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Thermoelektrika (TE) sind Materialien die Elektrizität aus Abwärme gewinnen können. Eine wichtige Kenngröße für die Effizienz, und damit die Anwendbarkeit, von TE ist ihre Gitterwärmeleitfähigkeit. In meiner Doktorarbeit habe ich die Invarianz dieser Größe im Kontext der Linear-Response Theorie (LR) bewiesen. Dies ermöglichte es, eine Korrektur der Boltzmann-Transport Gleichung (BTE) für die Gitterwärmeleitfähigkeit in kristallinen Materialien mittels LR herzuleiten. Diese Korrektur ist wichtig um zu beurteilen, wie genau die BTE die Wärmeleitfähigkeit eines Kristalls vorhersagen kann. Um die dafür notwendigen symbolischen Umformungen durchzuführen, habe ich ein Computer-Algebra System (CAS) entwickelt. Die Anzahl an Beiträgen zum finalen Resultat stellte sich als zu groß heraus um Grenzfälle zu analysieren oder prüfbare Approximationen herzuleiten. Aus diesem Grund habe ich alle Beiträge mit so wenigen Approximationen wie möglich ausgewertet. Dafür habe ich eine Software entwickelt, um diese Terme numerisch auszuwerten. Damit habe ich meine Korrektur für altbekannte wie auch vielversprechende TE ausgewertet, nämlich PbTe, Bi2Te3 , SnSe und B4 C. Zusätzlich habe ich MgO und KF untersucht. Das Resultat lässt sich wie folgt zusammenfassen: Die Korrektur zur BTE für die Gitterwärmeleitfähigkeit hat in keinem der untersuchten Materialien und bei keiner der simulierten Temperaturen einen nennenswerten Einfluss. Meine Untersuchung legt nahe, dass die BTE für eine große Bandbreite an Materialien sicher angewandt werden kann, auch besonders stark Anharmonische. Folglich ist diese Arbeit in Übereinstimmung mit der Literatur, dass die am stärksten anharmonischen Materialien genau die mit der niedrigsten Wärmeleitfähigkeit sind. Es scheint daher sinnvoll, dass sich zukünftige Forschung weniger auf die Herleitung solcher Korrekturen zur BTE als vielmehr auf die korrekte Berechnung des Phononpropagators in stark anharmonischen Materialien konzentrieren sollte., Thermoelectrics (TE) are materials that can be used to generate electricity from waste heat. A key quantity to the efficiency, and therefore the applicability, of TE is the lattice thermal conductivity. In this work, I prove the invariance of the lattice thermal conductivity in the context of linear-response theory (LR). This invariance enables me to derive novel formulas for a correction to the widely used Boltzmann-transport equation (BTE) for lattice thermal transport in crystalline solids using LR. It turned out that these derivations cannot be performed by a human by hand, using the formalism I chose. To perform the necessary symbolic manipulations, I programmed a computer algebra system (CAS), that implements LR, starting from expectation values, over Feynman diagrams to mathematical formulas. The number of resulting terms turned out to be too large for an analysis of all limiting cases. Consequently, I aimed at evaluating all terms, with as few approximations as possible, to generate a simple, numerical result. To do so, I developed a software package to evaluate the formulas numerically without further approximation and applied it to long-serving as well as promising new TE, namely PbTe, Bi2 Te3 , SnSe, and B4C. Additionally I investigated MgO and KF. The result can be summed up as follows: The correction to the BTE for the lattice thermal conductivity has almost no influence in the investigated materials at any simulated temperature. My investigation suggests that the BTE can be used for a wide range of materials, including the most anharmonic ones. Consequently, this work is in agreement with the literature, that the most anharmonic materials are exactly those with the lowest lattice thermal conductivity. It suggests that future theoretic work on lattice thermal conductivity should focus to find the correct phonon-propagator of strongly anharmonic systems.

