In this thesis I present contributions to the development, analysis and application of tensor network state methods for numerically exact quantum dynamics in one and two-dimensional lattice systems. The setting of numerically exact quantum dynamics is introduced in Chapter 2. This includes a discussion of exact diagonalization approaches and massively parallel implementations thereof as well as a brief introduction of tensor network states. In Chapter 3, I perform a detailed analysis of the performance of n-ary tree tensor network states for simulating the dynamics of two-dimensional lattices. This constitutes the first application of this class of tensor network to dynamics in two spatial dimensions, a long-standing challenge, and the method is found to perform on par with existing state-of-the-art approaches. Chapter 4 showcases the efficacy of a novel tensor network format I developed, tailored to electron-phonon coupled problems in their single-electron sector, through an application to the Holstein model. The applicability of the approach to a broad range of parameters of the model allows to reveal the strong influence of the spread of the electron distribution on the initial state of the phonons at the site where the electron is introduced, for which a simple physical picture is offered. I depart from method development in Chapter 5 and analyse the prospects of using tensor network states evolved using the time-dependent variational principle as an approximate approach to determine asymptotic transport properties with a finite, moderate computational effort. The method is shown to not yield the correct asymptotics in a clean, non-integrable system and can thus not be expected to work in generic systems, outside of finely tuned parameter regimes of certain models. Chapters 6 and 7 are concerned with studies of spin transport in long-range interacting systems using tensor network state methods. For the clean case, discussed in Chapter 6, we find that for sufficiently short-ranged interactions, the spreading of the bulk of the excitation is diffusive and thus dominated by the local part of the interaction, while the tail of the excitation decays with a powerlaw that is twice as large as the powerlaw of the interaction. Similarly, in the disordered case, analysed in Chapter 7, we find subdiffusive transport of spin and sub-linear growth of entanglement entropy. This behaviour is in agreement with the behaviour of systems with local interactions at intermediate disorder strength, but provides evidence against the phenomelogical Griffith picture of rare, strongly disordered insulating regions. We generalize the latter to long-ranged interactions and show that it predicts to diffusion, in contrast to the local case where it results in subdiffusive behaviour.

Pages 6 and 7 are labelled as the same page. / <p> The purpose of this work is to calculate phonon dispersion curves in metals paying particular attention to the evaluation of a new electron-ion matrix element by use of orthogonalized plane waves (OPW). The dynamic role of the electrons in screening the electron-ion interaction has been studied. Our formalism makes use of recent developments in the theory of the many-body problem. Applications of our theory have been made to aluminum. The pseudopotential part of the OPW electron-ion matrix element produced an overscreening of the frequency modes. Comparison is made to the use of the Bardeen matrix element. Our results strongly suggest that this calculation applied to lead would explain the magnitude of Kohn kinks observed by Brockhouse et al. (B 62a).</p> / Thesis / Doctor of Philosophy (PhD)

<p> Brillouin scattering technique is used to investigate the transverse acoustic phonon in (KBr)1-x(KCN)x alloy as a function of temperature for CN- concentration ranging from 0.20 to 0.50. Anomalies in phonon frequency and linewidth are observed and discussed in terms of coupling of the acoustic phonons with orientational motion of CN- ions based on a dynamic microscopic model suggested by Michel et al. The frequency and concentration dependence of the freezing temperature, which marks the formation of an orientational glass state, is examined.</p> <p> A high resolution tandem Fabry-Perot interferometer yields the first evidence of a complex spectrum which consists of the phonon peak and new equal-spaced modes. The Bayesian deconvolution technique is used to extract the spectra. The concentration, time and temperature dependence of these new modes are presented. It is proposed that they arise from the modification of the tunneling levels of the CN, and appear to have the uniform density of states which is the characteristic property of the glass.</p> / Thesis / Master of Science (MSc)

