| dc.description.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. | |
