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
The phenomenon of high temperature (high-Tc) superconductivity, although discovered 20 years ago, still remains mysterious. In conventional superconductors, the supercurrent is carried by a gas of... Show moreThe phenomenon of high temperature (high-Tc) superconductivity, although discovered 20 years ago, still remains mysterious. In conventional superconductors, the supercurrent is carried by a gas of weakly interacting pairs of electrons (Cooper pairs). Experiments suggest that the electron in high-Tc superconductors are at the verge of solidifying into a stripe-crystal, invalidating the conventional `gaseous' picture. Inspired by this problem, the work in this thesis offers an opposite paradigm for high-Tc superconductivity, based on the notion of the `almost ordered' superconductor. Formulating the problem in the field theoretical language of quantum elasticity and utilizing the duality transformation, quantum phases of matter are constructed which are as close as possible to a solid, which can be considered as quantum version of liquid crystals. We find that these ``dual shear superconductors'' are also genuine electromagnetic superconductors with properties which are however subtly different from conventional superconductors and invoke rather unconventional experiments: quantum-liquid crystalline orders, oscillations of magnetic screening currents, overscreening of Coulomb force, and especially a new collective mode found in the dynamical electromagnetic response. Show less