La matière condensée moderne porte un intérêt particulier pour la classe de matériaux formée par les isolants topologiques. Ils sont différents des isolants typiques par leurs intéressantes propriétés quantiques; ils se comportent comme des isolants dans leur intérieur, mais contiennent des états conducteurs sur leur surface. On peut mieux comprendre le comportement de certains systèmes en matière condensée, tel que les chaînes de polyacétylène, en étudiant un système unidimensionnel simple : le modèle de Su-Schrieffer-Heeger (SSH). Le modèle SSH décrit des fermions sans spin sautant sur un réseau unidimensionnel où les amplitudes de saut alternent d’un site à l’autre. Ce modèle, bien que simpliste, expose les propriétés clés des isolants topologiques tel que les états délocalisés dans tout le réseau ainsi que les états exponentiellement localisés aux frontières du réseau. Dans ce projet, nous étudions le modèle SSH, mais en ajoutant un défaut central dans le réseau qu’on appelle un soliton. Dans notre cas, le soliton consiste en un site central donc les amplitudes de saut sont les mêmes d’un côté et de l’autre. Nous trouvons un ensemble de solutions complet incluant des états de basse énergie localisés aux frontières ainsi que des états de haute énergie localisés au soliton. / Topological insulators are a class of materials that have attracted much attention in modern condensed matter. They are different from typical insulators as they exhibit interesting quantum properties; they behave as insulators in their interior but have conducting states on their surface. We can better understand the properties of low dimensional condensed matter systems (like poly-acetylene chains) by studying a toy model known as the Su-Schrieffer-Heeger (SSH) Model. The SSH model describes spinless fermions hopping on a one-dimensional lattice with staggered hopping amplitudes. Such a toy model exhibits key properties of topological insulators, such as bulk states (delocalized states across the lattice) and edge states (exponentially localized states at the boundaries of the lattice). In this project, we study the SSH model with an added central defect to the chain, which we call a soliton. In our case, the soliton consists of a central site with the same hopping amplitude on either side. We study the impact of such a defect on the properties of the system; we find a complete set of solutions including near-zero-energy edge states as well as high-energy states localized at the soliton.

Mixed ionic and electronic conductor oxides, in particular La1-xSrxCoyFe1-yO3-d (LSCF), have been widely used as the cathode materials in solid oxide fuel cells for high-temperature energy applications. The focus of this thesis is primarily on constructing the instability phase diagram of Sr segregations on LSCF surfaces at the experimentally relevant temperatures and oxygen partial pressures using the first-principles density functional theory (DFT). A generic first-principles free-energy functional is developed to obtain the nonstoichiometric oxygen vacancy concentrations for the bulk and surface phases. These results agree well with the corresponding thermo-gravimetry measurements, and furthermore suggest that the oxygen vacancies are energetically stabilized at surfaces for all temperatures and oxygen partial pressures, while such surface stabilization effects become stronger at higher temperatures and lower oxygen partial pressures. Based on these nonstoichiometric oxygen vacancy predictions, we construct the free-energy phase diagrams of the Sr-segregation reaction as a function of temperature, oxygen partial pressure, and CO2 partial pressure for both the bulk and surface LSCF phases. Our results suggest that Sr segregations strongly accumulate towards the LSCF surface phase where the oxygen vacancy nonstoichiometries are abundant. Our results also indicate that the Sr segregation reactions are significantly enhanced at high temperatures, low oxygen partial pressures, and high CO2 partial pressures. The computed reaction temperature ranges are consistent with the total reflection X-ray fluorescence (TXRF) measurements.

