Electron-phonon interactions (EPIs) are ubiquitous in condensed matter physics and materials science. They are crucial for understanding numerous phenomena, including conventional superconductivity, charge-transport and, most pertinent for this thesis, polaron formation. A polaron is a charge carrier (electron or hole) dressed with a “cloud” of phonons. The polaronic quasiparticle may have vastly different ground- and excited-state properties from that of the bare, constituent charge carrier. While polarons are well-studied and largely understood in canonical model Hamiltonians, recent advances have made it possible to study more complex, fully ab initio systems. Here, the numerically exact methods which are available for some model systems become much more challenging to apply, so accurate approximate methods are a necessity. In this dissertation, we present several advancements in approximate but accurate methods for different polaronic problems and polaron observables. With respect to polaron dynamics, we focus on low-scaling methods to produce wave vector-dependent single-particle spectral function. We present a thorough study of the accuracy of the second- and fourth-order cumulant expansions (CE) of the electronic Green’s function by comparing them against numerically-exact reference data for the one-dimensional Holstein model. We find that the second-order CE is accurate at zero electronic-momentum across a wide range of temperatures, while for non-zero electronic momenta, the CE is only accurate at high-temperatures. The fourth-order cumulant expansion improves on the dynamics at short times and can improve the spectra; however, it can also introduce non-physical divergences and negative spectral weight. The second-order cumulant expansion is thus a useful tool for determining spectral functions in some instances. However, increasing the order of the CE introduces pathologies that may persist at arbitrarily high-order. As an alternate approach to improving the CE, we introduce a new self-consistent cumulant expansion (SC-CE) which remedies many of the deficits of the CE. We compare the results for this new approximation against those from the second-order cumulant expansion as well as reference data for the one-dimensional Holstein model. Unlike the CE, the SC-CE can produce accurate spectra across the entire Brillouin-zone, and captures non-perturbative features excellently. The trade-off for this increased accuracy is the introduction of some degree of negative spectral-weight and the potential for rapid divergences in time in some instances. We find that these problems can be minimized, but not completely eliminated in the thermodynamic limit and in more realistic cases where phonon dispersion exists. We also demonstrate how the SC-CE fits into the greater scheme of Green’s function methods which approximate the self-energy non-diagrammatically as has recently been proposed by Pandey and Littlewood, and we note the potential applications of the SC-CE both in ab initio polaron problems and in general many-body problems. We finally consider a new method to determine the ground-state structure of the polaron in ab initio materials, a topic which has only recently appeared in the literature. We present a new all-coupling variational method based on the Nagy-Markoš variational ansatz for the Fröhlich model. The ansatz is a projected unitary transform which naturally interpolates between the weak-coupling (Lee-Low-Pines) ansatz and the strong-coupling adiabatic ansatz by modulating the momentum conservation of the electron-phonon scattering processes. We demonstrate our ab initio Nagy-Markoš ansatz on the Holstein model and the Fröhlich model, and show that it always improves upon the better of the weak or strong coupling result. We consider the ab initio case of lithium fluoride (LiF), and find that the ansatz provides accurate polaron binding energies for both the hole-polaron and the electron-polaron which are classical cases of small and large polarons, respectively. We note how our flexible variational ansatz is an ideal starting point for perturbative energy corrections and cumulant Green’s function methods. Future developments and applications of the efficient methodologies presented in this dissertation may enable quantitative calculations of polarons in large-intermediately coupled ab initio systems, such as the lead-halide perovskites and other systems where it has hitherto been difficult to fully understand the effects of the electron-phonon interactions.

Thesis (Ph.D.)--Ohio University, August, 2008. / Title from PDF t.p. Includes bibliographical references.

Thesis (Ph. D.)--University of Missouri-Columbia, 2005. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (November 13, 2006) Vita. Includes bibliographical references.

