Coupled charge-spin transport and spin-orbit phenomena in 2D Dirac materials

The advent of 2D layered materials, boasting high-crystal quality and rich electronic properties, has provided a unique arena for exploring exotic condensed-matter phenomena, including the emergence of ultra-relativistic Dirac fermions in graphene, topological insulating phases in WS_{2}, long-lived excitons in group-VI dichalcogenides and unconventional superconductivity in twisted bilayer graphene. The enhancement of spin-orbit effects in heterointerfaces, built from the vertical stacking of different 2D layers, is recently attracting much attention. A series of crucial experiments have demonstrated the induction of strong spin-orbit effects in graphene sheets proximity-coupled to group-VI dichalcogenides. Owing to a combination of room-temperature spin transport over long distances and gate-tunable spin orbit interactions, such systems hold great promise for all-electrical generation and manipulation of spin currents, which is key to the realisation of the next generation of spintronics devices. To fully unlock the potential of 2D Dirac materials for spintronics, these recent experimental findings call for the formulation of a solid theoretical framework which can underpin them, but also-and more importantly-predict novel phenomena. This thesis aims to develop the foundations of such a framework, with a focus on spin dynamics and coupled charge-spin transport in 2D Dirac materials with strong proximity-induced interactions. A number of key results are established. We show that charge-to-spin interconversion in 2D Dirac materials can be understood in terms of exact symmetry relations (Ward identities). Depending on the specific spin-orbit interactions present in a 2D Dirac system, the symmetry relations dictate the relative contributions of the so-called spin-Hall effect (SHE) and inverse spin Galvanic effect (ISGE). In particular, for materials with interfacial breaking of mirror symmetry and unbroken (broken) sublattice symmetry, the SHE contribution is suppressed (sizable), whereas the ISGE contribution stays typically large and robust in both scenarios. The extrinsic SHE has its origin in a peculiar skew scattering mechanism-emerging from the non-coplanar spin texture of spin-orbit-coupled Dirac bands-and can be tuned by a gate voltage. We propose a diagrammatic approach to obtain the coupled charge/spin diffusion equations, as well as the spin relaxation times and the charge-to-spin interconversion rates. We supplement this study with a density matrix-based approach, allowing one to gain more insight into the delicate competition of the various energy scales present in realistic systems, and to calculate the spin relaxation time anisotropy of experimental relevance. Finally, we examine ferromagnetic 2D Dirac materials, through a unified theory of charge carrier transport combining semiclassical and fully-quantum mechanical approaches. We identify an experimental signature that characterises the crossover from the nonquantised anomalous Hall effect to the topologically-nontrivial quantum anomalous Hall effect, which can help future experimental efforts to unlock this fascinating quantum state of matter with Dirac fermions.