Abstract: The pursuit for the next generation of nanodevices made scientists focus the attention to two dimensional materials. Experimental works of two dimensional materials are hardly free of structural defects, which, in turn, modify drastically the physical properties of its defect-free counterpart. In this work the presence of structural defects is study in two different materials. First, the dependence of the Hall, bend and longitudinal resistances to a perpendicular magnetic field and to vacancy defects in a four-terminal phosphorene single layer Hall bar is investigated. A tight-binding model in combination with the Landauer-Büttiker formalism is used to calculate the energy spectrum, the lead-to-lead transmissions, and the Hall and bend resistances of the system. It is shown that the terminals with zigzag edge orientation are responsible for the absence of quantized plateaus in the Hall resistance and peaks in the longitudinal resistance. A negative bend resistance in the ballistic regime is found due to the presence of high- and low- energy transport modes in the armchair and zigzag terminals, respectively. The system density of states, with single vacancy defects, shows that the presence of in-gap states is proportional to the number of vacancies. Quantized plateaus in the Hall resistance are only formed in a sufficiently clean system. The effects of different kinds of vacancies in the regime where the quantized plateaus are destroyed and a diffusive regime appears in the bend resistance are investigated. Next, we explore effects due to point defect clustering on the electronic and transport properties of bilayer graphene nanoribbons, for AA and AB stacking and zigzag and armchair boundaries, by means of the tight-binding approach and scattering matrix formalism. Evidence of vacancy concentration signatures exhibiting a maximum amplitude and an universality regardless of the system size, stacking and boundary types, in the density of states around the zero-energy level are observed. Our results are explained via the coalescence analysis of the strong sizeable vacancy clustering effect in the system and the breaking of inversion symmetry at high vacancy densities, demonstrating a similar density of states for two equivalent degrees of concentration disorder, below and above the maximum value.

Abstract: In this thesis we investigate the emergence of new phenomena in multigap superconductors and multicomponent Ginzburg-Landau theories in the presence of intraband and cross-band pairing. The first part contains a review of emergent phenomena in superconductors with only intraband pairing, in particular the mechanism behind gap resonances which are accompanied by Higgs and Leggett modes. Then we study the gap resonances induced by two-dimensional quantum confinement and describe its spatial profile using the Bogoliubov-de Gennes equations. In the second part we describe the conditions where the cross-band pair formation is feasible. Using the formalism of Green functions we obtain the equations governing the interplay between intraband and cross-band pairing. Also, we derived the Ginzburg-Landau equations considering both intraband and cross-band pairing. Finally, we describe the crossover between the intraband-dominated and crossband-dominated regimes. These two are delimited by a tendency towards a gapless state. When a magnetic field is applied close to the gapless state, we found new arrangements of vortices like square lattices, stripes, labyrinths or of vortex clusters. The experimental signatures and consequences of crosspairing are discussed for MgB2 and Ba0.6K0.4Fe2As2.