Theory of the Exciton-Phonon Coupling

The effect of electron-phonon interactions on optical absorption spectra requires a special treatment in materials with strong electron-hole interactions. We conceptualize these effects as exciton-phonon coupling. Through phonon absorption and emission, the optically accessible excitons are scattered into dark finite-momentum exciton states. We derive a practical expression for the exciton-phonon self-energy that relates to the temperature dependence of the optical transitions and their broadening. This expression differs qualitatively from previous approximated expressions found in literature

Dynamical and anharmonic effects on the electron-phonon coupling and the zero-point renormalization of the electronic structure

The renormalization of the band structure at zero temperature due to electron-phonon coupling is investigated in diamond, BN, LiF and MgO crystals. We implement a dynamical scheme to compute the frequency-dependent self-energy and the resulting quasiparticle electronic structure. Our calculations reveal the presence of a satellite band below the Fermi level of LiF and MgO. We show that the renormalization factor (Z), which is neglected in the adiabatic approximation, can reduce the zero-point renormalization (ZPR) by as much as 40%. Anharmonic effects in the renormalized eigenvalues at finite atomic displacements are explored with the frozen-phonon method. We use a non-perturbative expression for the ZPR, going beyond the Allen-Heine-Cardona theory. Our results indicate that high-order electron-phonon coupling terms contribute significantly to the zero-point renormalization for certain materials

Electronic transport in titanium carbide MXenes from first principles

We compute from first principles the electronic, vibrational, and transport properties of four known MXenes compound : Ti3C2, Ti3C2F2, Ti3C2(OH)2, and Ti2CF2. We study the effect of different surface terminations and monosheet thickness on the electrical conductivity, and show that the changes in conductivity can be explained by the squared velocity density of the electronic state, as well as their phonon scattering lifetime. We also compare the solution of the iterative Boltzmann transport equation (IBTE) to different linearized solutions, namely, the self-energy relaxation time approximation (SERTA) and the momentum relaxation time approximation (MRTA), and we show that the SERTA significantly underestimates the electrical conductivity while the MRTA yields results in better agreement with the IBTE. We compute from first principles the electronic, vibrational, and transport properties of four known MXenes: Ti3C2, Ti3C2F2, Ti3C2(OH)2, and Ti2CF2. We study the effect of different surface terminations and monosheet thickness on the electrical conductivity, and show that the changes in conductivity can be explained by the squared velocity density of the electronic state, as well as their phonon scattering lifetime. We also compare the solution of the iterative Boltzmann transport equation (IBTE) to different linearized solutions, namely, the self-energy relaxation time approximation (SERTA) and the momentum relaxation time approximation (MRTA), and we show that the SERTA significantly underestimates the electrical conductivity while the MRTA yields results in better agreement with the IBTE. The computed monolayer conductivity at 300K is in reasonable agreement with reported experimental measurements

Calculs ab initio de structures électroniques et de leur dépendance en température avec la méthode GW

Cette thèse porte sur le calcul de structures électroniques dans les solides. À l'aide de la théorie de la fonctionnelle de densité, puis de la théorie des perturbations à N-corps, on cherche à calculer la structure de bandes des matériaux de façon aussi précise et efficace que possible. Dans un premier temps, les développements théoriques ayant mené à la théorie de la fonctionnelle de densité (DFT), puis aux équations de Hedin sont présentés. On montre que l'approximation GW constitue une méthode pratique pour calculer la self-énergie, dont les résultats améliorent l'accord de la structure de bandes avec l'expérience par rapport aux calculs DFT. On analyse ensuite la performance des calculs GW dans différents oxydes transparents, soit le ZnO, le SnO2 et le SiO2. Une attention particulière est portée aux modèles de pôle de plasmon, qui permettent d'accélérer grandement les calculs GW en modélisant la matrice diélectrique inverse. Parmi les différents modèles de pôle de plasmon existants, celui de Godby et Needs s'avère être celui qui reproduit le plus fidèlement le calcul complet de la matrice diélectrique inverse dans les matériaux étudiés. La seconde partie de la thèse se concentre sur l'interaction entre les vibrations des atomes du réseau cristallin et les états électroniques. Il est d'abord montré comment le couplage électron-phonon affecte la structure de bandes à température finie et à température nulle, ce qu'on nomme la renormalisation du point zéro (ZPR). On applique ensuite la méthode GW au calcul du couplage électron-phonon dans le diamant. Le ZPR s'avère être fortement amplifié par rapport aux calculs DFT lorsque les corrections GW sont appliquées, améliorant l'accord avec les observations expérimentales.This thesis deals with electronic structure calculations in solids. Using density functional theory and many-body perturbation theory, we seek to compute the band structure of materials in the most precise and efficient way. First, the theoretical developments leading to density functional theory (DFT) and to Hedin's equations are presented. It is shown how the GW approximation allows for a practical scheme to compute the self-energy, whose results enhance the agreement of the band structure with experiments, compared to DFT. We then analyse the performance of GW calculations in various transparent oxides, namely ZnO, SnO2 and SiO2. A special attention is devoted to the plasmon-pole model, which allows to accelerate significantly the calculations by modelling the inverse dielectric matrix. Among the different plasmon-pole models, the one of Godby and Needs turns out to be the most accurate in the studied materials. The second part of the thesis concentrates on the interaction between vibrations of the crystal lattice with electronic states. It is first shown how the electron-phonon coupling affects the band structure at finite temperature and at zero temperature, which is called the zero-point renormalization (ZPR). Then, we use the GW method to compute the electron-phonon coupling in diamond. The ZPR turns out to be strongly amplified with respect to DFT upon the application of GW corrections, enhancing the agreement with experimental observations

