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: This piece of work is twofold. First, the time evolution of wave-packets in 2D systems is analyzed by the Split-Operator technique in three different scenarios: in multilayer phosphorene, the transient oscillations in the time-dependent average of position and momentum were observed due to the zitterbewegung effect, and the wave packet propagates non-uniformly along the space deforming itself into an elliptical shape. These results were corroborated by the Green’s function formalism except for large values of the wave-vector and long times; in 2D semiconductor quantum wires (QWs) with anisotropic effective masses and different angle orientations with respect to the anisotropic axis. We have shown that the greater this angle, the smaller is the energy levels spacing implying in an increase of the accessible electronic states. Additionally, for non-null magnetic field, the quantum Hall edge states are significantly affected by the edge orientation. In the anisotropic case damped oscillations in the average values of velocity in both x and y directions where obtained. Theses oscillations are originated by the QW geometry but also from subwavepackets with different momentum orientations, whereas for isotropic QWs the wavepacket disperses without splitting; in the third scenario the split-operator technique was used to study the Landau levels, the wave packet trajectories and velocities of electrons in graphene at low-energy regime described by a modified Dirac equation where the momentum-operator is written in a generalized form as result of applying the position-dependent translation operator formalism (PDTO). In the second part of this thesis, the electronic and tunneling properties of α − T3 lattices were studied. Electrons in these lattices behave analogous to integer-spin Dirac Fermions. The presence of a third atomic site in the unit cell leads to a flat band in the energy spectrum, providing unique electronic and tunneling properties. The presence of a super-periodic potential and the inclusion of symmetry-breaking terms results in deviations of the atomic equivalence between the atomic sites affecting the Dirac points and the band-gap. Small deviations in the equivalence between the atomic sites and the number of barriers change the transmission properties in these lattices. Additionally, new tunneling regions are possible by adjusting the symmetry between the atomic sites and affect the omnidirectional total transmission called super-Klein tunneling observed in these lattices. We compare those results to the tunneling probabilities through regions where the energy spectrum changes from linear with a middle flat band to a hyperbolic dispersion.

Abstract: Superconductivity is one of the most important discoveries of the last century. With many applications in physics, engineering, and technology, superconductors are crucial to our way of living. Several material and engineering issues however prevent their widespread usage in everyday life. Comprehensive studies are being directed at these materials and their properties to come up with new technologies that will address these challenges and enhance their superconductive capabilities. In this context, numerical modeling plays an important role in the search of new solutions to existing material and engineering issues. The time-dependent Ginzburg-Landau (TDGL) theory is a powerful predictive tool for modeling the macroscopic behavior of superconductors. However most of the numerical algorithms developed so far are incapable of describing many basic properties of real superconducting devices, and are too slow on current hardware for large-scale numerical simulations necessary for their accurate description. Therefore, the purpose of this thesis is to develop high-performing numerical solutions that can correctly describe material features to be used as modeling tools of laboratory experiments. Some important innovations introduced in this work include the numerical modeling of nonrectangular geometrical shapes with complex electrical and insulating components, the inclusion of dynamic heating of the material, and the description of different types of material inhomogeneities. These encompass the principal features necessary for a complete description of the superconductive physics in real material samples. In this thesis a numerical solution is developed for modeling superconducting thin films and used to study the superconductive properties of three experimental configurations: the dynamics of vortex matter in a Corbino disk, the motion of ultrafast vortices in an hourglass-shaped microbridge, and the photon detection process in a meander-patterned nanowire. Moreover, a numerical solution is developed for modeling three-dimensional superconductors which are studied here for the first time in the type-I superconducting regime. These numerical algorithms are optimized to exploit the computational horsepower of graphics processing units (GPUs) and multicore central-processing unit (CPU) clusters such that they can achieve high-performance and be used to model large-scale problems previously impossible on conventional machines. Several computational tools are also designed to assist with the modeling of superconducting devices. These include a numerical library of the TDGL equations, a novel mechanism for the generation of complex geometries, a closed-form solver to conduct numerical simulations, and a graphics user interface (GUI) to visualize the dynamic behavior of superconductors. The contributions in this thesis ultimately push the boundaries on what is possible in state-of-the-art numerical modeling of superconductivity.