<p> A unified approach, employing effective phonon frequency distributions, is used to investigate effects of phonon anisotropy in the hcp metals.</p> <p> Phonon information is included by means of empirical force constant models, and pseudopotentials are used to describe the electron-ion interaction.</p> <p> Zinc and thallium superconducting gaps are determined as a function of position on the Fermi surface. The gap anisotropy is used to calculate thermodynamic properties.</p> <p> The normal state electron-phonon mass enhancement and the imaginary part of the electron self-energy are calculated as a function of temperature and Fermi surface position. Anisotropic transport scattering times are defined, calculated and used to obtain the polycrystalline and single crystal resistivities. Comparison is made with resistivities obtained by the variational approach.</p> / Thesis / Doctor of Philosophy (PhD)

Thesis advisor: David Broido / Despite its deceptive simplicity and because of its scientific and technological importance, bcc Fe is still the subject of research and debate. We develop an ab initio theoretical framework and apply it to calculate temperature-dependent phonon modes and magnetic interaction parameters in bcc Fe. This framework incorporates realistic thermal disorder in a coupled spin-lattice system. Thermal spin-lattice coupling is found to significantly renormalize the phonon modes and magnetic interaction strength, resulting in significant temperature-dependencies. A method for treating magnetic systems of unknown entropy is developed and applied to calculate phonon modes and investigate the anomalous thermal expansion of the classical invar alloy, Fe0.65Ni0.35. Results over the temperature range 50K to room temperature are consistent with the observed low thermal expansion of this material. Excellent agreement with measured data is achieved for calculated phonon modes in both bcc Fe and the invar alloy. / Thesis (PhD) — Boston College, 2020. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

<p dir="ltr">First-principles method is a powerful approach to study atomic scale physics. With its introduction into thermal transport community, the \textit{ab initio} description of quantized lattice vibrations, phonons, achieved great success in predicting thermal transport properties in the past decade. Though such method is well established, recent theoretical and experimental efforts uncovered new physics and raised new challenges to our community. In particular, high-order phonon anharmonicity, which was assumed to be negligible, shows great impact on thermal transport. Highly nonequilibrium electron and phonon transport occurs in emerging materials with nonuniform temperature field and the equilibrium assumption is no longer valid. Finite temperature effect is found to change the potential landscape even in systems that are quite harmonic, and the previous quasi-harmonic approximation fails. These physical understandings are also closely related to applications that are being extensively studied today: high thermal conductivity materials in thermal management, hot electrons phenomenon in thermal photovoltaic, high temperature radiative properties in thermal barrier coatings, etc.</p><p><br></p><p dir="ltr">In this Dissertation, we seek to establish new physical understanding in thermal transport by studying four-phonon scattering, phonon nonequilibrium behavior, phonon renormalization scheme and their interplay in a wide range of solid state systems. For the benefit of the community, we develop an efficient open-source computational program, \textsc{FourPhonon}, and keep updating its core features to drive sustained scientific innovations. This program is capable of calculating phonon-phonon scattering rates up to the fourth-order and the lattice thermal conductivity of solids ($\kappa$).</p><p><br></p><p dir="ltr">The Raman peak position and linewidth provide insight into phonon anharmonicity and electron-phonon interactions in materials. For monolayer graphene, prior first-principles calculations have yielded decreasing linewidth with increasing temperature, which is opposite to measurement results. Here, we explicitly consider four-phonon anharmonicity, phonon renormalization, and electron-phonon coupling, and find all to be important to successfully explain both the $G$ peak frequency shift and linewidths in suspended graphene sample over a wide temperature range. Four-phonon scattering contributes a prominent linewidth that increases with temperature， while temperature dependence from electron-phonon interactions is found to be reversed above a doping threshold ($\hbar\omega_G/2$, with $\omega_G$ being the frequency of the $G$ phonon).</p><p><br></p><p dir="ltr">While the Raman spectra concerns one particular optical phonon mode, we move to consider $\kappa$ that is determined by full phonon spectrum. The thermal conductivity of monolayer graphene is widely believed to surpass that of diamond even for few-micron size samples and was proposed to diverge with system size. Here, we predict the thermal conductivity from first principles by considering four-phonon scattering, phonon renormalization, an exact solution to phonon Boltzmann transport equation (PBTE), and an unprecedented sampling grid. We show that at room temperature the thermal conductivity saturates at 10~$\rm\upmu m$ size and above and converges to 1300~W/(m$\cdot$K), which is lower than that of diamond. This indicates that four-phonon scattering overall contributes 57\% to the total thermal resistance and becomes the leading phonon scattering mechanism over three-phonon scattering. On the contrary, considering three-phonon scattering only yields higher-than-diamond values and divergence with size due to the momentum-conserving normal processes of flexural phonons.