Quantum Field Theory of Material Properties: Its Application to Models of Rashba Spin Splitting

In this thesis, we argue that microscopic field theories, which as such are already scientifically established, have emerged as a new paradigm in materials physics. We hence seek to elaborate on such field theories which underlie modern ab initio calculations, and we apply them to the bismuth tellurohalides (BiTeX with X = I, Br, Cl) as a prototypical class of spin-based materials. For this purpose, we begin by constructing tight-binding models which approximately describe the spin-split conduction bands of BiTeI. Following this, we derive the theory of temperature Green functions systematically from their fundamental equations of motion. This in turn enables us to develop a combined functional renormalization and mean-field approach which is suitable for application to multiband models. For the Rashba model including an attractive, local interaction, this approach yields an unconventional superconducting phase with a singlet gap function and a mixed singlet-triplet order parameter. We further investigate the unusual electromagnetic response of BiTeI, which is caused by the Rashba spin splitting and which includes, in particular, an orbital paramagnetism. Finally, we conclude by summarizing the Functional Approach to electrodynamics of media as a microscopic field theory of electromagnetic material properties which sits in accordance with ab initio physics