Dirac malzemeleri ile nanoelektronik ve spintronik: grafen, topolojik yalıtkan ve weyl yarı metallerinin özellikleri

Dirac materials are a class of condensed matter systems in which the relativistic Dirac equation describes the dynamics of charge carriers. In this thesis, we investigate various quantum transport phenomena in these exotic materials, particularly graphene, topological insulators, and Weyl semimetals, as well as propose spintronics and valleytronics applications. We also focus on spin-orbit coupling induced by adatoms on graphene, and we explore how valley and spin degrees of freedom interact with each other in the presence of deposited adatoms. We hence investigate methods to convert valley currents into extractable and measurable spin currents, which is pivotal in designing spin- and valleytronics devices. Furthermore, we study current-induced spin accumulation effect at the surfaces of three-dimensional topological insulators (3DTIs), and we show how to extract these spins into topologically trivial materials commonly used in electronic devices. We find that, unlike the corresponding conventional effect in two-dimensional electron gases, the mixing of the electron and hole degrees of freedom at the TI surface allows for additional methods of spin manipulation. In particular, we expose a way to use electrical gate potentials to locally manipulate spins in regions smaller than the spin precession length, the conventional length over which the spins can be manipulated. We devise a new scheme for spin manipulation based on the admixture of the electron and hole degrees of freedom at TI surfaces. Next, we study hyperfine interactions between nuclear spins and itinerant electrons at 3DTIs surfaces. We find that hyperfine interactions induce elastic backscattering processes through spin-flip transitions between the surface states at each plane of a 3DTI in addition to forward scattering through intra-transitions within the surface states. Moreover, we find an additional forward scattering processes for the edges of crystals that are not in the growth direction. Finally, we study Weyl heterostructures between opposing chiralities which can be obtained by shifting the nodes with specific chirality in opposing directions in momentum space. We find a new magnetoelectric effect in Weyl semimetal junctions, similar to the giant magnetoresistance effect in ferromagnets. We thus introduce a new chirality-valve device and investigate the robustness of this effect against the presence of nonmagnetic and magnetic impurities in junctions based on Weyl semimetals.