The work presented in this thesis concerns the dynamics in π-conjugated hydrocarbon systems. Due to the molecular bonding structure of these systems there exists a coupling between the electronic system and the phonons of the lattice. If this interaction, which is referred to as the electron-phonon (e-ph) coupling, is sufficiently strong it may cause externally introduced charge carriers to self-localize in a polarization cloud of lattice distortions. These quasi-particles are, if singly charged, termed polarons, the localization length of which, aside from the e-ph coupling strength, also depend upon the structural and energetic disorder of the system. In disordered systems localization is strong and transport is facilitated by nonadiabatic hopping of charge carriers from one localized state to the next, whereas in well-ordered systems, where extended states are formed, adiabatic transport models apply.Despite great academic efforts a unified model for charge transport in π-conjugated systems is still lacking and further investigations are necessary to uncover the basic physics at hand in these systems. The call for such efforts has been the main guidelines for the work presented in this thesis and are related to the topics of papers I-IV. In order to capture the coupled electron-lattice dynamics, we use a methodological approach where we obtain the time-dependence of the electronic degrees of freedom from the solutions to the time-dependent Schrödinger equation and determine the ionic motion in the evolving charge density distribution by simultaneously solving the lattice equation of motion within the potential field of the ions. The Hamiltonian used to describe the system is derived from an extension of the famous Su-Schrieffer-Heeger (SSH) model extended to three-dimensional systems.In papers I-III we explore the impact of phenylene ring torsion on delocalization and transport properties in poly(para-phenylene vinylene) (PPV). The physics that we are particularly interested in relates to the reduced electron transfer integral strength across the interconnection between the phenylene rings and the vinylene groups upon ring torsion. Keeping this in mind, we demonstrate in paper I the impact of static ring torsion on intrachain mobility and provide a detailed analysis of the influence of the potential barriers (due to consecutive ring torsion) on the nature of charge carrier propagation. In paper II we extend our initial approach to include also the dynamics of ring torsion. We show that without any externally applied electric field, this type of dynamics is the dominant property controlling intrachain propagation, but that when an external electric field is applied, charge carriers may traverse the potential barriers through a process that involves nonadiabatic effects and a temporary delocalization of the polaron state. Finally, in paper III we study the impact of the lattice dynamics on the electron localization properties in PPV and show that the phenylene ring torsion modes couples strongly to the electronic wave function which gives rise to electron localization at room temperature.In papers IV and V we focus on the dynamics of molecular crystals using a stack of pentacene molecules in the single crystal configuration as a model system, but study, in paper IV, the transport as a function of the intermolecular interaction strength, J. We observe a smooth transition from a nonadiabatic to an adiabatic polaron drift process over the regime 20<J<120 meV. For intermolecular interaction strengths above J≈120 meV the polaron is no longer stable and transport becomes band-like. In paper V, finally, we study the internal conversion processes in these systems, which is the dominant relaxation channel from higher lying states. This process involves the transfer of energy from the electronic system to the lattice. Our results show that this process is strongly nonadiabatic and that the relaxation time associated with large energy excitations is limited by transitions made between states of different bands. / I dagens samhälle är elektroniken ett allt viktigare och större inslag i vår vardag. Vi ser på TV, talar i mobiltelefoner, och arbetar på datorer. I hjärtat av denna teknologi finner vi diskreta komponenter och integrerade kretsar utformade främst för att styra strömmen av elektroner genom halvledande material. Traditionellt sett har kisel eller olika former av legeringar använts som det aktiva materialet i dessa komponenter och kretsar, men under de senaste 20 åren har såväl transistorer som solceller och lysdioder realiserats där det aktiva materialet är organiskt, d.v.s., kolbaserat.Vi befinner oss för tillfället mitt uppe i det kommersiella genombrottet för organisk elektronik. Redan idag säljs många MP3-spelare och mobiltelefoner med små skärmar där varje pixelelementen utgörs av organiska ljusemitterande dioder (OLEDs), men teknologin håller redan på att introduceras i mer storskaliga produkter som datorskärmar och TV-apparater som därigenom skulle kunna göras energieffektivare, tunnare, flexiblare och på sikt också billigare. Andra tekniska tillämpningsområden för organisk elektronik som förutspås en lysande framtid är RFID-märkning, organiska solceller, och elektronik tryckt på papper, men även smarta textiler och bioelektronik har stor utvecklingspotential.Den kanske största utmaningen kvarstår dock, att skapa elektroniska kretsar och komponenter uppbyggda kring enskilda molekyler, s.k. molekylär elektronik. Mycket snart närmar vi oss den fysikaliska gränsen för hur små komponenter som vi kan realisera med traditionella icke-organiska material som kisel och en stor drivkraft bakom forskningen på halvledande organiska material har varit just visionen om molekylär elektronik som inte är mer än några miljondelars milimeter stora. För detta ändamål krävs en mycket nogrann kontroll av tillverkningsprocesserna liksom en detaljförståelse för hur molekylerna leder ström och hur denna förmåga kan manipuleras för att realisera såväl traditionella som nya komponenter.I denna avhandling presenteras en översikt av den fysik som möjliggör ledningsförmåga hos särskilda klasser av organiska material, s.k. π-konjugerade system, samt de forskningsresultat som utgör mitt bidrag till denna disciplin. En av utmaningarna på området är den komplexitet som de organiska materialen erbjuder: laddningsprocesserna påverkas nämligen av en rad olika faktorer såsom laddningstäthet, temperatur, pålagd spänning, samt molekylernas former och inbördes struktur. I detta arbete har jag utifrån en vidareutveckling av existerande modeller genom numeriska datasimuleringar undersökt effekten av de senare tre faktorerna på elektronstrukturen, laddnigstransporten och energidissipation i denna klass av material. / Center of Organic Electronics (COE)

The study of topological phases in condensed matter physics has seen remarkable advancements, primarily focusing on systems with a well-defined bulk and boundary. However, the emergence of topological phenomena on self-similar systems, characterized by the absence of a clear distinction between bulk and boundary, presents a fascinating challenge. This thesis focuses on the topological phases on self-similar systems, shedding light on their unique properties through the lens of adiabatic charge pumping. We observe that the spectral flow in these systems exhibits striking qualitative distinctions from that of translationally invariant non-interacting systems subjected to a perpendicular magnetic field. We show that the instantaneous eigenspectra can be used to understand the quantization of the charge pumped over a cycle, and hence to understand the topological character of the system. Furthermore, we establish a correspondence between the local contributions to the Hall conductivity and the spectral flow of edge-like states. We also find that the edge-like states can be approximated as eigenstates of the discrete angular-momentum operator, with their chiral characteristics stemming from this unique perspective. We also investigate the effect of local structure on the topological phases on self-similar structures embedded in two dimensions. We study a geometry dependent model on two self-similar structures having different coordination numbers, constructed from the Sierpinski gasket. For different non-spatial symmetries present in the system, we numerically study and compare the phases on both structures. We characterize these phases by the localization properties of the single-particle states, their robustness to disorder, and by using a real-space topological index. We find that both structures host topologically nontrivial phases and the phase diagrams are different on the two structures, emphasizing the interplay between non-spatial symmetries and the local structure of the self-similar unit in determining topological phases. Furthermore, we demonstrate the presence of topologically ordered chiral spin liquid on fractals by extending the Kitaev model to the Sierpinski Gasket. We show a way to perform the Jordan-Wigner transformation to make this model exactly solvable on the Sierpinski Gasket. This system exhibits a fractal density of states for Majorana modes and showcases a transition from a gapped to a gapless phase. Notably, the gapped phase features symmetry-protected Majorana corner modes, while the gapless phase harbors robust zero-energy and low-energy self-similar Majorana edge-like modes. We also study the vortex excitations, characterized by remarkable localization properties even in small fractal generations. These localized excitations exhibit anyonic behavior, with preliminary calculations hinting at their fundamental differences from Ising anyons observed in the Kitaev model on a honeycomb lattice.