</p><p><br></p><p dir="ltr">Higher-order phonon scattering affects heat conduction and thermal radiation at high temperature to a larger degree than at room temperature. We establish a computational framework to compute temperature-dependent full spectrum optical properties and high temperature $\kappa$ of ceramics materials. From ultraviolet to mid-infrared region, light-matter interaction mechanisms in semiconductors progressively shift from electronic transitions to phononic resonances and are affected by temperature. Here, we present a parallel temperature-dependent treatment of both electrons and phonons entirely from first principles, enabling the prediction of full-spectrum optical responses. At elevated temperatures, \textit{ab initio} molecular dynamics (AIMD) is employed to find thermal perturbations to electronic structures and construct effective force constants describing potential landscape. Four-phonon scattering and phonon renormalization are included in an integrated manner in this approach. As a prototype ceramic material, cerium dioxide (CeO$_2$) is considered. Our first-principles calculated refractive index of CeO$_2$ agrees well with measured data from literature and temperature-dependent ellipsometer experiment.</p><p><br></p><p dir="ltr">The lattice thermal conductivity ($\kappa$) of two ceramic materials, CeO$_2$ and magnesium oxide (MgO), is then computed up to 1500~K using first principles and the PBTE with the same level of physics, and compared to time-domain thermoreflectance (TDTR) measurements up to 800~K. Our calculated thermal conductivities from the PBTE agree well with literature and our TDTR measurements. Other predicted thermal properties including thermal expansion, frequency shift, and phonon linewidth also compare well with available experimental data. Our results show that high temperature softens phonon frequency and reduces four-phonon scattering strength in both ceramics. The temperature scaling law of $\kappa$ is $\sim T^{-1}$ for three-phonon scattering only and remains the same after phonon renormalization. This scaling for three- plus four-phonon scattering is $\sim T^{-1.2}$ but is weakened to $\sim T^{-1}$ by phonon renormalization. This indicates that four-phonon scattering can play an important role in systems where measured $\kappa$ decays with temperature as $\sim T^{-1}$, which was conventionally attributed to three-phonon only. Compared to MgO, we find that CeO$_2$ has weaker four-phonon effect and renormalization greatly reduces its four-phonon scattering rates.</p><p> </p><p dir="ltr">Phonon-phonon scattering, together with electron-phonon coupling, can often show strong selectivity and drive system out of thermal equilibrium. Measurements and a previous multitemperature model (MTM) resolving phonon temperatures at the polarization level have uncovered remarkable nonequilibrium among different phonon polarizations in laser irradiated graphene and metals. Here, we develop a semiconductor-specific MTM (SC-MTM) by including electron-hole pair generation, diffusion, and recombination, and show that a conventional phonon polarization-level model does not yield observable polarization-based nonequilibrium in laser-irradiated molybdenum disulfide (MoS$_2$). In contrast, appreciable nonequilibrium is predicted between zone-center optical phonons and the other modes. The momentum-based nonequilibrium ratio is found to increase with decreasing laser spot size and interaction with a substrate. This finding is relevant to the understanding of the energy relaxation process in two-dimensional optoelectronic devices and Raman measurements of thermal transport. </p><p><br></p><p dir="ltr">In summary, this Dissertation leverages first-principles method to explore thermal transport in emerging materials with a focus on high-order phonon scattering, phonon nonequilibrium behavior, and phonon renormalization. We reveal the importance of these effects in various phenomena including thermal conductivity, optical properties, Raman thermometry and thermal radiation control. </p>

