In my thesis I study Majorana fermions from three different perspectives. The first one corresponds to non-interacting Majorana fermions that, however, pose non-trivial topological properties. The... Show moreIn my thesis I study Majorana fermions from three different perspectives. The first one corresponds to non-interacting Majorana fermions that, however, pose non-trivial topological properties. The second one corresponds to strongly interacting Majoranas and the third to relic neutrinos. No one knows for sure if they have Dirac or Majorana nature. 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