The Fröhlich coupling describes the interaction between electrons and infrared-active vibrations at long wavelength in polar semiconductors and insulators, and may result in the formation of polaronic quasiparticles. Polarons are electrons dressed by a phonon cloud, which can strongly affect the electronic properties of the crystal. Despite their ubiquitous role in a broad range of technologies, first-principles investigations of the electron-phonon interaction in polar materials are scarce. In this thesis we develop a general formalism for calculating the electron-phonon matrix element in polar semiconductors and insulators from first principles, which represents a generalization of the Fröhlich model and can be used to compute the polar electron-phonon coupling as a straightforward post-processing operation. We apply this procedure to explore an important material for photovoltaics, the hybrid lead halide perovskite CH₃NH₃PbI₃. In this case we show that the temperature dependence of emission line broadening is dominated by Fröhlich coupling. Our method is formulated in conjunction with an ab initio interpolation technique based on maximally localized Wannier functions, which allows to describe all forms of electron-phonon coupling on the same footing. We demonstrate the validity of this approach on the prototypical examples GaN and SrTiO₃. Focusing on anatase TiO₂, a transition metal oxide of wide technological interest, we establish quantitatively the effect of including the ab initio Fröhlich coupling in the calculation of electron lifetimes. The rest of the thesis is devoted to exploring the quasiparticle properties in doped oxides. In particular, we investigate angle-resolved photoemission spectra from first principles in doped anatase TiO₂ by proposing a novel framework that combines our ab initio matrix elements, including the dynamical screening arising from the added carriers, and the cumulant expansion approach. We compare our results with experimental data, and show that the transition from a polaronic to a Fermi liquid regime with increasing doping concentration originates from nonadiabatic polar electron-phonon coupling. We further validate this mechanism by calculating angle-resolved photoemission spectra in the ferromagnetic semiconductor EuO.

Made available in DSpace on 2014-12-17T15:14:51Z (GMT). No. of bitstreams: 1 CarlosAB.pdf: 4650783 bytes, checksum: f2e26def9a10e7ffcd8eb8baa0c4d1cc (MD5) Previous issue date: 2009-06-26 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / In the first part of this work our concern was to investigate the thermal effects in organic crystals using the theory of the polarons. To analyse such effect, we used the Fr?hlich s Hamiltonian, that describes the dynamics of the polarons, using a treatment based on the quantum mechanics, to elucidate the electron-phonon interaction. Many are the forms to analyzing the polaronic phenomenon. However, the measure of the dielectric function can supply important information about the small polarons hopping process. Besides, the dielectric function measures the answer to an applied external electric field, and it is an important tool for the understanding of the many-body effects in the normal state of a polaronic system. We calculate the dielectric function and its dependence on temperature using the Hartree-Fock decoupling method. The dieletric function s dependence on the temperature is depicted by through a 3D graph. We also analyzed the so called Arrhenius resistivity, as a functionof the temperature, which is an important tool to characterize the conductivity of an organic molecule. In the second part we analyzed two perovskita type crystalline oxides, namely the cadmium silicate triclinic (CdSiO3) and the calcium plumbate orthorhombic (CaPbO3), respectively. These materials are normally denominated ABO3 and they have been especially investigated for displaying ferroelectric, piezoelectric, dielectrics, semiconductors and superconductors properties. We found our results through ab initio method within the