The ability of uniquely functional thermoelectric materials to convert waste heat directly into electricity is critical considering the global energy economy. Profitable, energy-efficient thermoelectrics possess thermoelectric figures of merit ZT ≥ 1. We examined the effect of metal nanoparticle – oxide film interfaces on the thermal conductivity κ and Seebeck coefficient α in bilayer and multilayer thin film oxide thermoelectrics in an effort to improve the dimensionless figure of merit ZT. Since a thermoelectric's figure of merit ZT is inversely proportional to κ and directly proportional to α, reducing κ and increasing α are key strategies to optimize ZT. We aim to reduce κ by phonon scattering due to the inclusion of metal nanoparticles in the bulk of thermoelectric thin films deposited by Pulsed Laser Deposition. XRD, AFM, XPS, and TEM analyses were carried out for structural and compositional characterization. The electrical conductivities of the samples were measured by a four-point probe apparatus. The Seebeck coefficients were measured in-plane, varying the temperature from 100K to 310K. The thermal conductivities were measured at room temperature using Time Domain Thermoreflectance. / Master of Science

Les phonons mous et le couplage électron-phonon sont considérés comme responsables d’un grand nombre de transition de phase. Pour en comprendre complétement les mécanismes, il est nécessaire d’étudier à la fois les modifications structurales, les changements de configuration électronique et les dynamiques de réseau cristallin. De toute évidence, cela représente une charge de travail expérimental et théorique considérable, voire même hors d’atteinte.Néanmoins, il est parfois possible d’introduire certaines simplifications et d’ainsi rendre une telle étude réalisable. C’est le cas pour les deux systèmes au cœur de ce travail de thèse, pour lesquels la transition de phase peut être diviser en deux instabilités : l’une est structurale, intrinsèque aux éléments constitutifs du système et l’autre, superposée, provient de la configuration électronique. L’interaction entre ces instabilités est illustrée à travers l’exemple de deux systèmes à priori hétérogènes, la famille des bronzes monophosphate de tungstène d’une part et l’antimoine d’autre part, qui révèleront finalement posséder des similarités inattendues. La combinaison des techniques de diffusion diffuse et de diffusion inélastique de rayons X permet des observations qualitatives et une meilleure compréhension de la situation pour les deux systèmes.Les bronzes monophosphate de tungstène font partie de la famille des oxydes quasi-2D, (PO2)4(WO3)2m, qui ont la particularité d’être sujet à des instabilités de type onde de densité de charges (ODC). Ces bronzes sont constitués d’une structure de perovskite vide composée par des couches octaédriques (WO3)2m. L’épaisseur de chacune de ces couches est définie par la valeur de m, qui mène ainsi à différents types de phase d’ODC. Le cas du terme m=2 a aussi été étudié car le fait que les chaînes zig-zag y soient isolées conduit à une instabilité quasi-1D. La présence d’une phase d’ODC a été découverte à TC=270K avec q=0.25b*. Cette phase est engendrée par le mouvement à corps rigide, plus exactement, par les basculements corrélés des octaèdres. Pour les autres termes (m=6,7 et 8), l’instabilité structurale a une origine différente et est liée à l’agencement en couches de WO3, plus particulièrement aux déplacements corrélés des chaînes W-O-W-O. Ces derniers sont la cause d’une forte diffusion diffuse sur des plans spécifiques, résultant de la présence de phonons ’relativement’ mous localisés dans la même région. Ensuite, l’emboitement de la surface de Fermi quasi-2D est à l’origine de l’ancrage du vecteur de modulation sur une valeur spécifique de transfert de moment, définit par l’interaction de deux instabilités, structurale et électronique. De façon remarquable, l’amplitude des déplacements des atomes de tungstène dans le terme m=8 est beaucoup plus élevée que dans le m=6.L’antimoine à température ambiante possède une structure rhomboédrique, dérivant d’une légère distorsion de la structure cubique primitive (CP) par transition de Peierls. Sous pression, la distorsion se réduit sans toutefois disparaître complétement, puisque l’antimoine se transforme dans un premier temps en une série de structures complexes, pour finalement adopter celle possédant la plus grande symétrie, la structure cubique centrée (CC). De la même façon que pour les bronzes, les caractéristiques de la diffusion diffuse ainsi que, dans une certaine mesure, les particularités de la dynamique du réseau rhomboédrique, s’expliquent à travers de l’instabilité du réseau cubique primitif. Cette dernière est liée aux déplacements corrélés dans les chaînes avec direction pseudo-cubique <100>. En outre, les détails de la transition de phase peuvent être explicités par l’association de l’analyse des vecteurs critiques de la transformation CC-CP avec les résultats expérimentaux obtenus sur la dépendance en pression de l’énergie des phonons. / A large number of phase transitions can be interpreted as being driven by phonon softening and/or electron-phonon coupling. Thus, a full mechanistic description requires the understanding of structural transformation, changes in electronic structure and lattice dynamics. All together this represents an enormous, for many cases unrealisable, experimental and theoretical effort.However, with the introduction of appropriate assumptions the problem may be simplified. Here we concentrate on two systems, where the interpretation of the phase transition may be split into an intrinsic instability of the building