Searching for 2D Superconductivity in La2?xSrxCuO4 Single Crystals

A new experimental method – the "Stiffnessometer", is developed to measure elementary properties of a superconductor, including the superconducting stiffness and the critical current. This technique has many advantages over existing methods, such as: the ability to measure these properties while minimally disturbing the system; the ability to measure large penetration depths (comparable to sample size), as necessary when approaching the critical temperature; and the ability to measure critical currents without attaching contacts and heating the sample. The power of this method is demonstrated in a study of the penetration depth of LSCO, where striking evidence is found for two separate critical temperatures for the in-plane and out-of-plane directions. The results in the thesis are novel, important and currently have no theoretical explanation. The stiffnessometer in a tool with great potential to explore new grounds in condensed matter physics.