High temperature superconductors exist in a wide variety of complex crystal forms. Their maximum transition temperature varies widely between crystals sharing the same basic copper oxide in-plane electronic structure. These variations cannot be explained by theoretical models focusing only on the in- plane structure, so it has long been hypothesized that there must be an out-of- plane influence that reorganizes the underlying electronic states and thereby controls the maximum critical temperature achievable. Much attention has focused on the pyramidal arrangement of five oxygen atoms surrounding each copper atom and, in particular, on the out-of-plane apical site. Here I report the first direct determination in a high temperature superconductor (Bi2Sr2CaCu2O8+δ) of the effect of varying interatomic distances on the superconducting energy gap Δ within individual unit cells. Scanning tunneling spectroscopy and a newly developed lock-in image processing technique are used to exploit naturally occurring periodic variations in the unit cell geometry, revealing a 9% variation in the gap energy, apparently anti-correlated with the apical height of the CuO5 pyramid. These effects are consistent in several key ways with those of the other main local cause of gap energy variation, namely, dopant atoms, making it likely that both act through the same geometric and electronic mechanism.
 
The measurement and identification of the bosonic mode most strongly coupled to the electronic states of Bi2Sr2CaCu2O8+δ is also described, explaining the most prominent peak in the first derivative of the density of states spectrum. By measuring and comparing isotope-substituted samples, it is demonstrated that this mode is a local vibration, most likely involving the atoms of the copper oxide plane. Finally, the heavily overdoped regime of the cuprate phase diagram is explored by producing and measuring a heavily overdoped (δ = 0.23) sample of Bi2Sr2CaCu2O8+δ, significantly past the proposed critical doping level at which other experimental techniques have observed major electronic changes. Evidence is found confirming the evolution of Fermi surface topology, and the occurrence of quasiparticle coherence anisotropy reversal. On the other hand, energy gap heterogeneity, seen at all lower doping levels, is found to persist into the heavily overdoped state.
 
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Atomic-Scale Impact of Unit Cell Dimensions on Pairing in a High-Temperature Superconductor
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