In its normal state, Sr₂RuO₄ is a prototypical Fermi liquid below ∼ 25 K. At ∼ 1.5 K it undergoes a superconducting transition, but it has long remained challenging to determine the symmetry or order parameter of the superconducting state. Recent experiments have shown that uniaxial strain can cause T_c to peak in Sr₂RuO₄ and non-Fermi liquid behaviour to emerge in the normal state.

In this thesis, we investigate the electronic structure of Sr₂RuO₄ using a novel approach to ARPES experiments under uniaxial strain. Our approach is based on strain tuning by sample geometry, which we precisely design with the use of a focused ion beam (FIB). Our μ-focused laser-ARPES experiment resolves the progression of a van Hove singularity (vHs) through the Fermi level, which has been proposed to drive the peak in T_c. We do not, however, resolve any change in the self-energies concomitant with this behaviour. It is presently unclear whether this result is consistent with reports of correlation enhancements due to the proximity of a vHs to the Fermi level.

We further show how FIB technology can be used to design desired cleavage planes in crystals. We use this sample preparation technique to demonstrate a-c cleaves in Sr₂RuO₄ and show preliminary ARPES measurements of the Fermi surface in this plane. We further show that this technique can be used to produce high quality surfaces of the structurally 3D perovskite SrTiO₃ for ARPES experiments.

Finally, we study the temperature dependence of the quasiparticle scattering rate and quasiparticle residue Z in Sr₂RuO₄ as it evolves out of the Fermi liquid regime and through the metal-nonmetal crossover in the c-axis resistivity at ∼ 130 K. Analysing the renormalisation of the quasiparticle dispersion, we demonstrate that Z increases with temperature. This is in good agreement with dynamical mean-field theory and corrects earlier experimental reports of a vanishing quasiparticle weight at elevated temperatures.