Abstract
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 edgestate 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 onedimensional topological superconductor.
Chapter 2 of this thesis contains a detailed review and a discussion of k.ptheory.
The k.ptheory 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 semiconductorbased 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 twodimensional 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 inplane magnetic field would break time reversal symmetry, suppress the conductance and open an energy gap in the edgestate 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.psimulation, explains this unexpected observation.
Experimental group of L.P. Kouwenhoven investigated experimentally the details of spinorbit 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 spinsplitting 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 spinorbit splitting inherent to this system.
This leads to a unique situation in which the Fermi energy in InAs/GaSb crosses a single spinresolved band, resulting in a full spinorbit 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 gfactor in higher subbands of smalleffectivemass semiconducting nanowires can lead to the gfactors that are larger by an order of magnitude or more than a bulk value.
One of the most characteristic properties of topological insulators are the topologically protected edge states.
While the bulk of the material stays insulating, the edgestate 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 onedimensional topological superconductor.
Chapter 2 of this thesis contains a detailed review and a discussion of k.ptheory.
The k.ptheory 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 semiconductorbased 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 twodimensional 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 inplane magnetic field would break time reversal symmetry, suppress the conductance and open an energy gap in the edgestate 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.psimulation, explains this unexpected observation.
Experimental group of L.P. Kouwenhoven investigated experimentally the details of spinorbit 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 spinsplitting 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 spinorbit splitting inherent to this system.
This leads to a unique situation in which the Fermi energy in InAs/GaSb crosses a single spinresolved band, resulting in a full spinorbit 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 gfactor in higher subbands of smalleffectivemass semiconducting nanowires can lead to the gfactors that are larger by an order of magnitude or more than a bulk value.
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  23 May 2018 
Electronic ISBNs  9789085933441 
DOIs  
Publication status  Published  2018 
Keywords
 topology
 magnetism
 spinorbit
 k.p theory
 discretization