Interplay between Superconductivity and Electronic Orders in $\mathrm{FeSe}_{1-x}\mathrm{Te}_{x}$ and $A\mathrm{V}_{3}\mathrm{Sb}_{5}$

Quantum materials offer a fertile ground for discovering emergent phenomena that arise from interactions between charge, spin, orbital, and lattice degrees of freedom. Using thermodynamic and transport measurements, this thesis explores two families of such materials: the iron-chalcogenide superconductors $\mathrm{Fe}_{1+y}\mathrm{Se}_{1-x}\mathrm{Te}_{x}$ and kagome metals $A\mathrm{V}_{3}\mathrm{Sb}_{5}$ ($A=\mathrm{Cs}, \mathrm{Rb}, \mathrm{K}$).

In $\mathrm{Fe}_{1+y}\mathrm{Se}_{1-x}\mathrm{Te}_{x}$, bulk thermodynamic measurements establish a phase diagram with two distinct superconducting domes. In the first dome, associated with the nematic phase, heat-capacity data indicate either accidental nodes or strong gap anisotropy, which is progressively lifted with Te substitution. Thermal-expansion measurements further show that orthorhombicity and superconductivity couple cooperatively in this regime, similar to the behavior in Fe(Se,S). In the second dome, where long-range nematic order is absent, the thermodynamic response is dominated by a single electronic band, and the c-axis response becomes strongly enhanced, pointing to substantial changes in the electronic structure. ... mehrThree-point-bending measurements show a hardening of $C_{66}$ in the superconducting phase for the optimally doped composition, consistent with strong competition between superconductivity and nematic fluctuations. The nemato-elastic effects and the Grüneisen parameter are also discussed.

In kagome $A\mathrm{V}_{3}\mathrm{Sb}_{5}$ compounds, we performed zero-field calorimetry and transport measurements to characterize the charge-density-wave (CDW) transition, and high-field Shubnikov-de Haas, de Haas-van Alphen, and magnetostriction measurements to probe its impact on the Fermi surface. While $\mathrm{KV}_{3}\mathrm{Sb}_{5}$ undergoes a continuous CDW transition, $\mathrm{RbV}_{3}\mathrm{Sb}_{5}$ exhibits a weak first-order transition. Quantum oscillation spectra reveal multiple low-frequency orbits consistent with CDW-induced Fermi-surface reconstruction. The evolution of mid-frequency orbits across the Cs-Rb-K series is consistent with the reported differences between staggered Star-of-David / inverse-Star-of-David (SD/ISD) and mixed $\mathrm{SD}+\mathrm{ISD}$ superlattices. Finally, comparison of magnetostriction and magnetization data for $\mathrm{RbV}_{3}\mathrm{Sb}_{5}$ shows that the small elliptical pockets linked to the anomalous Hall effect are only weakly affected by $c$-axis strain.