functional density theory (DFT) in the GGA-PBE and LDA-CAPZ approximations. After the geometry optimization for the two structure using the in two approximations, we found the structure parameters and compared them with the experimental data. We still determined further the angles of connection for the two analyzed cases. Soon after the convergence of the energy, we determined their band structures, fundamental information to characterize the nature of the material, as well as their dielectrics functions, optical absorption, partial density of states and effective masses of electrons and holes / Na primeira parte deste trabalho nos preocupamos em desvendar os efeitos t?rmicos, usando a teoria dos polarons, em cristais org?nicos. Para analisarmos tais efeitos usamos o Hamiltoniano de Fr?hlich que prop?s um modelo para a din?mica dos polarons (acoplamento el?tron-f?non) usando um tratamento qu?ntico. Muitas s?o as formas de se analisar o fen?meno polar?nico, tais como, a medida da fun??o diel?trica que pode fornecer informa??es importantes sobre o processo de hopping dos small polarons . Al?m disso, a fun??o diel?trica mede a resposta a um campo el?trico externo aplicado e ?e uma importante ferramenta para entender os efeitos de muitos-corpos no estado normal de um sistema polar?nico. Calculamos a fun??o diel?trica e conseq??ntemente a sua depend?ncia com a temperatura usando o desacoplamento de Hartree-Fock. A depend encia da temperatura ? verificada na fun??o diel?trica em um gr?fico 3D em fun?ao da frequ?ncia e temperatura reduzida. Analisamos ainda a chamada resistividade de Arrhenius em fun??o da temperatura, importante ferramenta na caracteriza??o da condutividade de uma mol?cula org?nica. Nas segunda etapa analisamos dois ?xidos cristalinos tipo perovskita: o silicato de c?dmio tricl?nico ( CdSiO3) e o plumbato de calcio ortorrombico (CaPbO3), respectivamente. Estes materiais s ao genericamente denominados ABO3 e t?m sido especialmente investigados por exibirem propriedades ferroel?tricas, piezoel?tricas, diel?tricas, semicondutoras e supercondutoras. Apresentamos os nossos resultados via o m?todo ab initio dentro do formalismo da teoria do funcional densidade (DFT) nas aproxima??es GGAPBE e LDA-CAPZ. Depois da otimiza??o geom?trica encontramos, para as duas estruturas e nas duas aproxima??es, os par?metros de rede e os comparamos com os dados experimentais. Determinamos ainda os angulos de liga??o para os dois casos analizados. Logo ap?s a converg?ncia energ?tica, determinamos as estuturas de bandas, fundamentais para se conhecer a natureza do material, fun??es diel?tricas, absor?c?o?ptica, densidade parcial de estados e massas efetivas de el?trons e buracos

Orientador: Bernardo Laks / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-07-24T19:10:29Z (GMT). No. of bitstreams: 1 DelNero_Jordan_M.pdf: 1272378 bytes, checksum: 9c34f8d6136058a98b04ffdea9e5ac08 (MD5) Previous issue date: 1995 / Resumo: Este trabalho é um estudo teórico da estrutura eletrônica de uma classe de poliremos conjugados, neste caso a Policarbonitrila. Tratou-se, em especial, o problema de desordens configuracionais. Os problemas que investigamos: (1) determinação da conformação mais estável de oligômeros da policarbonitrila; (2) a caracterização da estrutura eletrônica sob efeito de protonação na policarbonitrila. Utilizamos o método de Huckel Simples Modificado com os defeitos distribuídos uniformemente e também aleatoriamente. Não verificou-se nesta aproximação a transição metálica; (3) Efeitos na estrutura eletrônica da policarbonitrila na presença de pólarons. Observamos a presença de estados estendidos na região original do gap, mas não houve fechamento total do gap. A metodologia utilizada neste trabalho está baseada na técnica de HS modificado, EHT, Hiickel com compressibilidade, AM1( Austin Model 1) e NFC(Negative Factor Counting) / Abstract: Not informed / Mestrado / Física / Mestre em Física

