Spectroscopy and phenomenology of unconventional superconductors

The challenge of condensed matter physics is to understand how various states of matter emerge from periodic or amorphous arrangements of atoms. This is typically easier if there are no impurities in the material under investigation. However, many of the properties that make materials technologically useful stem from the very disorder and impurities that complicate their study. In this work we investigate three unconventional superconductors with the dirty BCS framework of superconductivity, with impurities treated in the selfconsistent t-matrix approximation. The three materials behave quite differently and allow us to explore and reveal a rich, subtle, and poorly appreciated range of effects that must be considered when studying superconducting materials and probing the limits of applicability of current theories of superconductivity. Microwave spectroscopy measurements of FeSe, a member of the iron-based family of superconductors, were performed at frequencies below 1 GHz using a novel helical resonator. The measurements show that the material is particularly clean, with an electronic mean free path that exceeds that of all known binary compounds. They also reveal the presence of a finite gap on both superconducting bands, strongly constraining which pairing states should be considered for FeSe. Nb-doped SrTiO3 has an extremely low carrier concentration and multiple electronic bands at the Fermi sruface. Microwave spectroscopy measurements, this time with a stripline resonator, reveal a single spectroscopic gap despite clear evidence for multiple superconducting bands. Elastic scattering introduced via Nb dopants is proposed as the mechanism by which the two bands homogenize into a single spectroscopic signature, as per Anderson's theorem. The impurity hypothesis is tested with single-band fits to the superfluid density and is found to be in good agreement with measured data. Finally La2−xSrxCuO4, a member of the famous cuprate family of superconductors is explored in detail under the assumption that Born scattering with large amounts of impurities can explain a number of puzzling measurements that have caused controversy in the high-Tc community over the past few years. Many features of the experimental measurements can quantitatively be accounted for with very few free parameters and no fine tuning.