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In the past few years the field of topological materials has uncovered many materials which have topological bands: bands which cannot be continuable to a trivial, “atomic” limit, and which are characterized by an integer topological index. We will review the progress in the field and the new types of topological behavior that is expected from the many predictions in the field. We will also show how, using a new theory called Topological Quantum Chemistry, thousands of new topological materials can be predicted, classified and discovered. The result is that- so far - out of 30000 materials investigated - at least 30 percent of all materials in nature can be classified as topological. One ultimately aims for a full classification of topological materials, available on database websites such as www.topologicalquantumchemistry.com

For the purpose of identifying novel absorber materials based on experimental or computational material screening, it is useful to identify the basic ingredients required to make a good solar cell out of the combination of different absorber and contact materials. Figures of merit are needed that quantify whether a certain material is likely to perform well as a solar cell. To answer the question, which parameters are most important, we look into the key properties of good solar cells such as high absorption coefficient, mobility and charge carrier lifetime and study their interdependences and how they determine the efficiency at different thickness of the solar cell. Finally, we study some microscopic parameters such as the effective mass or electron-phonon coupling in a device to identify key microscopic properties that are likely to lead to a combination of high absorption, high mobilities and long lifetimes and thereby high photovoltaic efficiencies

The seminar summarizes three recent studies (1,2,3) since that share some common elements: they concern porous materials and the method used is NMR spectroscopy. Yet, the aims differ. In the first study (1), the unknown is the pore structure. In particular, pore structure in hydrogels is difficult to access as water cannot be removed without affecting the pores and in the presence of water the well-honed gas sorption and mercury porosimetries just do not work. The method we invented to remedy this situation is called size-exclusion quantification (SEQ) NMR and it can be seen as the multiplexed analogue of inverse size exclusion chromatography. In effect, we sample by diffusion NMR the size distribution in a polydisperse polymer solution before and after it had been equilibrated with a porous matrix. Size-dependent polymer ingress reveals the pore structure. The method has several advantages over possible alternatives, not least its speed. In the second study (2), we sample the self-diffusion of neat water and other molecules like dimethyl sulfoxide (DMSO) and their mixtures by NMR diffusion experiments for those fluids imbibed into controlled pore glasses (CPG, pore size range 7.5 to 73 nm). Their highly interconnected structure is scaled by pore size and exhibits pore topology independent of size. Relative to the respective diffusion coefficients obtained in bulk phases, we observe a reduction in the diffusion coefficient that is independent of pore size for the larger pores and becomes stronger toward the smaller pores. Geometric tortuosity governs the behavior at larger pore sizes, while the interaction with pore walls becomes the dominant factor toward smaller pore diameters. Deviation from the trends predicted by the popular Renkin equation and variants (4) indicates that the interaction with the pore wall is not just a simple steric one. In the third study (3), the porous material is hydrated cellulose. In that matrix, we identify by using 2H MAS NMR two different groups of water molecules being in slow exchange with each other. Water molecules in one of the groups exhibit anisotropic molecular motions with a high order parameter. Based on, among other things, the observed behavior with increasing vapor pressure, we argue that this water is an integral structural element of the cellulose fibril, that itself is an aggregate of the basic units, the cellulose nanofibrils.

We use a local magnetic imaging technique, scanning SQUID microscopy, to map the spatial distribution of electronic states near surfaces and interfaces. We track conductivity, superconductivity and magnetism in systems undergoing phase transitions, where the local picture is particularly meaningful. I will describe two measurements: At the superconductor-insulator transition in NbTiN we map superconducting fluctuations and detect a non-trivial behavior near the quantum critical point. Near the metal to insulator transition at the 2D LaAlO3/SrTiO3 interface, we find that the conduction landscape changes dramatically and identify the way different types of defects control the behavior.