and to lay out the basis to obtain reliable phonon band structures from high-throughput calculations, as well as optimizing the approach to standard phonon simulations

First-principles study of Ce3+^{3+} doped lanthanum silicate nitride phosphors: Neutral excitation, Stokes shift, and luminescent center identification

We study from first principles two lanthanum silicate nitride compounds, LaSi$_{3}$N$_{5}$ and La$_{3}$Si$_{6}$N$_{11}$, pristine as well as doped with Ce$^{3+}$ ion, in view of explaining their different emission color, and characterising the luminescent center. The electronic structures of the two undoped hosts are similar, and do not give a hint to quantitatively describe such difference. The $4f\rightarrow 5d$ neutral excitation of the Ce$^{3+}$ ions is simulated through a constrained density-functional theory method coupled with a ${\Delta}$SCF analysis of total energies, yielding absorption energies. Afterwards, atomic positions in the excited state are relaxed, yielding the emission energies and Stokes shifts. Based on these results, the luminescent centers in LaSi$_{3}$N$_{5}$:Ce and La$_{3}$Si$_{6}$N$_{11}$:Ce are identified. The agreement with the experimental data for the computed quantities is quite reasonable and explains the different color of the emitted light. Also, the Stokes shifts are obtained within 20\% difference relative to experimental data.Comment: 12 pages, 10 figure

First-principles Study of the Luminescence of Eu2+-doped Phosphors

The luminescence of fifteen representative Eu$^{2+}$-doped phosphors used for white-LED and scintillation applications is studied through a Constrained Density Functional Theory. Transition energies and Stokes shift are deduced from differences of total energies between the ground and excited states of the systems, in the absorption and emission geometries. The general applicability of such methodology is first assessed: for this representative set, the calculated absolute error with respect to experiment on absorption and emission energies is within 0.3 eV. This set of compounds covers a wide range of transition energies that extents from 1.7 to 3.5 eV. The information gained from the relaxed geometries and total energies is further used to evaluate the thermal barrier for the $4f-5d$ crossover, the full width at half-maximum of the emission spectrum and the temperature shift of the emission peak, using a one-dimensional configuration-coordinate model. The former results indicate that the $4f-5d$ crossover cannot be the dominant mechanism for the thermal quenching behavior of Eu$^{2+}$-doped phosphors and the latter results are compared to available experimental data and yield a 30$\%$ mean absolute relative error. Finally, a semi-empirical model used previously for Ce$^{3+}$-doped hosts is adapted to Eu$^{2+}$-doped hosts and gives the absorption and emission energies within 0.9 eV of experiment, underperforming compared to the first-principles calculation.Comment: 17 pages, 13 figures, (Phys. Rev. B 2017 Accept

Ab Initio Approach to Second-order Resonant Raman Scattering Including Exciton-Phonon Interaction

Raman spectra obtained by the inelastic scattering of light by crystalline solids contain contributions from first-order vibrational processes (e.g. the emission or absorption of one phonon, a quantum of vibration) as well as higher-order processes with at least two phonons being involved. At second order, coupling with the entire phonon spectrum induces a response that may strongly depend on the excitation energy, and reflects complex processes more difficult to interpret. In particular, excitons (i.e. bound electron-hole pairs) may enhance the absorption and emission of light, and couple strongly with phonons in resonance conditions. We design and implement a first-principles methodology to compute second-order Raman scattering, incorporating dielectric responses and phonon eigenstates obtained from density-functional theory and many-body theory. We demonstrate our approach for the case of silicon, relating frequency-dependent relative Raman intensities, that are in excellent agreement with experiment, to different vibrations and regions of the Brillouin zone. We show that exciton-phonon coupling, computed from first principles, indeed strongly affect the spectrum in resonance conditions. The ability to analyze second-order Raman spectra thus provides direct insight into this interaction.Comment: 10 pages, 8 figure

Assessment of First-Principles and Semiempirical Methodologies for Absorption and Emission Energies of Ce3+^{3+}-Doped Luminescent Materials

In search of a reliable methodology for the prediction of light absorption and emission of Ce$^{3+}$-doped luminescent materials, 13 representative materials are studied with first-principles and semiempirical approaches. In the first-principles approach, that combines constrained density-functional theory and $\Delta$SCF, the atomic positions are obtained for both ground and excited states of the Ce$^{3+}$ ion. The structural information is fed into Dorenbos' semiempirical model. Absorption and emission energies are calculated with both methods and compared with experiment. The first-principles approach matches experiment within 0.3 eV, with two exceptions at 0.5 eV. In contrast, the semiempirical approach does not perform as well (usually more than 0.5 eV error). The general applicability of the present first-principles scheme, with an encouraging predictive power, opens a novel avenue for crystal site engineering and high-throughput search for new phosphors and scintillators.Comment: 12 pages, 3 figure