blocks combined with a superimposed electronic instability. We illustrate the interplay between the framework and electron-phonon-related instabilities using the seemingly heterogeneous examples of phosphate tungsten bronzes and elementary antimony. Based on the combined results from diffuse and inelastic X-ray scattering, we propose for the two systems a picture that explains the experimental observations. The similarities found between these two systems are deemed to be rather surprising.Monophosphate tungsten bronzes are a family of quasi-2D-oxides, (PO2)4(WO3)2m, that exhibits charge density wave (CDW) instability. They contain empty perovskite WO3 slabs with varying thickness between different members, characterised by the $m$ value. This thickness defines the sequence of charge density wave phases that appear on cooling. The degenerate case of $m$=2, presenting a quasi-1D instability, was explored since the WO3-octahedra zig-zag chain is isolated. A CDW phase (TC=270K and q=0.25b*) is found to be linked to a rigid-body motion, precisely, to a correlation in the tilting of the octahedra. For the others studied members, as m=6,7 and 8, we found another kind of structural instability. In this case the origin comes from the WO$_3$ slabs framework, realised as correlated displacements of tungsten atoms along the octahedral 4-fold axis direction (W-O-W-O direction). This leads to a strong x-ray diffuse scattering localised in specific planes, linked to relatively soft phonons modes. Specific Fermi surface nesting, close to the 2D case, gives rise to a freezing of the modulations at the specific momentum transfer, defined by the interplay of two instabilities, the structural and electronic one. Remarkably, the displacements of W for m=8 are much superior than in m=6.Elemental antimony at ambient condition has an A7 rhombohedral structure, obtained by small distortion from primitive cubic (PC) lattice through a Peierls transition. Under pressure, the distortion is reduced, but remains finite, as antimony transforms through a series of highly complex structures, before adopting as last the highest-symmetry body-centred cubic (BCC) phase. The main diffuse scattering features and to some extent the peculiarities in the lattice dynamics of the A7 phase – as above - can be explained by the instability of the primitive cubic network with respect to correlated displacements along the chains with <100> pseudo-cubic directions. Analysis of critical vectors for the BCC-PC transformation together with experimentally obtained phonon-energies pressure dependence provides further insights into the details of the phase transformation.

L'objectif de cette thèse est de caractériser la résistance thermique de contact au niveau de deux interfaces bien distinctes. La première est une interface physique entre le Silicium(111) et l'Hélium-4 superfluide. La résistance thermique de contact est alors mesurée expérimentalement pour des températures allant 0.3K à 2.0K et en variant la pression depuis la pression de vapeur saturante jusqu'à la pression de solidification de l'Hélium-4 (i.e. 25bars). L'analyse des résultats expérimentaux par le modèle d'Adamenko et Fuks montre la prédominance de la nano-rugosité de surface dans la transmission de la chaleur à l'interface entre ces deux matériaux. Lors de la solidification de l'Hélium-4, une transition du premier ordre dans la résistance thermique est mise en évidence. La deuxième interface étudiée est une forte constriction créée par une jonction de taille micrométrique entre deux membranes suspendues. Sans discontinuité de matériaux, les simulations numériques Monte-Carlo montrent la présence d'une résistance thermique de contact entre la membrane et l'entrée de la jonction dans le régime de diffusion des phonons les parois du système. Les simulations permettent alors d'explorer les effets des dimensions de la jonction ainsi que de la rugosité de surface des micro-structures bidimensionnelles et tridimensionnelles. / This thesis aims at characterizing the thermal contact resistance at two interfaces of different nature. The first is a physical interface between Silicon(111) and superfluid Helium-4. The thermal contact resistance is evaluated experimentally for temperatures between 0.3K and 2.0K while varying pressure from the saturated vapor pressure to the Helium-4 solidification pressure (i.e. 25bars). Experimental results, analysed with Adamenko and Fuks model, show that nanoscale surface roughness governs heat transmission at this interface. Furthermore, a first order transition in the thermal contact resistance is revealed due to Helium-4 solidification. The second studied interface is an abrupt constriction created by a micro-junction between two suspended membranes. Even though there is no material discontinuity, Monte-Carlo numerical simulations show the existence of a thermal contact resistance between the membrane and the entrance of the junction. Using simulations we explore the effects of geometry and nanoscale surface roughness in bidimensional and tridimensional micro-structure.

