Ion-size effects on cuprate High Temperature Superconductors

The cuprates are a family of strongly electronically-correlated materials which exhibit high-temperature superconductivity. There has been a vast amount of research into the cuprates since their discovery in 1986, yet despite this research effort, the origins of their electronic phases are not completely understood. In this thesis we focus on a little known paradox to progress our understanding of the physics of these materials.   There are two general ways to compress the cuprates, by external pressure or by internal pressure as induced by isovalent-ion substitution. Paradoxically, they have the opposite effect on the superconducting transition temperature. This thesis seeks to understand the salient difference between these two pressures.  We study three families of cuprates where the ion size can be systematically altered; Bi₂(Sr₁.₆₋xAx)Ln₀.₄CuO₆₊δ, ACuO₂ and LnBa₂−xSrxCu₃O₇₋δ where Ln is a Lanthenide or Y and A={Mg,Ca,Sr,Ba}. We utilise a variety of techniques to explore different aspects of our paradox, for example; Raman spectroscopy to measure the antiferromagnetic superexchange energy and energy gaps, Density Functional Theory to calculate the density of states, Muon Spin Relaxation to measure the superfluid density as well as a variety of more conventional techniques to synthesize and characterise our samples.  Our Raman studies show that an energy scale for spin fluctuations cannot resolve the different effect of the two pressures. Similarly the density of states close to the Fermi-energy, while an important property, does not clearly resolve the paradox. From our superfluid density measurements we have shown that the disorder resulting from isovalent-ion substitution is secondary in importance for the superconducting transition temperature.  Instead, we find that the polarisability is a key property of the cuprates with regard to superconductivity. This understanding resolves the paradox! It implies that electron pairing in the cuprates results from either (i) a short-range interaction where the polarisability screens repulsive longer-range interactions and/or (ii) the relatively unexplored idea of the exchange of quantized, coherent polarisation waves in an analogous fashion to phonons in the conventional theory of superconductivity. More generally, we have also demonstrated the utility of studying ion-size effects to further our collective understanding of the cuprates.