Electronic structure of the quantum wires with spin-orbit interactions under the influence of in-plane magnetic fields

In this thesis, we have made a theoretical investigation of electronic ground state structure of a parabolically confined quantum wire subjected to an in-plane magnetic field, including spin-orbit interactions and exchange-correlation effects. In this study, the effect of generally off-neglected cubic Dresselhaus spin-orbit interaction has also been taken into account. The energy dispersion has been numerically calculated in a wide range of linear electron densities. The effects of the exchange-correlation interaction have been investigated within the noncollinear local-spin density approximation. A self-consistent solution of the Kohn-Sham equations has been implemented. The energy eigenvalues and the eigenfunctions of the system have been obtained from numerical solutions of Schrödinger equation. One-dimensional finite elements method based on Galerkin procedure has been used.It has been seen that the structure of energy subband depends strongly on the strength of spin-orbit interaction, the magnitude and the orientation angle of magnetic field and the exchange-correlation effects. It has been shown that in the presence of an external magnetic field the interplay of different types of spin-orbit interaction and Zeeman effect leads to complicated and intriguing energy dispersion for different spin branches. Including exchange-correlation energy has been caused anomalous plateaus which could play an important role for understanding of the conductance. We have seen that our results are compatible with the studies in the litterateur. We have found different results for exchange-correlation effect especially in low density limits that could be due to the use of different parametrization for exchange-correlation energy functional.