Phenomenology of unconventional superconductors

In this thesis, we report the results of theoretical and numerical investigation of three different classes of unconventional superconductors. In the first part of this thesis, we use a dirty-limit BCS model to semi-quantitatively explain a wide range of electrodynamic and thermodynamic properties of two overdoped cuprate superconductors: La2−xSrxCuO4 (LSCO) and Tl2Ba2CuO6+δ (Tl-2201). This work is motivated by superfluid density measurements of Božović et al. on overdoped LSCO thin films, and the subsequent THz conductivity study of Mahmood et al. on a similar set of samples. These authors argued that their data are inconsistent with the predictions of the BCS theory. In contrast to the claims of Božović et al. and Mahmood et al., we show that the perplexing results can in fact be well understood within the Landau-BCS framework when the dominant sources of scattering are weak, out-of-plane defects. Our starting points are realistic tight-binding parameterizations of the Fermi surfaces of LSCO and Tl-2201. The impurity potentials of out-of-plane defects are obtained from a series of ab-initio calculations. Our results indicate the electrodynamic properties of high quality MBE thin films used in the Božović et al. study can be accurately described by apical oxygen vacancy concentrations in the range of 6%. Furthermore, we find a strong correlation between the concentration of apical oxygen vacancies and the wide Drude peaks observed in the THz spectra. In the next part of this thesis, we investigate the pairing symmetry of one of the most studied organic superconductors: κ-(ET)2Cu(SCN)2. The superfluid density obtained from microwave conductivity spectra shows a roughly quadratic temperature dependence, indicating the presence of line nodes. Simultaneous fits of a double Drude model to the data show a large collapse in scattering rate below Tc. We find two different lifetime scales over a wide temperature range, and we explore a scenario in which the two lifetimes may result from an interaction between dxy pairing, forward-scattering impurities, and Fermi surface anisotropy. Finally, we employ a two-band BCS model to explain the temperature dependence of absolute superfluid density in LaNiC2. We provide unambiguous evidence for the two-isotropic-gap scenario.