In polar semiconductors and insulators, thermal vibrations of the ionic lattice give rise to long-ranged electric fields that can scatter electrons and holes very efficiently. This interaction is known as Fröhlich coupling, and it is the source for a range of intriguing many-body effects in these materials. We consider two scenarios: Firstly, the normal state, in which Fröhlich coupling can give rise to a coupled electron-phonon state, or “polaron”, which causes a strong renormalisation of the electronic energy with major implications for excitation energies and charge-carrier mobilities in a material. A characteristic feature of polaron spectra, e.g. as observed in photoemission experiments, are low-energy sidebands near the main photoemission peak whose energetics are of the order of the most strongly coupled phonon modes. These sidebands are often referred to as “polaron satellites”. Secondly, the superconducting state, in which Fröhlich coupling provides the attractive pairing potential required for the formation of Cooper pairs. A paradigmatic example for the large class of polar semiconductors is SrTiO3, which hosts a strongly renormalised polaronic state in the conduction band, and whose phase diagram features a superconducting dome as a function of electron doping. In this thesis, we employ an analytical model of Fröhlich-type coupling between a parabolic electron band with finite electron occupation and a dispersionless LO phonon to study the coupled electron-phonon state in doped SrTiO3. Our analytical approach allows us to model all the relevant interactions with arbitrary resolution and provides insights into the intriguing many-body effects in Fröhlich-type semiconductors. In the normal state, we calculate the interacting electron spectral function from a Green’s function theory of electron phonon coupling for a range of doping levels and coupling strengths. Electron-phonon coupling is taken into account at the level of the Fan-Migdal self-energy. We compare the spectral functions obtained from two approximations to the interacting Green’s function for a wide range of Fermi energies and coupling strengths, derive analytical expressions for the quasiparticle renormalisation as a function of electron doping, and discuss limiting cases of the second-order self-energy approximation. In the superconducting state, we employ Migdal-Eliashberg theory to calculate the critical temperature TC of doped SrTiO3 as a function of doping level. In particular, our analytical approach allows us to explicitly model the attractive Fröhlich interaction and repulsive Coulomb interaction at generalised frequencies and momenta. Very good qualitative agreement of our results with experimental data is obtained. We emphasise the major contribution of free-carrier screening to the effective pairing potential, and we investigate promising avenues for improving the predictive power of ab initio calculations of the superconducting TC.

Cataloged from PDF version of article. Thesis (Ph.D.): Bilkent University, Department of Physics, İhsan Doğramacı Bilkent University, 2022. Includes bibliographical references (leaves 93-120). Two-dimensional (2D) metal oxides (MOs) and metal chalcogenides (MChs) are emerging classes of 2D materials. Depending on the constituent elements, these materials can display various electronic and optical properties making them promising candidates in many device applications, such as solar cells and transparent circuits. Binary graphene-like structures of II-VI are the most straightforward structures of 2D MOs and MChs. We systematically examined the electronic and optical properties of selected 2D structures from this category: BeO, BaTe, CdO, CaO, CaS, MgO, SrS, SrSe and ZnO. The dynamical stability of these materials has been reported in previous studies. In 2D semiconductors, excitonic effects dominate the optical properties. Theoretical investigation of such phenomena requires employing many-body approaches beyond standard density functional theory. We utilized a single shot of GW approximation to predict the electronic band structure and solved the Bethe- Salpeter equation in the Tamm-Dancoff approximation to consider excitonic effects. Our results show that all structures possess indirect band gaps except ZnO and CdO. Furthermore, the considered structures have large exciton binding energies ranging from 0.72 eV in CdO to 2.84 eV in BeO. CdO has the smallest calculated optical band gap with a value of 1.43 eV. Analyzing the optical absorption spectra reveals that the CdO can absorb 7.9 % of the incident light in its optical band gap. The maximum amount of absorption appears in BeO, which can absorb 28% of incident light in the ultraviolet region. Among the structure mentioned above, there is a close matching between the lattice constants of ZnO and MgO, promising for creating lateral and vertical heterostructures. Due to the enhanced performance resulting from mixing distinct properties of individual monolayers, van der Waals heterostructures (vdWHs) are regarded as a revolutionary class among a plethora of presently fabricated or predicted 2D materials. Alongside vdWHs, recent studies have also reported 2D heterostructures with interlayer bonding. Motivated by the flourishing properties of vertical heterostructures, we comprehensively examined the mechanical, electronic and optical properties of ZnO/MgO structures in four different stackings. Structural relaxation has indicated two vdWHs and two structures with interlayer binding. All considered structures are mechanically stable. In addition, phonon dispersion curves show that the AB stacking formed by placing the Mg atom on top of the O atom of the ZnO layer is also dynamically stable at zero temperature. The s orbital of Zn atom dominates the minimum of the first conduction band of these structures. The optical absorbance spectra show that strong excitonic effects reduce the optical band gap to the visible light spectrum range, and all structures can absorb around 8% of incident light. by Mahsa Seyedmohammadzadeh Ph.D.

