Superconductivity in cuprates has many mysterious facets, but the central question is why the critical temperature (Tc ) is so high. Our experiments target this question.

We use atomic-layer-by-layer molecular beam epitaxy to synthesize atomically perfect thin films and multilayers of cuprates and other complex oxides. We measure the absolute value of penetration depth λ to accuracy better than 1%. Using a continuous spread in composition we tune the doping level in steps of 0.01%. We study magneto-resistance and Hall effect in fields up to 90 T and measure accurately the coherence length ξ.

We have shown that HTS films can be quite homogeneous, a very uniform SC gap. Charge density waves and charge glass are observed in underdoped LSCO samples, but none at optimal doping. Phase fluctuations are seen up to 15-20 K above Tc, so the pseudogap likely has a different origin. In-plane charge excitations are strongly coupled to out-of-plane lattice vibrations. Superfluid can be confined to a single CuO2 layer, with Tc equal to that in bulk samples. Pairs exist on both sides of the superconducting transition, be it induced thermally or by doping. [1]

I will present the results of a comprehensive study thousands of cuprate samples, perhaps without precedence in Condensed Matter Physics. We have measured the key physical parameters (Tc, λ, and ξ) of the superconducting state and established their precise dependence on doping, temperature, and external fields. The large statistics reveals clear trends and intrinsic properties; this is essential when dealing with complex materials such as cuprates. The findings challenge the commonly held beliefs, rule out many models, and answer our initial question.