In absence of external fields, vibrational modes of periodic systems are usually considered as linearly polarized and, as such, they do not carry angular momentum. Our work proves that non-adiabatic effects due to the electron-phonon coupling are time-reversal symmetry breaking interactions for the vibrational field in systems with non-collinear magnetism and large spin-orbit coupling. Since in these systems the deformation potential matrix elements are necessarily complex, a nonzero synthetic gauge field (Berry curvature) arises in the dynamic equations of the ionic motion. As a result, phonon modes are elliptically polarized in the non-adiabatic framework and intrinsic vibrational angular momenta occur even for non-degenerate modes and without external probes. These results are validated by performing fully relativistic ab-initio calculations on two insulating platinum clusters and a metallic manganese compound, with non-collinear magnetism. In both cases, non-adiabatic vibrational modes carry sizeable angular momenta comparable to the orbital electronic ones in itinerant ferromagnets.

This thesis presents an experimental and theoretical study of the collision dynamics of OH(A²Σ⁺) with Kr and Xe. These two systems both exhibit a significant degree of electronically non-adiabatic behaviour, and a particular emphasis of the work presented here is to characterise the competition and interplay between electronic quenching on the one hand, and electronically adiabatic collisional processes on the other. Quenching takes place close to the bottom of the deepest potential well for both systems. In collisions that remain in the excited electronic state, this same region of the potential is also largely responsible for rotational energy transfer (RET) and the collisional depolarisation of angular momentum. Therefore, the direct competition between these processes suppresses the cross-sections for RET and collisional depolarisation from their expected value in the absence of quenching. To investigate this, experiments were carried out to measure cross-sections for the collisional transfer of electronic, vibrational and rotational energy in OH(A, v=0,1) + Kr and OH(A, v=0) + Xe. In addition, measurements were made of the j-j' correlation -- that is, the relationship between the angular momentum of the OH radical before and after a collision -- in collisions with Kr and Xe, using the experimental technique of Zeeman quantum beat spectroscopy. Collisions with both Kr and Xe tend to effectively depolarise the angular momentum of the OH radical, due to the very anisotropic character of the potential on which the process occurs. Electronic quenching, which plays an essential role in both systems, is more prevalent with xenon as the crossing to the ground state potential is located in a more accessible location. These experimental results were compared with single surface quasi-classical trajectory (QCT) calculations, where the overestimate of rotational energy transfer or collisional depolarisation helps to elucidate the degree to which the presence of quenching suppresses these processes. Surface hopping QCT was then used to account for non-adiabatic transitions in the theory, which led to an improvement in agreement with experiment. However, standard surface hopping QCT theory failed to account for the full extent of quenching in these two systems. A major focus of this work is therefore on the development of an extension to standard surface hopping QCT theory to incorporate rovibronic couplings. In non-linear configurations, the excited state of the OH + Kr, Xe systems has A' symmetry, while the ground state is split into symmetric (A') and antisymmetric (A'') components. For these symmetry reasons, coupling is restricted to the two states of the same symmetry, however a rotation of the correct (A'') symmetry can induce transitions to the A'' state too. Inclusion of all three electronic states, and the relevant couplings between them, is found to be crucial for a proper description of experimental reality.

