Topological band theory and Majorana fermions : With focus on self-consistent lattice models

Sammanfattning: One of the most central concepts in condensed matter physics is the electronic band structure. Although band theory was established more than 80 years ago, recent developments have led to new insights that are formulated in the framework of topological band theory. In this thesis a subset of topological band theory is presented, with particular focus on topological supercon- ductors and accompanying Majorana fermions. While simple models are used to introduce basic concepts, a physically more realistic model is also studied intensely in the papers. Through self- consistent tight-binding calculations it is confirmed that Majorana fermions appear in vortex cores and at wire end points when the superconductor is in the topologically non-trivial phase. Many other properties such as the topological invariant, experimental signatures in the local density of states and spectral function, unconventional and odd-frequency pairing, the precense of spin-polarized currents and spin-polarization of the Majorana fermions, and a local π-phase shift in the order parameter at magnetic impurities are also investigated.