Quantum materials are a growing field of interest in condensed matter physics and materials science due to their manifestation of quantum mechanical effects on the macroscale. Interactions between the charge, spin, lattice, and orbital degrees of freedom, combined with topology and often reduced dimensionality lead to the emergence of electronic ground states which defy understanding in terms of classical physics. Within the field of quantum materials, particular interest is placed on unconventional superconductors as possible candidates for use in quantum information science. Considerable inquiry is focused on the pairing mechanism in unconventional superconductors, as well as interplay between superconducting states and adjacent low-temperature states such as charge density wave (CDW) order and ferroelectricity. This thesis focuses on optical characterization of the quantum materials SrTiO3 and CsV3Sb5, both unconventional superconductors. I will discuss the methods used to characterize these materials: second harmonic generation (SHG) and pump-probe spectroscopy. The results I have obtained clarified interesting and previously ambiguous phenomena in these materials: SHG techniques supported a connection between ferroelectricity and superconductivity in SrTiO3, pump-probe spectroscopy explained the origin of CDW order in CsV3Sb5.

In quantum materials, phenomena occurring at the subatomic level can manifest as properties on a macroscopic scale. The exploration of quantum effects in materials with nontrivial band topology and strongly correlated electrons holds great promise for technological advancement in fields such as quantum computing. This thesis examines properties of three such quantum materials using computational methods.The primary material system investigated is strontium titanate, an incipient ferroelectric that gives rise to an unconventional superconducting state at exceptionally low doping levels. The polar phase can be stabilized through strain or chemical substitution. Remarkably, superconductivity is enhanced within the polar phase, suggesting that the polar instability plays a pivotal role in the superconducting pairing mechanism. We develop a simplified free energy model combined with statistical mechanics methods to assess the character of the polar transition, which we find to be neither order-disorder nor displacive. We explore the effects of doping on the structural phase transitions and find that, in agreement with experiment, the polar distortion and formation of polar nanodomains are suppressed in the presence of free carriers, while antiferrodistortive order remains essentially unchanged. The single-domain nature and insensitivity to doping suggest that the antiferrodistortive order does not play an important role in Cooper pairing. By calculating electronic properties in the polar phase, we analyze parameters that are relevant to superconductivity such as the density of states at the Fermi level, the Rashba splitting of the energy bands, and the Migdal ratio. We explore the chemical phase space of the naturally occurring minerals herbertsmithite [ZnCu3(OH)6Cl2] and Zn-substituted barlowite [ZnCu3(OH)6BrF], which both feature perfect kagome layers of spin-1/2 copper ions and display experimental signatures consistent with a quantum spin liquid state at low temperatures. To identify other possible candidates within this material family, we perform a systematic first-principles combinatorial exploration of structurally related compounds [ACu3(OH)6B2 and ACu3(OH)6BC] by substituting nonmagnetic divalent cations (A) and halide anions (B, C). We select several promising candidate materials that we believe deserve further attention. Finally, we examine CsV3Sb5, a member of the AV3Sb5 (A = K,Rb,Cs) family of kagome metals, whose low-energy physics is dominated by an unusual charge density wave phase. We elucidate the nature of the charge density wave order parameter using first-principles density functional theory calculations which support the findings of experimental coherent phonon spectroscopy measurements. Through our study of the structural phase space of CsV3Sb5, we find that the charge density wave can be described as tri-hexagonal ordering with interlayer modulation along the c-axis.

First-principles techniques are often limited by their inability to incorporate the effects of temperature and disorder. Here, we augment first-principles density functional calculations using statistical mechanics methods such as the Metropolis Monte Carlo algorithm and Langevin dynamics to incorporate temperature effects on large, disordered supercells to simulate the thermal phase space of strontium titanate. The chemical phase of the herbertsmithite material family is systematically explored through high-throughput first-principles pseudo-convex hull calculations and an assessment of defect formation energy. We use frozen phonon calculations to investigate the structural phase space of CsV3Sb5 and find that the charge density wave order expands beyond the previously studied 2x2x1 construction. Our techniques can be applied more broadly to other material systems to expand the capabilities of computational methods to accurately capture thermal effects and structural disorder in quantum materials.

Light-matter interactions are one of the primary methods by which scientists study structure-property relationships in materials. Optical characterization – a set of tech- niques that use wavelengths of light visible to the human eye – has proven to be a powerful class of methods to reveal the structure and symmetry of materials. Here, we use second harmonic generation (SHG) and time-resolved optical pump probe spectroscopy to study phase transitions in complex oxide thin films with perovskite-like structure.A primary focus of this work is the study of electronic symmetry breaking in thin films of epitaxially-strained Sr2RuO4. Once thought to be a candidate solid-state analogue of the A phase of superfluid helium-3, Sr2RuO4 has been the subject of renewed research interest after the hypothesis of its spin-triplet superconductivity was struck down. Ostensibly a textbook example of a Fermi liquid, Sr2RuO4 has one of the most well studied normal states of any material, and its crystal growth has been refined to achieve mean free paths of over a micrometer. With an extraordinarily well-studied fermiology, Sr2RuO4 is well poised as a testing ground for theories of correlated electrons. Here, we study epitaxially strained Sr2RuO4 with time-resolved optical pump probe spectroscopy and reveal the presence of an electronic nematic phase in the normal state. The temperature dependence of both a static optical dichroism and a transient reflectivity anisotropy are modeled well by an Ising-like order parameter. A microscopic explanation of the electronic symmetry breaking is offered through the Emery model, which explains nematic ordering through a redistribution of electron density. Our evidence of electronic nematicity in the normal state of Sr2RuO4 may have important consequences for a successful theory of the as-yet unexplained superconducting phase. Separately, a discussion is presented of strained, doped films of SrTiO3 grown by molecular beam epitaxy. As the first known semiconducting (and unconventional) superconductor, bulk SrTiO3 is known to be an incipient ferroelectric that avoids a polar transition at low temperatures. SHG is used to reveal the presence of a polar phase in strained, doped films of SrTiO3, and moreover links the ferroelectric phase with enhanced superconductivity exhibited in this system. Films are doped across various carrier densities to find the polar phase boundary, which is shown to coincide with aborted super- conductivity, clarifying the role of polar fluctuations as a pairing mechanism. The effect of magnetic dopants is also studied, where Eu is used to introduce localized, unpaired f-electrons. It is found that both the polar and superconducting phases are insensitive to magnetic dopants up to a few percent and are surprisingly robust to even higher levels of magnetic doping. The paradigm of local polar order is also discussed in the context of superconducting pairing. Although enhanced superconductivity in SrTiO3 is intricatelylinked with broken inversion symmetry, it appears that a global polar phase is not re- quired to mediate electron pairing; rather, polar nanodomains are sufficient to support the superconducting phase. Finally, a brief chapter is included that presents preliminary measurements of Ca2RuO4 thin films. Optical pump probe measurements support the discovery of a photoinduced picosecond volume expansion which results in a later-time insulator-metal transition. The effects of temperature and optical pump fluence on the transient response are also explored; a nontrivial dependence on pump fluence is discovered at low temperature, as well as coherent oscillations, which motivate future investigation of the system.