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Abstract
I theoretically studied the transport properties in 2D materials using quantum kinetic theory, especially in semiconductors and topological insulators. Firstly, I calculated the Coulomb drag in a magnetic doped 3D topological insulator. Coulomb drag is caused by the transfer of momentum between electrons in different layers due to the interlayer electron-electron scattering. I determined the role played by the anomalous Hall effect in Coulomb drag in doped massive Dirac fermion systems. The transverse response of the active layer is dominated by a topological term arising from the Berry curvature and the topological mechanism does not contribute to Coulomb drag, yet the longitudinal drag force in the passive layer gives rise to a transverse drag current. This anomalous Hall drag current is independent of the active-layer magnetization, a fact that can be verified experimentally. It depends non-monotonically on the passive-layer magnetization, exhibiting a peak that becomes more pronounced at low densities. Then I calculated the Rashba spin-orbit coupling correction to Hall coefficient in 2D hole systems up to the second order. In this work, I demonstrated that quantum spin dynamics induced by the spin-orbit interaction are directly observable in the classical charge transport. I determined the Hall coefficient RH in 2D hole systems at a low magnetic field and showed that it has a sizable spin-orbit contribution, which depends on the density ñ, is independent of temperature, is a strong function of the top gate electric field, and can reach 30% of the total. This work provides a general method for extracting the spin-orbit parameter from magnetotransport data, applicable even at higher temperatures where Shubnikov-de Haas oscillations and weak antilocalization are difficult to observe. Furthermore, using the analytical calculation and the classical Monte-Carlo simulation, I study the phase diagram of an interacting 2D electron gas with Rashba and Dresselhaus spin-orbit coupling. I found the out-of-plane spin-polarization phase is shrinking when Dresselhaus spin-orbit interaction is stronger and stronger. By mapping the interacting 2D electron gas with equal Rashba and Dresselhaus spin-orbit coupling system onto the 2D electron gas system, we found out-of-plane spin-polarization phase disappears and only in-plane spin polarization phase exists when rS>2.01. The possibilities of the experimental finding of the novel phases are also discussed here.