Since the early 1960s, Abrikosov-Gorkov theory has been used to describe superconductors with paramagnetic impurities. Interestingly, the density of states resulting from the theoretical framework has to date only been known approximately, as a numeric solution of a complex polynomial. An analytical solution to the theory was discovered and applied to extract the spin polarization from the tunneling conductance of superconducting aluminium with 3-dimensional (3-D) amorphous (a-) gadoliniumxsilicon1-x (GdxSi1-x) as a counter electrode (Al/Al2O3/a-GdxSi1-x planar tunnel junction measured at T = 25 mK and H less than or equal to 3.0 T) in the quantum critical regime (QCR). The analytical solution is valid in the whole regime of Abrikosov-Gorkov theory independent of the presence of an energy gap. Applying the spin polarized Abrikosov-Gorkov theory to describe aluminium gives a larger spin polarization in GdxSi1-x than the spin polarized Bardeen-Cooper-Schrieffer (BCS) theory. The purpose of this study is to extract polarization at various applied magnetic fields, but no specific relationship between the two could be determined. Results obtained shows a transition from a superconductor with a gap to a gapless superconductor in varying external magnetic fields was observed. To improve understanding of GdxSi1-x near the metal-insulator transition (MIT) and compare it with prior work, the initial experimental attempts to investigate the transport property of GdxSi1-x near the MIT in the 2-dimensional limit are presented. A low temperature ultra high vacuum quench condensation system was used to make thin films of GdxSi1-x and in-situ measurements were performed. The transport properties for different values of x and thicknesses were measured for T = 4.2 K to ~10 K. In addition to other possible causes, the uncertainty in the electron impact emission spectroscopy (EIES) appeared to be a major reason behind the observed error in x when gadolinium and silicon are co-evaporated. The problems faced during the co-evaporation are also discussed.