Abstract

Inelastic light scattering (ILS) is an important experimental technique that has helped characterize superconductors (SCs) and study their collective modes, whose proper accounting may give us hints on the superconducting pairing interactions and mechanisms. However, despite decades of efforts on modelling the fermionic contributions to the ILS response from different SCs, interpretations of experimental data remain loosely qualitative, as the models are applied in the isotropic Fermi-surface limit and usually consider decoupled energy bands, with the inclusion of pairing-interaction effects – essential to account for collective modes – being limited. In fact, most known SCs are multiband, with anisotropic Fermi surfaces having possibly non-trivial topologies. As these effects go mostly unaccounted for in ILS models, the interpretation of experimental data of more complex systems is hindered.

To help improve the interpretation of ILS data from SCs, in this thesis, we develop an encompassing theoretical framework to compute the non-resonant ILS response, in the presence of phase collective modes in any polarization channel, from fermionic degrees of freedom in two-dimensional multiband spin-singlet SCs with possibly non-trivial Fermi-surface topologies. Using a diagrammatic approach, we renormalize the ILS vertex with multiband pairing interactions and write a practical set of formulæ using the pairing-interaction eigenbasis. The framework allows us to compute the response from different systems more easily, whilst accounting for material-specific properties self-consistently.

With our framework, we analyse the line spectra of multiband systems having different ground states and Fermi surfaces, with our analyses showing that the ILS response is almost always composed of collective-mode induced features. We also demonstrate that the response from multiband SCs is sensitive to the sign of interactions, which leads to new many-body-induced physics selection rules. Moreover, we identify the conditions for collective modes to become ILS-active with distinct spectral weights. Furthermore, in addition to modelling experimental data, we explore the effects of non-trivial Fermi-surface topologies and of anisotropic interactions in the ILS line spectrum in different collective-mode scenarios, establishing direct relations between spectral features and properties of SCs.