Lewis acids like tris(pentafluorophenyl)borane (BCF) offer promising routes for efficient $p$-doping of organic semiconductors. The intriguing experimental results achieved so far call for a deeper understanding of the underlying doping mechanisms. In a first-principles work, based on state-of-the-art density-functional theory and many-body perturbation theory, we investigate the electronic and optical properties of donor/acceptor complexes formed by quarterthiophene (4T) doped by BCF. For reference, hexafluorobenzene (C$_6$F$_6$) and BF$_3$ are also investigated as dopants for 4T. Modelling the adducts as bimolecules \textit{in vacuo}, we find negligible charge transfer in the ground state and frontier orbitals either segregated on opposite sides of the interface (4T:BCF) or localized on the donor (4T:BF$_3$, 4T:C$_6$F$_6$). In the optical spectrum of 4T:BCF, a charge-transfer excitation appears at lowest-energy, corresponding to the transition between the frontier states, which exhibit very small but non-vanishing wave-function overlap. In the other two adducts, the absorption is given by a superposition of the features of the constituents. Our results clarify that the intrinsic electronic interactions between donor and acceptor are not responsible for the doping mechanisms induced by BCF and related Lewis acids. Extrinsic factors, such as solvent-solute interactions, intermolecular couplings, and thermodynamic effects, have to be systematically analyzed for this purpose.

Phonons, or quantized normal modes of crystal vibrations, are responsible for much of the thermophysical behavior in solid-state systems. This behavior includes properties like thermal expansion, defined as the change in material volume in response to temperature. Typically, materials expand upon heating and contract upon cooling; however, some undergo anomalous or negative thermal expansion (NTE). This study focuses on a material with NTE, cuprous oxide (Cu2O), commonly known as cuprite. Using computational and experimental methods, we identify the underlying mechanisms of the NTE and how these mechanisms relate to temperature-dependent phonon behavior with temperature, using both computational and experimental methods. Computationally, we interpret temperature-dependent changes in phonon energies with perturbation theory. Assuming that the bonds between atoms behave like simple harmonic oscillators, we model the observed random motion of the atoms around their equilibrium positions with quasi-harmonic (QH) and anharmonic (AH) approximations. Furthermore, the perturbations in the atom position allow us to model phonon energy changes in response to temperatures. While these models, particularly AH models, have proven accurate in predicting the phonon behavior, experimental methods, like inelastic neutron scattering (INS), remain the gold standard for validation. This study presents INS data from single-crystal cuprite measured on the Wide-Angular Range Chopper Spectrometer (ARCS) at the Oak Ridge National Laboratory (ORNL) Spallation Neutron Source (SNS). We present INS data collected at 10 K, 300 K, 700 K, and 900 K. The post-processing workflow included: (1) binning with the software package Mantid, (2) reducing with a multiphonon background correction for polyatomic crystals, and (3) condensing into a single irreducible wedge in the first Brillouin zone (BZ). From this, we obtain a four-dimensional scattering function S(Q, E). Our AH calculations use the stochastic-Temperature Dependent Effective Potential (sTDEP) and the Machine Learning Interatomic Potential (MLIP) methods. The former method uses perturbation theory to include cubic and quartic AH contributions. The latter uses machine learning (ML), which in principle, includes all orders of AH terms. This investigation of the NTE of cuprite demonstrates that QH and AH models successfully predict anomalous NTE behavior. However, only AH calculations show the temperature-dependent phonon behavior seen in INS results. This discrepancy likely stems from a fortuitous cancellation of cubic and quartic AH terms giving an apparent success of QH models for the NTE. Ultimately, a correct prediction of thermal expansion with incorrect phonons reinforces the need to look at the role of higher-order terms in the temperature-dependent behavior of this material. Despite the success of sTDEP at predicting phonon frequency shifts, it could not account for the newly observed diffuse inelastic intensity (DII) in the INS phonon spectra. For this, MLIP was more effective. This work provides complementary models to explain the origins of the DII, which is likely an emerging category of AH feature best described as a local nonlinear many-body process. We investigate phonon dissipation, the dynamics of systems coupled to their environments, Brownian motion, and discontinuities due to impulse transfer effects. We conclude by addressing the potential applications of the results and their role in future work on thermal lattice dynamics.

