Rashba spin-orbit interaction in 1-dimensional nanowires

Abstract

Now that the first signatures of Majorana zero modes have been ob- served in experiments, a huge effort towards topological quantum com- putation is currently underway. Majorana zero modes can appear in nanowire systems, with their topological protection depending on the spin- orbit interaction strength. The spin-orbit interaction strength is therefore a crucial parameter in this experimental field. The largest contribution is expected to be Rashba spin-orbit interaction, which is the subject of this thesis. Spin orbit interaction in semiconducting systems is governed by sym- metry. Spin-orbit interaction is forbidden by symmetry if no additional symmetries are broken in [111] InSb nanowires. Upon reducing the spa- tial symmetry group, both Dresselhaus and Rashba spin-orbit interaction can emerge in the system. In this thesis a perturbative model for Rashba spin-orbit interaction, which occurs when an electric field reduces spatial symmetry, is developed to predict the interaction strength. This model is then compared to numerical simulations in quantum well systems per- formed with Mathematica and in nanowire simulations performed with Kwant. The model, incorporating the effect of changing geometric dimensions, subband number and the material, shows good agreement with the numer- ical simulations. Electrical fields resulting from Schrödinger-Poisson sim- ulations are then used to induce Rashba spin-orbit interaction in hexago- nal nanowire systems similar to experimental devices again matching the model. Finally, it is shown that the model can be used to calculate re- sults which are intractable to calculate via numerical simulations to find the effect of superconducting coverage of the nanowire on the spin-orbit interaction.