Nous proposons, par voie théorique, une sonde ayant la capacité de détecter et de caractériser les états de surface d'une chaîne Su-Schrieffer-Heeger (SSH). Cette sonde consiste d’un qubit interagissant avec un environnement, et exploite le phénomène de la décohérence afin de retirer de l’information sur l’environnement. Une approximation de faible couplage permet de démontrer analytiquement que le taux de décohérence du qubit est proportionnel à la densité d’états locale de l’environnement. Dans le cas d’un environnement possédant des états discrets, une mesure de la densité d’états locale peut être équivalente à une mesure de l’amplitude d’un état, permettant donc une caractérisation spatiale des états de l’environnement. Un système tripartite consistant d'un qubit couplé à une chaîne SSH discrète muni de canaux conducteurs aux extrémités est étudié afin de valider l’utilité de la sonde pour inférer et caractériser les états de surface. L’espace des paramètres de la sonde est discuté en détail. En étudiant l’impact du couplage des canaux conducteurs, nous notons l’émergence d’états de type-surface sur des sites interdits ainsi que dans des phases topologiques ne supportant pas d’états de surface dans le modèle SSH isolé. Ces excitations, que nous appelons états fantômes, apparaissent dû à un décalage des frontières de la chaîne SSH. / We propose a novel probe with the ability to detect topological edge states in lowdimensional materials. This probe, consisting of a qubit interacting with a system of interest, utilizes the dynamics of decoherence to study the qubit’s environment. We show analytically that, under a weak-coupling approximation, the decoherence rate of the qubit is proportional to the local density of states of the environment. In studying environments featuring finite subsystems with discrete states, the local density of states mapped by the qubit probe can extract state amplitude profiles, resulting in a full spatial characterization of states. We explicitly study a tripartite system consisting of a qubit coupled to a finite SSH chain with conducting leads attached to each end and demonstrate the probe’s ability to infer the presence of, and characterize, edge states. The parameter space of the probe is studied. Notably, we show the lead coupling strength effectively shifts the SSH chain boundaries resulting in emergent edge-type states, dubbed ghost states, with support on sites which are forbidden in an isolated SSH chain for a given topological phase.

Nous considérons une chaîne de Su-Schrieffer-Heeger (SSH) à laquelle nous attachons une chaîne semi-infinie non dimérisée aux deux extrémités. Nous étudions l’effet d’un tel couplage sur les propriétés du modèle de SSH. En particulier, la représentation d’un tel système infini sous forme de système effectif fini nous permet d’examiner ses états de surface topologiques. Nous montrons que, comme ce à quoi on s’attendrait, les états de surface initiaux évoluent à mesure que le couplage entre les systèmes augmente. Alors que ce couplage augmente, deux phénomènes sont observés: d’un côté, ces états de surface disparaissent progressivement, et de l’autre côté, de nouveaux états de surface émergent. Ces nouveaux états, que nous appelons états fantômes, sont aussi des états de basse énergie. Une particularité surprenante de ceux-ci est qu’ils sont localisés sur une nouvelle interface: celle-ci est passée du premier (et dernier) site au deuxième (et avant-dernier) site, ce qui suggère que la topologie du système est fortement influencée par les chaînes semi-infinies. La topologie du système tripartite peut être classifiée selon trois régimes. Pour le régime de faible couplage, le système est dans une phase topologique bien définie; pour de grands couplages, il est dans sa phase opposée; pour le régime intermédiaire, sa nature topologique n’est pas encore bien comprise. / We consider a Su-Schrieffer-Heeger (SSH) chain to which we attach a semi-infinite undimerized chain (lead) to both ends. We study the effect of the openness of the SSH model on its properties. In particular, an accurate representation of the infinite system using an effective Hamiltonian allows us to examine its topological edge states. We show that, as one would expect, the initial edge states evolve as the coupling between the systems is increased. As this coupling grows, these states slowly vanish, while a new type of edge states emerge. These new states, which we refer to as ghost states, are also low-energy states. A surprising property of these states is that they are localized on a new interface: the interface has moved from the first (and last) site to the second (and second to last) site. This suggests that the topology of the system is strongly affected by the leads, with three regimes of behaviour. For very small coupling the system is in a well-defined topological phase; for very large coupling it is in the opposite phase; in the intermediate region, its topological nature is yet to be understood.

In this thesis we explore in particular the dynamics of a special type of quasi-particle in pi-conjugated materials termed polaron, the origin of which is intimately related to the strong interactions between the electronic and the vibrational degrees of freedom within these systems. In order to conduct such studies with the particular focus of each appended paper, we simultaneously solve the time-dependent Schrödinger equation and the lattice equation of motion with a three-dimensional extension of the famous Su-Schrieffer-Heeger (SSH) model Hamiltonian. In particular, we demonstrate in Paper I the applicability of the method to model transport dynamics in molecular crystals in a region were neither band theory nor perturbative treatments such as the Holstein model and extended Marcus theory apply. In Paper II we expand the model Hamiltonian to treat the revolution of phenylene rings around the sigma-bonds and demonstrate the great impact of stochastic ring torsion on the intra-chain mobility in conjugated polymers using poly[phenylene vinylene] (PPV) as a model system. Finally, in Paper III we go beyond the original purpose of the methodology and utilize its great flexibility to study radiationless relaxations of hot excitons. / Report code: LiU-TEK-LIC-2007:4.