In this thesis, we seek to obtain certain molecular properties for species containing heavy elements or presenting atmospheric interests. For this, we use techniques to characterize the core electrons, with ionization potentials (IP) or with excitation energies (EE), allowing for example to respectively interpret X-ray Photoelectron Spectroscopy(XPS) and X-ray Absorption Spectroscopy (XAS). We also seek to characterize valence electrons through the polarizability, which is used for example to develop force fields. When we work with heavy elements or with core electrons, we must take relativistic effects into account. We therefore used the Dirac-Coulomb(-Gaunt) Hamiltonian. Furthermore, to compare our results with experiments, we need precise methods. Thus, we will work with the Coupled-Cluster (CC) method, and will use the Equation of Motion Coupled-Cluster (EOM-CC) method to obtain the IPs, EEs and electron affinities (EA). However, these two elements (4-component Hamiltonians and post-Hartree-Fock methods) imply considerable computational costs, requiring the resources of High Performance Computing (HPC) platforms.This thesis presents a study of the Core-Valence Separation (CVS) method, which will allow us to reach the properties of core electrons (IP and EE) with EOM-CC. We provide a detailed investigation of the performance of different Hamiltonians, in particular the exact two-component molecular mean field Hamiltonian. Second, we will focus on the perturbative approximations (Partioned and Many Body Perturbation Theory 2d order (MBPT (2)) to be applied to the EOM-CC matrix to limit computational costs, including for core processes. Finally, we present the work carried out in Exacorr, a new relativistic coupled cluster implementation for hybrid and massively parallel architectures. We will finish by outlining the formalism and working equations for the Linear Response Coupled-Cluster (LRCC) method, through which analytical (frequency-dependent) molecular polarizabilities can be obtained.; Dans cette thèse, nous cherchons à obtenir certaines propriétés moléculaires pour des espèces contenant des éléments lourds ou présentant des intérêts atmosphériques. Pour cela, nous utilisons des techniques permettant de caractériser les électrons de cœur, avec les potentiels d'ionisation (IP) ou avec les énergies d'excitation (EE), offrant la possibilité par exemple d'interpréter respectivement les expériences X-ray Photoelectron Spectroscopy (XPS) et X-ray Absorption Spectroscopy (XAS).Nous cherchons également à caractériser les électrons de valence au travers de la polarisabilité qui est utilisée par exemple pour développer des champs de force. Quand nous travaillons avec des éléments lourds ou avec des électrons de cœur, il faut prendre en compte les effets relativistes. Nous avons donc employé l'hamiltonien de Dirac-Coulomb(-Gaunt). De plus, pour comparer nos résultats aux expériences, il nous faut des méthodes précises. Ainsi, nous travaillerons avec la méthode Coupled-Cluster (CC) et pour obtenir les (IP), les (EE) et également les affinités électroniques (EA), nous utiliserons " Equation of Motion Coupled-Cluster " (EOM-CC). Cependant, ces deux éléments (hamiltoniens à 4-composantes et méthodes post-Hartree-Fock) impliquent des coûts de calcul considérables, nécessitant les ressources de plateformes de " High Performance Computing " (HPC).Cette thèse se présentera donc selon les éléments décrits précédemment. Premièrement, nous étudierons la méthode Core-Valence Separation (CVS) qui nous permettra, à partir de EOM-CC, d'atteindre les propriétés des électrons de cœur (IP et EE). Comme ces électrons sont proches du noyau où les effets relativistes sont les plus importants, nous étudierons différents hamiltoniens, notamment "exact two-component molecular mean field Hamiltonian ". Deuxièmement, nous nous intéresserons aux approximations perturbatives (" Partioned " et " Many Body Perturbation Theory 2d order " (MBPT(2)) à appliquer à la matrice EOM-CC pour limiter les coûts computationnels.Enfin, nous présenterons des travaux réalisés sur Exacorr, une nouvelle implémentation de Coupled-Cluster relativiste pour les architectures hybrides et massivement parallèles., un nouveau module de parallélisation des calculs pour des architectures hybrides et massivement parallèles. Nous terminerons en décrivant le formalisme et les équations de travail de la méthode Linear Response Coupled-Cluster (LRCC), grâce à laquelle des polarisabilités moléculaires analytiques (dépendantes de la fréquence) peuvent être obtenues.