Les signatures de l’existence des phonons sont omniprésentes dans les propriétés des matériaux. En première approximation, on peut scinder l'effet des phonons sur la structure électronique en deux contributions. D’une part, l'interaction électron-phonon capture la réponse électronique aux vibrations des noyaux du cristal, et d’autre, l'énergie libre de la population de phonons modifie le volume cristallin à l’équilibre. En plus d'être responsables de la dépendance en température de la structure électronique, ces deux mécanismes affectent les niveaux d'énergie à température nulle, à travers le mouvement du point zéro et l'énergie du point zéro. Cette thèse analyse l’apport de ces deux mécanismes à la renormalisation du point zéro (ZPR) de l'énergie de la bande interdite des semi-conducteurs. Une généralisation du modèle de Fröhlich prenant en compte l'anisotropie et les dégénérescences présentes dans les matériaux réels révèle que l'interaction non adiabatique entre les électrons et les noyaux domine le ZPR dans les matériaux polaires. La prise en compte de ce mécanisme dans l'évaluation de l'interaction électron-phonon est déterminante pour reproduire adéquatement les données expérimentales. L'approche développée par Grüneisen, qui néglige communément les effets du point zéro, reproduit la dilatation du point zéro du réseau (ZPLE) et sa contribution au ZPR obtenues avec la méthode standard basée sur la minimisation de l'énergie libre à moindre coût numérique, y compris pour les matériaux anisotropes. La contribution du ZPLE au ZPR total, qui a reçu peu d'attention dans la littérature, peut atteindre de 20% à plus de 80% de la contribution de l'interaction électron-phonon, y compris dans des matériaux constitués de noyaux légers. Elle domine même le ZPR du GaAs dans le contexte de la DFT semi-locale. Il est donc essentiel de traiter les deux contributions sur le même pied d'égalité pour modéliser le ZPR avec précision. L'inclusion du couplage spin-orbite (SOC) diminue le ZPR d'un ensemble substantiel de matériaux cubiques de structure zinc-blende, diamant et rock-salt. L'essentiel de cette variation tire son origine de l'effet du SOC sur les énergies électroniques statiques, qui provient en grande partie de la variation des masses effectives des bandes de valence au point \(\Gamma\). La réduction du ZPR peut être estimée à partir d'un modèle de Fröhlich généralisé auquel on a introduit le SOC. Les subtilités numériques liées au traitement de la séparation de Dresselhaus dans les matériaux non centrosymétriques sont discutées. On démontre enfin comment l'effet combiné de l'interaction électron-phonon et de la dilatation thermique affecte le diagramme de phase topologique du BiTeI. L'augmentation de la température repousse l'apparition de la phase d'isolant topologique \(\mathbb{Z}_2\) vers des pressions plus élevées et élargit la plage de pressions correspondant à la phase intermédiaire de type semi-métal de Weyl. Le caractère orbital dominant des extrema de bande influence significativement leur sensibilité à la pression et au changement de topologie. Pour guider la recherche expérimentale de phases topologiquement non triviales dans les matériaux de façon adéquate, les études numériques doivent donc considérer l'effet de la température. / Phonon signatures are ubiquitous in material properties. At first order, the effect of phonons on the electronic structure can be split into two contributions. On the one hand, the electron-phonon interaction captures the electronic response to the vibrations of the nuclei. On the other hand, the free energy of the phonon population modifies the crystalline volume at equilibrium. In addition to driving the temperature dependence of the electronic structure, these two mechanisms affect the energy levels at zero temperature through zero-point motion and zero-point energy. This thesis investigates the contribution of these two mechanisms to the zero point renormalization (ZPR) of the band gap energy of semiconductors. A generalized Fröhlich model taking into account the anisotropy and degeneracies occurring in real materials reveals that the non-adiabatic interaction between electrons and nuclei dominates the ZPR in polar materials. Taking this mechanism into account when evaluating the electron-phonon interaction is crucial to reproduce experimental data adequately. The Grüneisen formalism, which commonly neglects zero-point effects, reproduces the zero-point lattice expansion (ZPLE) and its contribution to the ZPR obtained from the standard method based on free energy minimization at lower numerical cost, including for anisotropic materials. The ZPLE contribution to the total ZPR, which has received little attention in the literature, can reach from 20% to more than 80% of the contribution of the electron-phonon interaction, including in materials containing light atoms. It even dominates the ZPR of GaAs within semilocal DFT. Therefore, both contributions should be treated on an equal footing to model the ZPR accurately. The inclusion of spin-orbit coupling (SOC) decreases the ZPR of a substantial set of cubic materials of zincblende, diamond and rocksalt structure. This variation originates mostly from the effect of SOC on the static electronic eigenvalues, which comes largely from the variation of the effective masses of the valence bands at the \(\Gamma\) point. The reduction of the ZPR can be estimated from a generalized Fröhlich model in which SOC has been introduced. Numerical subtleties related to the treatment of Dresselhaus separation in non-centrosymmetric materials are discussed. We finally show how the combination of electron-phonon interaction and thermal expansion affects the topological phase diagram of BiTeI. An increase in temperature pushes the \(\mathbb{Z}_2\) topological insulator phase towards higher pressures and widens the pressure range corresponding to the Weyl semi-metal intermediate phase. The leading orbital character of the band extrema significantly influences their sensitivity to variations in pressure and topology. To adequately guide the experimental search for topologically non-trivial phases in materials, numerical studies must therefore consider the effect of temperature.