<p>In this thesis we explore in particular the dynamics of a special type of quasi-particle in pi-conjugated materials termed polaron, the origin of which is intimately related to the strong interactions between the electronic and the vibrational degrees of freedom within these systems. In order to conduct such studies with the particular focus of each appended paper, we simultaneously solve the time-dependent Schrödinger equation and the lattice equation of motion with a three-dimensional extension of the famous Su-Schrieffer-Heeger (SSH) model Hamiltonian. In particular, we demonstrate in Paper I the applicability of the method to model transport dynamics in molecular crystals in a region were neither band theory nor perturbative treatments such as the Holstein model and extended Marcus theory apply. In Paper II we expand the model Hamiltonian to treat the revolution of phenylene rings around the sigma-bonds and demonstrate the great impact of stochastic ring torsion on the intra-chain mobility in conjugated polymers using poly[phenylene vinylene] (PPV) as a model system. Finally, in Paper III we go beyond the original purpose of the methodology and utilize its great flexibility to study radiationless relaxations of hot excitons.</p> / Report code: LiU-TEK-LIC-2007:4.

We studied the structural instabilities of one-dimensional (1D) and quasi-one-dimensional (Q1D) electron-phonon systems at low temperature through two models, SuSchrieffer-Heeger (SSH) and molecular crystal (CM) with and without spin. The phase diagrams are obtained using a Kadanoff-Wilson renormalization group approach (GR). For the 1D half-filled system the study of the frequency dependence of the electronic gap allowed us to connect continuously the two limits, adiabatic and non-adiabatic. The Peierls and Cooper channels interference and the quantum fluctuations reduce the gap. A regime change occurs when the frequency becomes of the order of mean field gap, marking a quantum-classical crossover that is the Kosterlitz-Thouless type. At this level, the effective coupling behaves in power law function on frequency. For the case with spin, a gapped Peierls state is maintained in the non-adiabatic limit, while for the case without spin, the system transits to ungapped disordered state, namely the Luttinger liquid stat (LL). For the SSH model without spin, the GR confirms the existence of a threshold phonon coupling beyond which the gap is restored. The study of the rigidities of the two models without spin allowed us to trace the main features of the LL state predicted by the bosonization method. The study of the Holstein-Hubbard model has allowed us not only to reproduce the phase diagrams already obtained by the Monte Carlo method, but to highlight two additional phases, namely, free fermions phase and the bond charge-density-wave phase. We have extended this study to the quarter-filled Q1D Peierls systems at finite temperature. Within the SSH model, an unconventional superconducting phase with spin singlet symmetry SS-s emerges at low temperature when the deviation to the perfect nesting of the Fermi surface is strong enough. Peierls-SS transition is characterized by the presence of a quantum critical point at low frequency and by a power law behavior of the transition temperature as a function of frequency with an exponent identical to one of 1D system. This exponent which universality has been verified contrasts with the BCS result. Coulomb interactions have been introduced through the study of the extended SSH-Hubbard model. The extension of this work to half-filled SSH and CM cases was also performed.

We study unconventional superconductivity in two-dimensional systems. Unbiased numerical calculations within two-dimensional Hubbard models have found no evidence for long-range superconducting order. Most of the two-dimensional theories suggest that the superconducting state can be obtained by destabilizing an antiferromagnetic or spin-liquid insulating state. An antiferromagnet is a half-filled system because each site has one electron or hole. However, in anisotropic triangular lattices, numerical calculation finds pairing enhancement at quarter-filling but no long-range superconducting order. Many organic superconductors are dimerized in nature. Such a dimer lattice is effectively half-filled because each dimer has one electron or hole. Some theories suggest that magnetic fluctuation in such a system can give superconductivity. However, at zero temperature, we performed density matrix renormalization group (DMRG) calculations in such a system, and we find no superconducting long-range order. We also find that the antiferromagnetic order is not necessary to get a superconducting state. Failure in explaining superconductivity in two-dimensional systems suggests that only repulsive interactions between electrons are not sufficient, and other interactions are required. The most likely candidate is the electron-phonon interaction. However, existing theories of superconductivity emphasize either electron-electron or electron-phonon interactions, each of which tends to cancel the effect of the other. We present direct evidence from quantum Monte Carlo calculations of cooperative, as opposed to competing, effects of electron-electron and electron-phonon interactions within the frustrated Hubbard Hamiltonian, uniquely at the band-filling of one-quarter. Bond-coupled phonons and the onsite Hubbard U cooperatively reinforce d-wave superconducting pair-pair correlations at this filling while competing with one another at all other densities. Our work further gives new insight into how intertwined charge-order and superconductivity appear in real materials.