In this contribution to the special issue “Celebrating 30 years of Steven Weinberg’s papers on Nuclear Forces from Chiral Lagrangians,” we emphasize the important role chiral effective field theory has played in leading nuclear physics into a precision era. To this end, we share our perspective on a few of the recent advances made in ab initio calculations of nuclear structure and nuclear matter observables, as well as Bayesian uncertainty quantification of effective field theory truncation errors.

The paper presents a brief review of the results in the self-consistent theory of the anharmonic effects of the second and third orders in the phonon production amplitude, based on the quantum many-body theory. Numerical (for second-order effects) and theoretical analyses of new, i.e., three- and four-quasiparticle correlations in the ground state (backward-going graphs) in magic nuclei and in nuclei with pairing are given. A formula for the probability of transition between one- and two-phonon states is obtained and compared to the solution of a similar problem within the quasiparticle-phonon model. It is shown that the approach under consideration contains a number of new effects.

Victory, i.e. vi enna c omputational to ol deposito ry , is a collection of numerical tools for solving the parquet equations for the Hubbard model and similar many body problems. In the current release, we focus on the single-band 2D Hubbard model, based on which generalizations to non-local interactions, multi orbitals and other lattices are straightforward. The parquet formalism is a self-consistent theory at both the single- and two-particle levels, and can thus describe individual fermions as well as their collective behavior on equal footing. This is essential for the understanding of various emergent phases and their transitions in many-body systems, in particular for cases in which a single-particle description fails. Our implementation of victory is in modern Fortran and it fully respects the structure of various vertex functions in both momentum and Matsubara frequency space. We found the latter to be crucial for the convergence of the parquet equations, as well as for the correct determination of various physical observables. In this release, we thoroughly explain the program structure and the controlled approximations to efficiently solve the parquet equations, i.e. the two-level kernel approximation and the high-frequency regulation. Program summary Program Title: Victory Program Files doi: http://dx.doi.org/10.17632/ym5kscj9sz.1 Licensing provisions: GPLv3 Programming language: Fortran 90 Nature of problem: The parquet equations require the knowledge of the fully irreducible vertex from which all one- and two-particle vertex and Green’s functions are calculated. The underlying two-particle vertex functions are large memory objects that depend on three momenta with periodic boundary conditions and three frequencies with open ones. The coupled diagrams of the parquet equations extend the frequency dependence of the reducible vertex functions to a larger frequency space where, a priori, no information is available. Solution method: The reducible vertex functions are found to possess the simplest structure among all two-particle vertex functions and can be approximated by functions with a reduced number of arguments, i.e. the kernel functions. The open boundary issue of the vertex functions in Matsubara-frequency space is then solved as follows: we solve the parquet equations with the reducible vertex functions whenever it is possible, otherwise we supplement these by the kernel functions.

We describe the first version (v1.0.0) of the code ADG that automatically (1) generates all valid Bogoliubov many-body perturbation theory (BMBPT) diagrams and (2) evaluates their algebraic expression to be implemented for numerical applications. This is achieved at any perturbative order $p$ for a Hamiltonian containing both two-body (four-legs) and three-body (six-legs) interactions (vertices). The automated generation of BMBPT diagrams of order $p$ relies on elements of graph theory, i.e., it is achieved by producing all oriented adjacency matrices of size $(p+1) \times (p+1)$ satisfying topological Feynman's rules. The automated evaluation of BMBPT diagrams of order $p$ relies both on the application of algebraic Feynman's rules and on the identification of a powerful diagrammatic rule providing the result of the remaining $p$-tuple time integral. The diagrammatic rule in question constitutes a novel finding allowing for the straight summation of large classes of time-ordered diagrams at play in the time-independent formulation of BMBPT. Correspondingly, the traditional resolvent rule employed to compute time-ordered diagrams happens to be a particular case of the general rule presently identified. The code ADG is written in Python2.7 and uses the graph manipulation package NetworkX. The code is also able to generate and evaluate Hartree-Fock-MBPT (HF-MBPT) diagrams and is made flexible enough to be expanded throughout the years to tackle the diagrammatics at play in various many-body formalisms that already exist or are yet to be formulated., 32 pages, 22 figures, 6 tables

