Mechanical metamaterials are man-made materials which derive their unusual properties from their structure rather than their composition. Their structure, or architecture, often consists of... Show moreMechanical metamaterials are man-made materials which derive their unusual properties from their structure rather than their composition. Their structure, or architecture, often consists of periodically arranged building blocks whose mutual interactions realize unusual properties. In this thesis, we investigate the role of two aspects of mechanical metamaterials: The beam ligaments and the microstructures of hinging squares. Both aspects play an important role in mechanical metamaterials, but give rise simultaneously to several open problems. First, although the mechanical behaviour of slender beam ligaments is well understood, the finite-width ligaments that often occur in mechanical metamaterials lead to new physics; wide beams exhibit a negative post-buckling stiffness, characterized by a decreasing force after buckling, which is not well understood. Second, fully filled microstructures of hinging squares constitute an auxetic mechanism, but possible new zero modes derived from (diluted) microstructures with missing squares remain largely unexplored. How does the number of zero modes increases in such diluted systems, can we count these additional modes, and what is their spatial structure? Here we address these open problems, thereby providing the necessary understanding to fully leverage the characteristics of wide beam ligaments and diluted collections of hinging squares for the design of novel mechanical functionalities. Show less
The central topic in this thesis is the effect of topological defects in two distinct types of condensed matter systems. The first type consists of graphene and topological insulators. By... Show moreThe central topic in this thesis is the effect of topological defects in two distinct types of condensed matter systems. The first type consists of graphene and topological insulators. By studying the long-range effect of lattice defects (dislocations and disclinations) we find that the graphene electrons mimic fundamental Dirac electrons in spaces with curvature and torsion. We show that these long-range effects influence interferometric transport measurements: (i) Emphasizing the importance of electron dephasing in graphene; (ii) Enabling a characterization of neutral Majorana states, which are important for quantum computation applications, and conjectured to exist in topological insulators. Considering also the microscopic structure of graphene dislocations, we interpret local tunneling experiments on graphite grain boundaries. The second type of systems we study are the high temperature cuprate superconductors, where the strongly interacting electrons lead to coexisting symmetry breaking orders in the pseudogap phase. We observe and describe the interplay of nematic (orientational) and stripe (translational) orderings in local tunneling experiments, with stripe dislocations playing the key role. We also describe the observed phonon anomaly in cuprates through the effect of metallic stripes. Show less
