This dissertation aims to study and understand relevant issues related to the electronic, spin and valley transport in two-dimensional Dirac systems for different given physical settings. In summary, four key findings are achieved.
First, studying persistent currents in confined chaotic Dirac fermion systems with a ring geometry and an applied Aharonov-Bohm flux, unusual whispering-gallery modes with edge-dependent currents and spin polarization are identified. They can survive for highly asymmetric rings that host fully developed classical chaos. By sustaining robust persistent currents, these modes can be utilized to form a robust relativistic quantum two-level system.
Second, the quantized topological edge states in confined massive Dirac fermion systems exhibiting a remarkable reverse Stark effect in response to an applied electric field, and an electrically or optically controllable spin switching behavior are uncovered.
Third, novel wave scattering and transport in Dirac-like pseudospin-1 systems are reported. (a), for small scatterer size, a surprising revival resonant scattering with a peculiar boundary trapping by forming unusual vortices is uncovered. Intriguingly, it can persist in arbitrarily weak scatterer strength regime, which underlies a superscattering behavior beyond the conventional scenario. (b), for larger size, a perfect caustic phenomenon arises as a manifestation of the super-Klein tunneling effect. (c), in the far-field, an unexpected isotropic transport emerges at low energies.
Fourth, a geometric valley Hall effect (gVHE) originated from fractional singular Berry flux is revealed. It is shown that gVHE possesses a nonlinear dependence on the Berry flux with asymmetrical resonance features and can be considerably enhanced by electrically controllable resonant valley skew scattering. With the gVHE, efficient valley filtering can arise and these phenomena are robust against thermal fluctuations and disorder averaging.