Topology, Magnetism, and Spin-Orbit: A Band Structure Study of Semiconducting Nanodevices

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Topological insulators and topological superconductors are novel states of matter.
One of the most characteristic properties of topological insulators are the topologically protected edge states.
While the bulk of the material stays insulating, the edge-state conductance is quantized and topologically protected from backscattering.
In topological superconductors the edge states manifest themselves in the form of Majorana bound states: zero energy states inside the superconducting gap that are located at the end of a one-dimensional topological superconductor.

Chapter 2 of this thesis contains a detailed review and a discussion of k.p-theory.
The k.p-theory allows one to go beyond commonly used effective models and obtain much more detailed description of a semiconductor's band structure around its gap.
Topological insulators are often semiconductor-based and topological superconductors can be realized in a hybrid structure that consists of a semiconductor and a conventional superconductor.
Chapter 3 covers implementation details of the numerical methods used in this thesis.

Quantum spin Hall effect is one example of a topological insulator.
Band inversion in HgTe/CdTe or InAs/GaSb two-dimensional system leads to a topological phase that is characterized by topologically protected helical edge states which carry electric current with a quantized conductance.

It was believed that in-plane magnetic field would break time reversal symmetry, suppress the conductance and open an energy gap in the edge-state dispersion.
However, the experiment conducted by Du et al. reported robust helical edge transport in InAs/GaSb persisting up to a magnetic fields of 12 T.
In Chapter 4 of this thesis we show that the burying of a Dirac point in the valence band, a feature of the system dispersion revealed only by the detailed k.p-simulation, explains this unexpected observation.

Experimental group of L.P. Kouwenhoven investigated experimentally the details of spin-orbit interaction in InAs/GaSb system in both topological and trivial phases.
In Chapter 5 we connect the results of this experiment with our band structure calculations: in the topological phase, a quenching of the spin-splitting is observed and attributed to a crossing of spin bands, whereas in the trivial regime, the Rashba coefficient changes linearly with electric field and the linear Dresselhaus coefficient is constant.

In Chapter 6 we take a look into the spin texture of the inverted InAs/GaSb system close to the hybridization gap.
Transport measurements conducted by the experimental group of C.M. Marcus in Copenhagen revealed a giant spin-orbit splitting inherent to this system.
This leads to a unique situation in which the Fermi energy in InAs/GaSb crosses a single spin-resolved band, resulting in a full spin-orbit polarization.

In the last chapter of this thesis we focus on semiconducting nanowires with induced superconductivity that are considered to be a promising platform for hosting Majorana bound states.
In this theoretical research conducted together with physcists from ETH Zurich we show that the orbital contribution to the electron g-factor in higher subbands of small-effective-mass semiconducting nanowires can lead to the g-factors that are larger by an order of magnitude or more than a bulk value.