Abstract: abstract not available

Abstract: Polarons are quasiparticles emerging in materials from the interaction of extra charge carriers with the surrounding atomic lattice. They appear in a wide va- riety of compounds and can have a profound impact on their properties, making the concept of a polaron a central and ubiquitous topic in material science. Al- though the concept is known for about 75 years, the origin of polarons is not yet fully elucidated. This thesis focuses on WO 3 as a well-known prototypical system for studying polarons, which inherent polaronic nature is linked to its remark- able electrical and chromic properties. The primary objective of this research is to provide a comprehensive atomistic description and understanding of polaron formation in WO 3 using first-principles density functional theory (DFT) calcula- tions. Additionally, the investigation explores the interactions between polarons and the possibility of bipolaron formation. Following a systematic strategy, we first extensively analyze the dielectric and lattice dynamical properties of WO 3 in both the room-temperature P 2 1 /n and ground-state P 2 1 /c phases. Our specific focus is on characterizing the zone-center phonons, which serve as the founda- tion for identifying the phonon modes involved in the polaron formation and charge localization process. Subsequently, we examine the impact of structural distortions on the electronic structure of WO 3 to elucidate the interplay between structural distortions and electronic properties, thereby laying the groundwork for understanding electron-phonon couplings. By incorporating these critical fac- tors, we address our primary research goals. The most common explanation for the polaron formation is associated with the electrostatic screening of the extra charge by the polarizable lattice. Here, we show that, even in ionic crystals, this is not necessarily the case. We demonstrate that polarons in this compound arise primarily from non-polar atomic distortions. We then unveil that this unexpected behavior originates from the undoing of distortive atomic motions, which lowers the bandgap. As such, we coin the name of anti-distortive polaron and validate its appearance through a simple quantum-dot model, in which charge localization is the result of balancing structural, electronic, and confinement energy costs. Then, we also study the polaron-polaron interaction and present the formation of the antiferromagnetic W 4+ bipolaronic state with relatively large formation energy. Our analysis of the W 4+ bipolaronic distortions on the global structure reveals the same behavior as in experiments where the highly distorted monoclinic phase transforms into a tetragonal phase as a function of doping. Additionally, leveraging our previous findings on asymmetric polaronic distortion and examin- ing different merging orientations, we stabilize the antiferromagnetic W 5+ -W 5+ bipolaronic state with an energy lower than the W 4+ state. This thesis clari- fies the formation of unusual medium-size 2D polarons and bipolarons in WO3,which might be relevant to the whole family of ABO 3 perovskites, to which WO 3 is closely related. The simplicity of the concept provides also obvious guidelines for tracking similar behavior in other families of compounds.

Abstract: It is standard practice in virtual reality applications to synthesize binaural audio based on a discrete set of directionally-dependent head-related impulse responses (HRIRs). This set of HRIRs is often time-aligned in a pre-processing step, to allow for high-fidelity interpolation between HRIRs corresponding with neighbouring directions. The fidelity of this operation depends on the similarity of neighbouring aligned HRIRs. The pairwise quality of similarity makes it a difficult criterion to optimize globally and consequently one often resorts to alignment methods based on a specific feature that can be extracted for each HRIR separately, e.g., the first-onset of the peak or the group delay. However, such proxies for similarity are very sensitive to noise and therefore require a high signal-to-noise ratio, which makes them less suitable for processing HRIRs acquired outside an anechoic room. In this paper, we advance a novel alignment method, which maximizes the similarity – defined as the correlation between the full-length HRIRs – between neighbouring aligned HRIRs for all directions at once. We show that this correlation-based alignment procedure outperforms the first-onset alignment with regards to the fidelity of the spherical harmonics representation of both the spectral and interaural time difference (ITD) information, when tested on the KEMAR HRIR and six human HRIRs. Finally, we show that the correlation-based alignment is more robust to noise.