Understanding thermal transport in nanoscale is important for developing nanostructured thermolelectric materials and for heat management in nanoelectronic devices. This dissertation is devoted to understand thermal transport through SiGe based superlattices. First, we systematically studied the cross-plane thermal conductivity of SiGe superlattices by varying the thickness of Si(Ge) spacers thickness. The observed additive character of thermal resistance of the SiGe nanodot/planar layers allows us to engineer the thermal conductivity by varying the interface distance down to ~1.5 nm. Si-Ge intermixing driven by Ge surface segregation is crucial for achieving highly diffusive phonon scattering at the interfaces. By comparing the thermal conductivity of nanodot Ge/Si superlattices with variable nanodot density and superlattices with only wetting layers, we find that the effect of nanodots is comparable with that produced by planar wetting layers. This is attributed to the shallow morphology and further flattening of SiGe nanodots during overgrowth with Si. Finally, the experiments show that the interface effect on phonon transport can be weakened and even eliminated by reducing the interface distance or by enhancing Si-Ge intermixing around the interfaces by post-growth annealing. The results presented in this dissertation are expected to be relevant to applications requiring optimization of thermal transport for heat management and for the development of thermoelectric materials and devices based on superlattice structures. / Verständnis des thermischen Transport auf Nanoskala ist sowohl grundlegend für die Entwicklung nanostrukturierter Materialien, als auch für Temperaturkontrolle in nanoelektronischen Bauteilen. Diese Dissertation widmet sich der Erforschung des thermischen Transports durch SiGe basierenden Übergittern. Variationen, der Si(Ge) Schichtdicken, wurden zur systematischen Untersuchung der Normalkomponente zur Wachstumsrichtung der Wärmeleitfähigkeit, von SiGe Übergittern, genutzt. Die Beobachtung des additiven Charakters, des thermischen Widerstands, der SiGe Schichten, mit oder ohne Inselwachstum, ermöglicht die Erstellung von Strukturen mit bestimmter Wärmeleitfähigkeiten durch die Variation der Schichtdicken bis zu einer Minimaldistanz zweier Schichtübergänge von ~1.5nm. Die Ge Segregation führt zu einer Vermischung, von Si und Ge, welche eine essentielle Rolle zur diffusen Phononenstreuung spielt. Unsere Untersuchungen, von planaren Übergittern und Übergittern mit variabler Inseldichte, zeigen, dass Inseln und planare Schichten zu einer vergleichbaren Reduktion, der Wärmeleitfähigkeit, führen. Diese Beobachtung lässt sich, sowohl auf die flache Morphologie als auch die Abplattung der SiGe Inseln, aufgrund der Überwachsung mit Si, zurückführen. Die Experimente zeigen außerdem, dass sich der Barriereneffekt, der Schichtgrenzen, durch Reduktion der Schichtabstände und durch verstärkte Vermischung im Bereich der Schichtgrenzen, durch Erhitzung, eliminieren lässt. Die präsentierten Messungen sind sowohl, für die Entwicklung jener Bauteile, die eine Optimierung des thermischen Transports oder Temperaturmanagment erfordern, als auch von thermoelektrischen Matieralien und Bauteilen, basierend auf Übergittern, relevant.