A investigação das propriedades ópticas e sua relação com as propriedades magnéticas dos semicondutores é de grande interesse para a comunidade científica, em virtude da enorme demanda por novas tecnologias e funcionalidades que podem surgir dessas pesquisas. Os calcógenos de európio são semicondutores intrinsecamente magnéticos, transparentes na região visível do espectro eletromagnético e integráveis em matrizes de silício e nitreto de gálio, sendo assim fortes candidatos a aplicações tecnológicas envolvendo magnetismo e óptica. Neste trabalho são investigados os espectros de absorção e fotoluminescência dos calcógenos de európio, com base no modelo 4f -> 5d(\'t IND. 2g\') da transição óptica de dipolo elétrico, o qual mostrou-se totalmente adequado para a descrição da absorção óptica nos calcógenos de európio em função do campo magnético aplicado, explicando a presença de linhas de absorção estreitas e dicróicas nos espectros em campo alto e a forma larga dos espectros de absorção em campo nulo. Nos espectros de fotoluminescência do EuTe, entretanto, foram detectados estados eletrônicos não contemplados pelo modelo 4f -> 5d(\'t IND. 2g\') , em especial uma banda de emissão denominada \'MX IND. 0\', acoplada a modos vibracionais da rede. Uma linha zero-fônon correspondente a uma transição que não produz fônons pôde ser bem definida e a partir do deslocamento dessa linha em função do campo magnético foi possível detectar inequivocamente a formação de polarons magnéticos no EuTe pela primeira vez; o raio polarônico foi estimado como R = 3.6a, onde a é o parâmetro de rede e a energia de ligação desse polaron foi estimada em \'E IND. p\' = 45 meV, um resultado que foi confirmado através de medidas do deslocamento da linha zero-fônon em função da temperatura. Adicionalmente procurou-se identificar o estado eletrônico associado à emissão \'MX IND. 0\': a partir de medidas da intensidade da fotoluminescência em função da potência de excitação foi possível sugerir que a emissão \'MX IND. 0\' provem de estados eletrônicos ligados a defeitos da rede e foi possível estimar a concentração desses defeitos como menor que 0.1 ppm. / Investigation of optical properties and their relation to magnetic properties of semiconductors is of great interest to scientific community, due to the large demand for new technologies and features that can arise from these studies. Europium chalcogenides are intrinsically magnetic semiconductors, transparent in the visible region of electromagnetic spectrum and integrable into silicon and gallium nitride matrices, beeing strong candidates for technological applications involving magnetism and optics. The present study investigates absorption and photoluminescence spectra of europium chalcogenides, based on the 4f -> 5d(t2g) model of the electric dipole optical transition, which proved to be entirely appropriate to describe polarized optical absorption in europium chalcogenides as a function of magnetic field, explaining the presence of narrow dichroic lines at high fields and the broad shape of the zero-field absorption spectrum. However, in photoluminescence spectra of EuTe, electronic states not covered by the 4f -> 5d(t2g) model were detected, in particular an emission band labeled MX0, which is coupled to vibrational modes of the lattice. A transition without production of phonons, corresponding to a zero-phonon line, could be well resolved and from the displacement of the zero-phonon line as a function of magnetic field the formation of magnetic polarons in EuTe could be detected unambiguously for the first time. The polaronic radius is estimated as R = 3:6a, where a is the lattice parameter, and the polaron binding energy is estimated as Ep = 45 meV, a result that was confirmed by measurements of zero-phonon line displacement as a function of temperature. Additionally, we sought to identify the electronic state associated with MX0 emission: from measurements of the photoluminescence intensity as a function of excitation power, it was possible to suggest that MX0 emission comes from an electronic state coupled to lattice defects of low concentration, which we estimate to be of less than 0.1 ppm.

