| In this dissertation, I present experimental investigations on two types of quantum materials -- topological insulators and high temperature superconductors. First, I investigated the indium substitution effect on the topological crystalline insulator Pb1-xSnxTe family, and found the indium doping leads to significant changes in the superconducting and topological properties. To understand the nature of the indium-induced superconductivity, inelastic neutron scattering was applied to study the anomalies in the phonon density of states in (Pb0.5Sn0.5)1-yInyTe powders, and the results indicate the bulk superconductivity in indium doped Pb1-xSnxTe compounds is driven by phonons, suggesting that they are more likely conventional BCS superconductors instead of topological superconductors. Second, inelastic neutron scattering was used to explore dynamic structural and electronic correlations in the strongly correlated electronic systems of La1.875Ba0.125CuO4+&dgr; and La1.75Sr0.25NiO4+&dgr;. La 2-xBaxCuO4+&dgr; is a family of high temperature superconductors, but with 1/8 Ba-doping, the three-dimensional superconductivity is mostly suppressed due to the formation of ordered, static stripes. The static nature is caused by pinning due to the tilting of the CuO6 octahedra, whose symmetry resembles that of the low-temperature-tetragonal (LTT) phase. To resolve a long-standing dispute on the tilt correlations in the disordered state, I explored the tilting patterns above the transition between the low-temperature-orthorhombic (LTO) and LTT phases in La1.875 Ba0.125CuO4+&dgr;, and found the dynamic LTT-like correlations exist even at high temperature. The La2-xSr xNiO4+&dgr; materials have a similar stripe structure, and their insulating nature facilitates studying their dynamic stripes. In La 1.75Sr0.25NiO4+&dgr;, the anisotropic low-energy dispersion above the stripe-ordering transition has been observed for the first time, providing evidence for the presence of electronic nematic order. With our experiments on these two materials, dynamic correlations related to high temperature superconductors are studied from two aspects: the structural view, obtained from studying the LTT-like tilt fluctuations above the LTO-LTT transition in La1.875Ba0.125CuO4+&dgr;; and the electronic view, obtained from studying dynamic charge stripes above the stripe-ordering transition in La1.75Sr0.25NiO4+&dgr; . |