Adaptive controllers and signal processors play a key role in dealing with parameter uncertainties. This paper proposes an adaptive and new information theoretic algorithm for secure and optimal source-coding. We optimise the volume of the achievable rate-distortion-equivocation region by the private Helen’s rate (HR), defining a stochastic mean-field game (MFG). The aforementioned stochasticity deals with the additional uncoded side-information (SI) at the encoder-decoder, or even possibly-decoded SI at the eavesdropper (Eve). The stochastic partial derivative equations (SPDEs), namely the Hamilton-Jacobi-Bellman (HJB) and the Fokker-Planck-Kolmogorov (FPK) are presented, being solved by a discretised Lagrangian. We explore the Information-flow over the resultant Riemann-Sphere and our proposed SMFG’s stability from a many-body-theoretic perspective. We also show that while the equivocation (uncertainty) rate is $\Delta \le min \{\mathcal {H}(\mathcal {X}),\mathcal {R}_{h} \}$ , $\mathcal {I}(\mathcal {Y};\mathcal {Z}|\mathcal {W})$ which is upper-bounded to $min\{ \mathcal {I}(\mathcal {X};\mathcal {Y}),\mathcal {I}(\mathcal {Y};\mathcal {Z}|\mathcal {W}) \}$ , versus $\mathcal {I}(\mathcal {X};\mathcal {Z}|\mathcal {W})$ theoretically converges to the information-Bottleneck-bound $\mathcal {H}(\mathcal {X})$ . Simulation results also show an out-performance of our scheme over the existing work, proving the SMFG’s stability and an adequate distance to Pareto-Optimal sets . Our generic solution covers a comprehensive field of studies determining smooth non-linearity .

Accurate predictions of charge excitation energies of molecules in the disordered condensed phase are central to the chemical reactivity, stability, and optoelectronic properties of molecules and critically depend on the specific environment. Herein, we develop a stochastic GW method for calculating these charge excitation energies. The approach employs maximally localized electronic states to define the electronic subspace of a molecule and the rest of the system, both of which are randomly sampled. We test the method on three solute-solvent systems: phenol, thymine, and phenylalanine in water. The results are in excellent agreement with the previous high-level calculations and available experimental data. The stochastic calculations for supercells representing the solvated systems are inexpensive and require $\sim 1000$ CPU$\cdot$hrs. We find that the coupling with the environment accounts for $\sim40\%$ of the total correlation energy. The solvent-to-solute feedback mechanism incorporated in the molecular correlation term causes up to 0.6 eV destabilization of the QP energy. Simulated photo-emission spectra exhibit red shifts, state-degeneracy lifting, and lifetime shortening. Our method provides an efficient approach for an accurate study of excitations of large molecules in realistic condensed phase environments., 9 pages, 4 figures

In the search for novel materials for vacuum electron sources, multi-alkali antimonides and in particular sodium-potassium-antimonides have been recently regarded as especially promising due to their favorable electronic and optical properties. In the framework of density-functional theory and many-body perturbation theory, we investigate the electronic structure and the dielectric response of two representative members of this family, namely Na2KSb and NaK2Sb. We find that both materials have a direct gap, which is on the order of 1.5 eV in Na2KSb and 1.0 eV in NaK2Sb. In either system, valence and conduction bands are dominated by Sb states with p- and s-character, respectively. The imaginary part of the dielectric function, computed upon explicit inclusion of electron–hole interactions to characterize the optical response of the materials, exhibits maxima starting from the near-infrared region, extending up to the visible and the ultraviolet band. With our analysis, we clarify that the lowest-energy excitations are non-excitonic in nature and that their binding energy is on the order of 100 meV. Our results confirm the potential of Na2KSb and NaK2Sb as photoemissive materials for vacuum electron sources, photomultipliers, and imaging devices.