Ce travail de thèse porte sur l’étude des propriétés optiques de boites quantiques anisotropes de (Cd,Mn)Te insérées dans des nanofils de ZnTe. Les boites quantiques étudiées contenant 10% de Mn sont allongées suivant l’axe du fil ce qui tend à favoriser un état fondamental à trou léger ayant une susceptibilité de spin perpendiculaire à l’axe du fil. L’objectif principal de la thèse est l’étude de la formation du Polaron Magnétique dans ces boites et la détermination de leur anisotropie magnétique.Nous avons étudié en premier les propriétés optiques de nanofils de ZnTe et de nanofils coeurs-coquilles ZnTe/(Zn,Mg)Te. Ces études nous ont amené à modéliser les contraintes élastiques dans le cœur, dans la coquille et dans des boites allongées insérées dans les nanofils. Ce modèle nous a permis d’estimer les splittings entre les niveaux de trou lourd et de trou léger dans la boite et dans le fil.Nous avons étudié ensuite des nanofils contenant des boites magnétiques et non magnétiques par spectroscopie magnéto-optique. Dans les boites magnétiques, les interactions d’exchange entre les porteurs localisés et les spins de Mn induisent un très fort décalage Zeeman de la raie excitonique (Effet Zeeman Géant). Pour extraire des paramètres quantitatifs, nous avons combiné différentes techniques expérimentales sur le même nanofil (photo et cathodoluminescence, analyse dispersive en énergie du rayonnement X). Nous avons utilisé différentes orientations du champ magnétique pour déterminer l’anisotropie du trou dans la boite. Les valeurs expérimentales sont plus petites que les valeurs théoriques ce qui suggère un mauvais confinement du trou dans la boite.Afin d’obtenir un meilleur confinement du trou, nous avons étudié des boites de (Cd,Mn)Te entourées d’une coquille de (Zn,Mg)Te. Grace au meilleur confinement du trou, nous avons réussi à observer la formation du Polaron Magnétique excitonique. Des mesures de photoluminescence résolues en temps sur des nanofils uniques nous ont permis d’extraire l’énergie et le temps de formation du Polaron Magnétique entre 5K et 50K. La raie d’émission des boites présente un effet Zeeman géant inhabituel caractéristique d’un Polaron Magnétique à trou léger. Nous avons développé un modèle théorique pour décrire la formation du Polaron Magnétique excitonique dans les boites quantiques. Ce model, basé sur l’énergie libre et valable pour des températures et des champs magnétiques arbitraires, a été utilisé pour rendre compte de l’ensemble des données expérimentales. Ce modèle a permis de déterminer les paramètres caractéristiques du polaron magnétique à trou léger (énergie, orientation and amplitude du moment magnétique, volume d’échange, anisotropie du trou). / In this PhD work we study the optical properties of anisotropic (Cd,Mn)Te magnetic quantum dots inserted in ZnTe nanowires. The quantum dots containing typically 10% of Mn spins are elongated along the nanowire axis which tend to stabilize a light hole ground state with a spin susceptibility perpendicular to the nanowire axis. The main goal was to study the formation of exciton Magnetic Polarons in such quantum dots and to determine their magnetic anisotropy.We investigate first the optical properties of ZnTe and ZnTe/(Zn,Mg)Te core shell nanowires. We model the elastic strain profile in core-shell nanowires and in elongated quantum dots. From the strain profiles, we estimate the value of the light hole heavy hole splitting expected in the dot and in the nanowire.In a second step we study single nanowires containing magnetic and non magnetic quantum dots by magneto-optical spectroscopy. The exchange interactions between confined carriers and Mn spins induce a large Zeeman shift of the exciton line (Giant Zeeman Effect). To extract quantitative parameters, we combine different experimental techniques (photo and cathodoluminescence, energy dispersive X ray spectroscopy) on the same nanowire. We use also different magnetic field orientations in order to determine the hole anisotropy in the dot. The experimental values are smaller than the theoretical ones suggesting a weak confinement of the holes in the dot due to a small (Cd,Mn)Te/ZnTe valence band offset.In a third step we study nanowires containing (Cd,Mn)Te quantum dots surrounded by a (Zn,Mg)Te alloy. Thanks to the better hole confinement induced by the (Zn,Mg)Te alloy, the formation of exciton magnetic polarons can be observed. We perform time resolved photoluminescence studies on single nanowires in order to determine the energy and the formation time of magnetic polarons from 5K to 50K. The quantum dot emission line shows an unusual Zeeman shift, characteristic of a light hole magnetic polaron. We develop a theoretical model describing the formation of exciton magnetic polaron in quantum dots. We use this model, based on the free energy and valid for any temperature and magnetic field, to fit the whole set of experimental data. It allows us to determine the characteristic parameters of the light hole magnetic polarons (energy, orientation and magnitude of the magnetic moment, exchange volume, hole anisotropy).

