@@ -16,14 +16,14 @@ One promising approach to create Majoranas relies on a theoretical prediction th
Whenever the device parameters are in the right regime, the Majoranas should appear at the edges of the nanowire.
\co{We fix the model by including several important physical effects, and use adaptive sampling to improve our results.}
The experimental results diverge from the predictions of the minimal theoretical model due to it missing several physical phenomena.
The experimental results diverge from the predictions made by the minimal theoretical model due to it missing several physical phenomena.
To model the Majorana nanowires more realistically, we include previously neglected physical effects by considering the full three-dimensional geometry of the nanowire.
These more complex models exceed the reach of analytical theories and require intensive numerical calculations instead.
To cope with the increasing computational complexity, we developed adaptive parallel sampling algorithms (discussed in the Ch.~\ref{ch:adaptive}), which in our research typically sped up simulations by at least an order of magnitude.
Our approach is illustrated on the cover of this thesis, which shows the conductance of a Majorana nanowire with the interesting regions sampled more accurately.
Using the improved models and efficient sampling, allowed us to unveil potential challenges that were not present in the simple model.
\co{Including the orbital effect leads us to serveral important considerations.}
\co{Including the orbital effect leads us to several important considerations.}
In Ch.~\ref{ch:orbitalfield}, we study how the electrons are influenced by the magnetic field while moving across the nanowire---an effect completely neglected in the minimal model.
We observe that this effect has a stronger impact on the Majoranas than what is included in the minimal model.
Specifically, we observe that the protection of Majoranas nearly vanishes when the electron density in the nanowire is high, and find that the magnetic field has to be precisely aligned with the nanowire to guarantee the presence of Majoranas.
