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Item Open Access Accurate electronic free energies of the 3d, 4d, and 5d transition metals at high temperatures(2017) Zhang, Xi; Grabowski, Blazej; Körmann, Fritz; Freysoldt, Christoph; Neugebauer, JörgFree energies of bulk materials are nowadays routinely computed by density functional theory. In particular for metals, electronic excitations can significantly contribute to the free energy. For an ideal static lattice, this contribution can be obtained at low computational cost, e.g., from the electronic density of states derived at T = 0 K or by utilizing the Sommerfeld approximation. The error introduced by these approximations at elevated temperatures is rarely known. The error arising from the ideal lattice approximation is likewise unexplored but computationally much more challenging to overcome. In order to shed light on these issues we have computed the electronic free energies for all 3d, 4d, and 5d transition elements on the ideal lattices of the bcc, fcc, and hcp structures using finite-temperature density-functional theory. For a subset of elements we have explored the impact of explicit thermal vibrations on the electronic free energies by using ab initio molecular dynamics simulations. We provide an analysis of the observed chemical trends in terms of the electronic density of states and the canonical d band model and quantify the errors in the approximate methods. The electronic contribution to the heat capacities and the corresponding errors due to the different approximations are studied as well.Item Open Access Polaritontransformation der gelben Magnetoexzitonen in Kupferoxydul(2017) Ertl, JanWird im Halbleiter ein Elektron aus dem Valenzband in das Leitungsband angeregt, so bleibt ein Loch im Valenzband zurück. Gebundene Elektronen-Loch-Paare, die sogenannten Exzitonen, können im Festkörper durch Absorption eines Photons angeregt werden. Trifft Licht auf den Festkörper so kann es mit den Exzitonen in Wechselwirkung treten. Diese Kopplung von Licht und Exzitonen wird durch ein neues Quasiteilchen, das Exziton-Polariton, beschrieben. Zur Beschreibung der Exziton-Polaritonen wird dann ein Basiswechsel, die Polaritontransformation, durchgeführt. In dieser Arbeit wird zur Beschreibung der Exzitonen ein wasserstoffartiges Modell angenommen. Damit wird die gelbe Exzitonenserie in Kupferoxydul für verschiedene Magnetfelder in der Coulomb-Sturm'schen Basis ausgewertet. Anschließend wird die Polaritontransformation durchgeführt und der Einfluss von verschiedenen Parametern auf die Polaritondispersion untersucht.Item Open Access Lithium intercalation in bilayer graphene devices(2017) Kühne, Matthias; Smet, Jurgen H. (Dr.)The subject of this dissertation is the experimental investigation of Lithium intercalation in bilayer graphene devices. An on-chip electrochemical cell architecture is implemented, consisting of a solidified polymer electrolyte confined at and covering only a small part of the perimeter of a patterned bilayer graphene device. This allows the operation of bilayer graphene as a single-phase mixed (electronic and ionic) conductor. Magnetotransport techniques as well as Raman spectroscopy are deployed to reveal Li intercalation-induced changes in situ during repeated lithiation and delithiation cycles. In combination with a range of ex situ characterization methods, evidence for efficient Li diffusion between graphene sheets only is brought forward. From a numerical analysis of time-dependent in situ Hall measurements, Lithium diffusion in bilayer graphene is revealed be exceptionally fast.Item Open Access The superconductor-insulator-transition in the LaAlO3-SrTiO3 electron system : tunneling and field effect investigations(2017) Kürten, Lukas; Mannhart, Jochen (Prof. Dr.)The work described in this thesis investigated the superconductor-insulator- and BKT-transitions in a two-dimensional superconductor based on transition-metal oxides: the electron system at the LaAlO3-SrTiO3 interface. Thin films of insulating LaAlO3 grown onto insulating SrTiO3 substrates exhibit a two-dimensional electron system (2DES) with a superconducting ground state at the interface of the two materials. The ground state can be switched from superconducting to insulating behavior by application of a gate voltage. Therefore it is a useful tool for the investigation of these phase transitions. Additionally, LaAlO3-SrTiO3 exhibits a phase similar to the cuprate pseudogap phase in which electron transport is resistive, but a gap can be observed in the density of states in tunneling experimentswhich is not explicable by the standard BCS theory of superconductivity. The phase transitions were investigated by two complimentary pathways: by tunneling experiments on backgated samples and through the construction of superconducting transistors in which the electron system is influenced by the application of topgate voltages.Item Open Access PT-symmetric dipolar Bose-Einstein condensates : embedding in a Hermitian system and higher-order exceptional points(2017) Gutöhrlein, Robin; Main, Jörg (Prof. Dr.)Item Open Access Ablenk-Systeme für die Multi-Elektronenstrahllithografie auf Basis CMOS-kompatibler Fertigungsprozesse(2017) Jurisch, Michael; Burghartz, Joachim N. (Prof. Dr.