Fermi Surface and Quantum Critical Phenomena of High Temperature Superconductors Introduction to Iron Based Superconductors Theory Experimental Setup BaFe2(As1 xPx)2 A Quantum Critical Superconductor LiFeAs and LiFeP Stoichiometric Superconductors YBa2Cu408 Numerical Phase Sensitive Detection in Matlab Publications Bibliography. This thesis provides a detailed introduction to quantum oscillation measurement and analysis and offers a connection between Fermi surface properties and superconductivity in high temperature superconductors. It also discusses the field of iron based superconductors and tests the models for the appearance of nodes in the superconducting gap of a 111 type pnictide using quantum oscillation measurements combined with band structure calculation. The same measurements were carried out to determine the quasiparticle mass in BaFe2(As1 xPx)2 which is strongly enhanced at the expected quantum critical point. While the lower superconducting critical field shows evidence of quantum criticality the upper superconducting critical field is not influenced by the quantum critical point. These findings contradict conventional theories demonstrating the need for a theoretical treatment of quantum critical superconductors which has not been addressed to date. The quest to discover similar evidence in the cuprates calls for the application of extreme conditions. As such quantum oscillation measurements were performed under high pressure in a high magnetic field revealing a negative correlation between quasiparticle mass and superconducting critical temperature.