Quasiparticles and phonon satellites in spectral functions of semiconductors and insulators: Cumulants applied to full first principles theory and Fr\"ohlich polaron

The electron-phonon interaction causes thermal and zero-point motion shifts of electron quasiparticle (QP) energies $\epsilon_k(T)$. Other consequences of interactions, visible in angle-resolved photoemission spectroscopy (ARPES) experiments, are broadening of QP peaks and appearance of sidebands, contained in the electron spectral function $A(k,\omega)=-{\Im m}G_R(k,\omega) /\pi$, where $G_R$ is the retarded Green's function. Electronic structure codes (e.g. using density-functional theory) are now available that compute the shifts and start to address broadening and sidebands. Here we consider MgO and LiF, and determine their nonadiabatic Migdal self energy. The spectral function obtained from the Dyson equation makes errors in the weight and energy of the QP peak and the position and weight of the phonon-induced sidebands. Only one phonon satellite appears, with an unphysically large energy difference (larger than the highest phonon energy) with respect to the QP peak. By contrast, the spectral function from a cumulant treatment of the same self energy is physically better, giving a quite accurate QP energy and several satellites approximately spaced by the LO phonon energy. In particular, the positions of the QP peak and first satellite agree closely with those found for the Fr\"ohlich Hamiltonian by Mishchenko $\textit{et al.}$ (2000) using diagrammatic Monte Carlo. We provide a detailed comparison between the first-principles MgO and LiF results and those of the Fr\"ohlich Hamiltonian. Such an analysis applies widely to materials with infra-red active phonons. We also compare the retarded and time-ordered cumulant treatments: they are equivalent for the Fr\"ohlich Hamiltonian, and only slightly differ in first-principles electron-phonon results for wide-band gap materials.Comment: 21 pages, 19 figure

The temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation

The renormalization of electronic eigenenergies due to electron-phonon interactions (temperature dependence and zero-point motion effect) is important in many materials. We address it in the adiabatic harmonic approximation, based on first principles (e.g. Density-Functional Theory), from different points of view: directly from atomic position fluctuations or, alternatively, from Janak's theorem generalized to the case where the Helmholtz free energy, including the vibrational entropy, is used. We prove their equivalence, based on the usual form of Janak's theorem and on the dynamical equation. We then also place the Allen-Heine-Cardona (AHC) theory of the renormalization in a first-principle context. The AHC theory relies on the rigid-ion approximation, and naturally leads to a self-energy (Fan) contribution and a Debye-Waller contribution. Such a splitting can also be done for the complete harmonic adiabatic expression, in which the rigid-ion approximation is not required. A numerical study within the Density-Functional Perturbation theory framework allows us to compare the AHC theory with frozen-phonon calculations, with or without the rigid-ion terms. For the two different numerical approaches without rigid-ion terms, the agreement is better than 7 $\mu$eV in the case of diamond, which represent an agreement to 5 significant digits. The magnitude of the non rigid-ion terms in this case is also presented, distinguishing specific phonon modes contributions to different electronic eigenenergies

Peningkatan Layanan Perpustakaan Sekolah SMPN 2 Purwosari Melalui Penyederhanaan Modul Aplikasi SLiMS

Demi memenuhi kebutuhan pelanggan yang terus berkembang, perpustakaan di seluruh dunia telah menggunakan sistem manajemen perpustakaan sebagai alat penting dalam menyederhanakan operasional dan meningkatkan pengalaman pengguna perpustakaan. Pengabdian ini menyajikan studi kasus keberhasilan implementasi aplikasi SLiMS Senayan untuk meningkatkan layanan perpustakaan di SMP Negeri 2 Purwosari. Studi ini mengeksplorasi bagaimana SMP Negeri 2 Purwosari memanfaatkan aplikasi SLiMS Senayan untuk memperbarui layanannya, dengan fokus pada bidang-bidang utama Manajemen Katalog dan Layanan Sirkulasi. Studi kasus ini menyoroti dampak transformatif penerapan SLiMS Senayan di SMP Negeri 2 Purwosari. Dengan menerapkan sistem manajemen perpustakaan yang kuat ini, perpustakaan tidak hanya memodernisasi layanannya tetapi juga memposisikan dirinya sebagai institusi yang dinamis dan berpusat pada pengguna. Program yang telah dilakukan dalam meningkatkan layanan administrasi perpustakaan yaitu dengan menggunakan aplikasi SLiMS yang dimodifikasi. Program pengabdian ini berisi beberapa kegiatan seperti: koordinasi bersama tim dan mitra, kegiatan pelatihan, kegiatan modifikasi aplikasi SLiMS, pendampingan pengguna dan aplikasi SLiMS, dan terakhir dilakukan evaluasi terhadap program yang telah dilaksanakan. Hasil evaluasi menunjukkan tingkat pemahaman yang baik sesudah pelatihan SLiMS. Petugas perpustakaan dapat menjalankan aplikasi SLiMS dengan mandiri setelah kegiatan pengabdian ini selesai