Charge Transport in Two Dimensional Systems With Arbitrary Rashba and Dresselhaus Interactions

In this thesis we discuss two different transport phenomena that occur in a two-dimensional electron system endowed with linear Rashba and Dresselhaus spin-orbit interactions of arbitrary values. First, in a semiclassical formalism we calculate the non-linear charge currents that appear in response to the simultaneous application of in-plane electric and magnetic fields. Working in a rotated system of coordinates that introduces $\alpha \pm \beta$ as effective couplings on perpendicular directions, we formulate a transport theory that relies on a second order distribution function derived in a local energy approximation and on chiral dependent relaxation times to show that the currents exist for all values of the chemical potential even in the absence of additional interactions of higher order in the electron momentum, such as the cubic Dresselhaus. For a spin-orbit energy larger than the Zeeman splitting, the non-linear currents that flow perpendicular to the direction of the magnetic field are found to be proportional with $\alpha\pm \beta$ when $\mathbf{E}\perp \mathbf{B}$ and with $(\alpha \pm \beta)^2/(\alpha \mp \beta)$ when $\mathbf{E}\parallel \mathbf{B}$. Further, for a given direction of the electric field, the non-linear longitudinal current, parallel with $\mathbf{E}$, and the planar-Hall current perpendicular to $\mathbf{E}$ are not proportional with each other when $\alpha\beta \neq 0$. We complete the analysis by looking at the high magnetic field limit, when the Zeeman interaction is larger than the spin-orbit coupling. In this case, we show that a spin-polarized system does not support non-linear charge currents since the available phase space is reduced to an almost nil interval. Then, we evaluate the quantum corrections to the linear conductivity in a tubular nanowire in the presence of an axial magnetic field. In the large radius limit, we approximate the electron gas as a two dimensional system wrapped around the wire core and for this model we use the standard localization formalism to determine the changes induced in the magnetoconductivity by the spin-orbit coupling.