Electrical Transport in Dirac Systems Across Dimensions

In this thesis we study electrical transport in bilayer graphene with a gap tuned by a displacement field, and magnetic centrosymmetric Weyl semimetals. In the case of a magnetic Weyl semimetal we consider the possibility of controlling textures of the underlying magnetization with a transport current. We propose a novel way to achieve such control using the orbital angular momentum of quasiparticles in Weyl systems. We show that a transport current induces an axial orbital magnetization, as well as an axial current if the axial magnetization is non-uniform. Given that in Weyl semimetal axial currents are equivalent to spin polarization, such spin polarization can be used to exert torques on magnetization. We demonstrate feasibility of this proposal with numerical simulations of a magnetic vortex switching with a transport current in nanomagnets. We find that transport currents around $0.5\mathrm{Amp/\mu m^2}$ can switch chirality of a magnetic vortex in a magnet with dimensions of tens of nanometers. In the context of gapped bilayer graphene, we consider transport through gate-defined p-n junctions. It has been shown by Nandkishore and Levitov (Proc. Natl. Acad. Sci. 108, 14021 (2011)) that elastic tunneling through such junctions has oscillatory dependence on the gap. We consider the temperature dependence of the transport through the junctions, and show that it stems from phonon-assisted processes. The resultant junction conductance has depends linearly on temperature at moderate temperatures, and has monotonic dependence on the gap in the electronic spectrum.