A investigação das propriedades ópticas e sua relação com as propriedades magnéticas dos semicondutores é de grande interesse para a comunidade científica, em virtude da enorme demanda por novas tecnologias e funcionalidades que podem surgir dessas pesquisas. Os calcógenos de európio são semicondutores intrinsecamente magnéticos, transparentes na região visível do espectro eletromagnético e integráveis em matrizes de silício e nitreto de gálio, sendo assim fortes candidatos a aplicações tecnológicas envolvendo magnetismo e óptica. Neste trabalho são investigados os espectros de absorção e fotoluminescência dos calcógenos de európio, com base no modelo 4f -> 5d(\'t IND. 2g\') da transição óptica de dipolo elétrico, o qual mostrou-se totalmente adequado para a descrição da absorção óptica nos calcógenos de európio em função do campo magnético aplicado, explicando a presença de linhas de absorção estreitas e dicróicas nos espectros em campo alto e a forma larga dos espectros de absorção em campo nulo. Nos espectros de fotoluminescência do EuTe, entretanto, foram detectados estados eletrônicos não contemplados pelo modelo 4f -> 5d(\'t IND. 2g\') , em especial uma banda de emissão denominada \'MX IND. 0\', acoplada a modos vibracionais da rede. Uma linha zero-fônon correspondente a uma transição que não produz fônons pôde ser bem definida e a partir do deslocamento dessa linha em função do campo magnético foi possível detectar inequivocamente a formação de polarons magnéticos no EuTe pela primeira vez; o raio polarônico foi estimado como R = 3.6a, onde a é o parâmetro de rede e a energia de ligação desse polaron foi estimada em \'E IND. p\' = 45 meV, um resultado que foi confirmado através de medidas do deslocamento da linha zero-fônon em função da temperatura. Adicionalmente procurou-se identificar o estado eletrônico associado à emissão \'MX IND. 0\': a partir de medidas da intensidade da fotoluminescência em função da potência de excitação foi possível sugerir que a emissão \'MX IND. 0\' provem de estados eletrônicos ligados a defeitos da rede e foi possível estimar a concentração desses defeitos como menor que 0.1 ppm. / Investigation of optical properties and their relation to magnetic properties of semiconductors is of great interest to scientific community, due to the large demand for new technologies and features that can arise from these studies. Europium chalcogenides are intrinsically magnetic semiconductors, transparent in the visible region of electromagnetic spectrum and integrable into silicon and gallium nitride matrices, beeing strong candidates for technological applications involving magnetism and optics. The present study investigates absorption and photoluminescence spectra of europium chalcogenides, based on the 4f -> 5d(t2g) model of the electric dipole optical transition, which proved to be entirely appropriate to describe polarized optical absorption in europium chalcogenides as a function of magnetic field, explaining the presence of narrow dichroic lines at high fields and the broad shape of the zero-field absorption spectrum. However, in photoluminescence spectra of EuTe, electronic states not covered by the 4f -> 5d(t2g) model were detected, in particular an emission band labeled MX0, which is coupled to vibrational modes of the lattice. A transition without production of phonons, corresponding to a zero-phonon line, could be well resolved and from the displacement of the zero-phonon line as a function of magnetic field the formation of magnetic polarons in EuTe could be detected unambiguously for the first time. The polaronic radius is estimated as R = 3:6a, where a is the lattice parameter, and the polaron binding energy is estimated as Ep = 45 meV, a result that was confirmed by measurements of zero-phonon line displacement as a function of temperature. Additionally, we sought to identify the electronic state associated with MX0 emission: from measurements of the photoluminescence intensity as a function of excitation power, it was possible to suggest that MX0 emission comes from an electronic state coupled to lattice defects of low concentration, which we estimate to be of less than 0.1 ppm.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.