Title: Strain effects on phase transitions in 2H-NbSe₂ and Ca₃Ru₂O₇
Description: Strain control of correlated electron phenomena has been a theme of condensed matter research in recent years. Two primary areas of investigation have been controllable symmetry breaking and measurements of susceptibility with respect to elastic deformation and in this thesis we present an example of each. In 2H-NbSe₂ explore the effect of lattice anisotropy on the charge-ordered superconductor. Using a novel strain apparatus, we measure the superconducting transition temperature 𝑇_{sc} as a function of uniaxial strain. It is found that 𝑇_{sc} is independent of tensile(compressive) strain below a threshold of 0.2% (0.1%), but decreases strongly with larger strains with an average rate of 1.3𝐊/% (2.5𝐊/%). Transport signatures of charge order are largely unaffected as a function of strain. We employ theoretical considerations to show that the change in the behavior of 𝑇_{sc} with strain coincides with a phase transition from 3𝐐 to 1𝐐 charge order in the material. The spectral weight on one of the Fermi surface bands is found to change strongly as a consequence of this phase transition, providing a pathway to tune superconducting order.

In the bilayer ruthenate Ca₃(Ru₁₋ₓTiₓ)₂O₇ a material that is unique among correlated insulators for its hybrid improper ferroelectricity and, at elevated temperatures, transitioning to a polar metallic phase, we investigate phase textures and their susceptibility to strain. Through multi-messenger low-temperature infrared and Kelvin probe nano-imaging, we reveal a spontaneous striped texture of coexisting insulating and metallic domains in single crystals across their insulator-metal phase transition at T=50-100K. Under in situ uniaxial strain, we image anisotropic nucleation and growth of these domains, rationalized through on-demand control of a spontaneous Jahn-Teller distortion. Through spatially correlative transmission electron microscopy and nano-scale strain mapping, we also reveal the selective interplay between this textured phase coexistence and domain boundaries between polar twins in these crystals. We study the strain susceptibility of the striped phase mixture and explain our results in terms of homogeneous phase susceptibilities and the strain susceptibility of domains.

We study the anisotropy in bulk response functions (resistivity and elastosusceptibility) and we find that the results are consistent with a network model of the phase texture. We also perform low-temperature infrared nanoimaging and elastosusceptibility of the nonequilibrium current-driven metal-insulator transition in Ca₃(Ru₁₋ₓTiₓ)₂O₇. Our results are consistent with the emerging consensus explanation in terms of Joule heating.