Topology and applications of 2D Dirac and semi-Dirac materials

Two dimensional (2D) Dirac materials, such as graphene, hold promise of being useful in energy storage, and thus have merged as candidates that are worth exploring through the last couple of decades. In this chapter, we mainly focus on three aspects of these materials, namely, the electronic properties, via computing the band structure, the topological properties through the topological invariants, and the prospects of these 2D materials for spintronic applications, via studying the spin polarized transport. All of these properties are correlated, and hence warrant a thorough discussion. Further, in order to ascertain whether a band deformation induces noticeable effects on the electronic, topological and spintronic properties, we have considered a 2D semi-Dirac system, that does not have Dirac cones, however the conduction and the valence bands touch at an intermediate to the Dirac points in the Brillouin zone. From our studies, we infer that the behaviour of these semi-Dirac systems is quite distinct from their Dirac counterpart. Finally, in order to have noticeable spin polarized transport, we use heavy adatoms (such as, Au) on the graphene matrix which enhances the spin–orbit coupling, and thereby propose a mechanism that will ramify on the spintronic applications.