-Ing.)Item Open Access Thermodynamic efficiency of learning a rule in neural networks(2017) Goldt, Sebastian; Seifert, UdoBiological systems have to build models from their sensory input data that allow them to efficiently process previously unseen inputs. Here, we study a neural network learning a binary classification rule for these inputs from examples provided by a teacher. We analyse the ability of the network to apply the rule to new inputs, that is to generalise from past experience. Using stochastic thermodynamics, we show that the thermodynamic costs of the learning process provide an upper bound on the amount of information that the network is able to learn from its teacher for both batch and online learning. This allows us to introduce a thermodynamic efficiency of learning. We analytically compute the dynamics and the efficiency of a noisy neural network performing online learning in the thermodynamic limit. In particular, we analyse three popular learning algorithms, namely Hebbian, Perceptron and AdaTron learning. Our work extends the methods of stochastic thermodynamics to a new type of learning problem and might form a suitable basis for investigating the thermodynamics of decision-making.Item Open Access Modell mit Mastergleichung zur Beschreibung der Exziton-Phonon-Wechselwirkung in Cu2O(2017) Rommel, PatricExzitonen in äußeren Feldern sind ein wertvolles Modellsystem, um theoretische Vorhersagen über eine Vielzahl verschiedener Effekte experimentell zugänglich zu machen und zu überprüfen. Wichtig ist hier in erster Linie der Einfluss der Bandstruktur, durch welchen sich wichtige Korrekturen im Vergleich zum wasserstoffartigen Modell ergeben. Sie bildet unter anderem die reduzierte Symmetrie im Kristallgitter ab. Andererseits gibt es im Festkörper neben den Exzitonen auch andere Quasiteilchen deren Effekte zu beachten sind. In dieser Arbeit soll es dabei um die Exziton-Phonon-Wechselwirkung und ihren Einfluss auf das Eigenwertspektrum der Exzitonen gehen.Item Open Access Efficient approach to compute melting properties fully from ab initio with application to Cu(2017) Zhu, Li-Fang; Grabowski, Blazej; Neugebauer, JörgApplying thermodynamic integration within an ab initio-based free-energy approach is a state-of-the-art method to calculate melting points of materials. However, the high computational cost and the reliance on a good reference system for calculating the liquid free energy have so far hindered a general application. To overcome these challenges, we propose the two-optimized references thermodynamic integration using Langevin dynamics (TOR-TILD) method in this work by extending the two-stage upsampled thermodynamic integration using Langevin dynamics (TU-TILD) method, which has been originally developed to obtain anharmonic free energies of solids, to the calculation of liquid free energies. The core idea of TOR-TILD is to fit two empirical potentials to the energies from density functional theory based molecular dynamics runs for the solid and the liquid phase and to use these potentials as reference systems for thermodynamic integration. Because the empirical potentials closely reproduce the ab initio system in the relevant part of the phase space the convergence of the thermodynamic integration is very rapid. Therefore, the proposed approach improves significantly the computational efficiency while preserving the required accuracy. As a test case, we apply TOR-TILD to fcc Cu computing not only the melting point but various other melting properties, such as the entropy and enthalpy of fusion and the volume change upon melting. The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional and the local-density approximation (LDA) are used. Using both functionals gives a reliable ab initio confidence interval for the melting point, the enthalpy of fusion, and entropy of fusion.Item Open Access Dynamik von PT-symmetrischen und symmetriebrechenden Zweimodenmodellen, eingebettet in ein zeitabhängiges Viermoden-Bose-Hubbard-System(2017) Mathea, TinaBose-Einstein-Kondensate mit ausgeglichenem Gewinn und Verlust in einer optischen Doppelmulde stellen einen möglichen Kandidaten für die experimentelle Realisierung von PT-Symmetrie dar. Dieses System kann im Mean-Field-Limit unter Verwendung komplexer Potentiale mithilfe einer Gross-Pitaevskii-Gleichung beschrieben werden, was einer nicht-hermiteschen Beschreibung entspricht. Durch Einbettung dieses Systems in ein optisches Viermuldenpotential mit zeitabhängigen Parametern können die PT-symmetrischen Zustände des nicht-hermiteschen Systems in den inneren Mulden des hermiteschen Viermuldensystems eingestellt werden. Somit stellt das zeitabhängige Viermuldensystem eine Möglichkeit der experimentellen Realisierung von PT-Symmetrie dar. Da in dem beschriebenen System Vielteilcheneffekte eine wichtige Rolle spielen, stellt sich die Frage, ob sich das Verhalten der PT-symmetrischen Zustände des offenen Quantensystems auch im Vielteilchensystem einstellen lässt. In der vorliegenden Arbeit wird gezeigt, dass es unter Verwendung entsprechender Zeitabhängigkeiten der Kontrollparameter und unreiner Anfangszustände (d.h. Zustände, die sich nicht als Produkt der Einteilchenzustände darstellen lassen) möglich ist, das Verhalten der PT-symmetrischen Zustände in der Einteilchendynamik des Vielteilchensystems zu realisieren. Dazu wird ein Verfahren entwickelt, wie sich passende Anfangszustände konstruieren lassen. Die Vielteilchenbeschreibung des Systems erfolgt dabei mit dem Bose-Hubbard-Modell und der Bogoliubov-Backreaction-Methode.