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In materials with heavy elements, both strong spin-orbit coupling and Coulomb interactions are possible to exist. Both can significantly change the properties of materials. The coexistence of them can induce more interesting phenomena in solids. In this dissertation, three different cases involved with spin-orbit coupling and Coulomb interaction are separately studied. In the first case, impurity states in topological Kondo insulators are studied. Both in-gap and deep-bound impurity states are explicitly examined. The in-gap impurity states have properties similar to those of the topological surface states. It can explain some anomalous properties observed in SmB6, a possible topological Kondo insulator. In the second one, it is proposed that spin-orbit coupling can be strongly enhanced by Coulomb interaction in 5f metals. Modest values of the Coulomb interaction can induce up to a four-fold enhancement. In the third case, a model is presented to characterize spin-orbit enhancement in a strongly correlated two-dimensional system. By our calculation, it is shown that a possible nonlinear Rashba effect can emerge in such a system. It can explain the presence of giant Rashba constants in some two-dimensional devices. / Physics

This thesis presents both technological developments of broadband time-resolved ultrafast spectroscopy and investigation of the dynamics of photoexcited carriers and topological phonons in chiral Weyl semimetals. In the first portion of this thesis, we describe a novel, optical pump supercontinuum probe technique based upon a nonlinear photonic crystal fiber and a digital micro-mirror device enabling the use of single element detector and lock-in demodulation of the signal, along with rapid, repeated averaging over the spectrum. Using a bismuth test sample, we demonstrate that the apparatus is capable of measuring time-resolved changes in reflectivity ΔR of a sample over the 1.5 - 3.0 eV energy range with 25 fs temporal resolution, while also being sensitive to relative changes in reflectivity as low as ΔR/R ~ 10^(-4). A more conventional broadband pump-probe technique was applied to the chiral Weyl semimetal RhSi (S.G. 198) with the aim of investigating the dynamics of chiral single particle excitations and collective modes of topological, Weyl quasiparticles. In S.G. 198 materials, lack of crystallographic mirror symmetries allows for Weyl nodes to exist with a relative displacement of ~ 330 meV in energy, permitting optical investigation of the dynamics of a single Weyl node without interference from other bands or the opposite chirality Weyl node. The probe wavelength was independently scanned over the 0.4 -1.0 eV energy range to monitor the photoinduced changes in reflectivity fixing the pump wavelength at energies 0.57, 0.73 & 1.03 eV in order to excite one node, two nodes, and non-topological portions of the band structure, respectively. A single fast decay process (relaxation time τ ~ 300 - 500 fs) was observed over the entire energy regime studied, consistent with previous measurements of photoexcited charge dynamics in other Dirac and Weyl semimetals. Significantly, measurements of time-resolved Kerr effect spectroscopy yielded evidence of a T representation chiral lattice excitation whose observed frequency matched the calculated frequency using density functional theory. / Physics

In materials with heavy elements, both strong spin-orbit coupling and Coulomb interactions are possible to exist. Both can significantly change the properties of materials. The coexistence of them can induce more interesting phenomena in solids. In this dissertation, three different cases involved with spin-orbit coupling and Coulomb interaction are separately studied. In the first case, impurity states in topological Kondo insulators are studied. Both in-gap and deep-bound impurity states are explicitly examined. The in-gap impurity states have properties similar to those of the topological surface states. It can explain some anomalous properties observed in SmB6, a possible topological Kondo insulator. In the second one, it is proposed that spin-orbit coupling can be strongly enhanced by Coulomb interaction in 5f metals. Modest values of the Coulomb interaction can induce up to a four-fold enhancement. In the third case, a model is presented to characterize spin-orbit enhancement in a strongly correlated two-dimensional system. By our calculation, it is shown that a possible nonlinear Rashba effect can emerge in such a system. It can explain the presence of giant Rashba constants in some two-dimensional devices. / Physics

I will present a new ultrafast time-resolved photoluminescence technique using two-photon absorption detection (TPAD). In this femtosecond photoluminescence (PL) experiment the PL dynamics are monitored by focusing the PL signal and an ultrafast gate pulse on a GaN photodiode with nonlinear properties. Specifically, after sample excitation with a femtosecond excitation pulse the emitted photons from the sample and the gate pulse couple together to create electron hole pairs with the combined photon energy (two-photon absorption) in the high bandgap photodiode. The bandgap of the photodiode is large enough that linear absorption of the PL or the gate pulse is negligible. Techniques with a time resolution in the femtosecond range provide insight into dynamic processes including charge and energy relaxation, recombination and transfer. Following the discussion of the TPAD experiments I will give an overview of already existing time-resolved PL techniques which will allow to compare the performance of the presented technique with these techniques.

Determining the accurate structure of a material is a critical step in understanding its physics. Standard electronic structure methods have not achieved systematic accuracy, especially for materials with strong electron correlation effects. Many-body methods can potentially deliver higher accuracy, but they all face significant algorithmic obstacles for structural optimization in solids. In this thesis, I present a direct, ab initio computation of forces and stresses with auxiliary field quantum Monte Carlo (AFQMC). AFQMC is a many-body computational method that has shown excellent performance in computing the total energy and charge density. Our method for computing forces and stresses requires minimal approximations and can be used to predict the potential energy surface at a much higher efficiency than an energy-only approach. In addition, we propose a fast and robust structural optimization algorithm with statistically noisy forces. Applying this algorithm to our forces and stresses, we demonstrate efficient, accurate, and full degrees-of-freedom optimizations in solids. Phonon calculations also become more efficient with AFQMC forces, though a naive frozen-phonon approach amplifies noises and struggles to retrieve the signal. We solve this problem by proposing a population control scheme in the correlated sampling framework, obtaining fast and accurate phonon spectra for solids. Finally, we demonstrate the possibility of computing Berry phases, polarizations, and the Chern number in AFQMC with a correlated sampling based algorithm. The systematic methods and techniques in this thesis pave the way for a wide range of applications, including but not limited to prediction of structures, thermodynamics, ferroelectricity, and topological properties of quantum materials.

Transverse Field muon spin relaxation (TF-muSR) experiments were performed in external magnetic fields 1.0, 2.7, 3.0, 4.5, 5.5, 6.0 and 7.0 T along the Bi2212 crystalline c-axis. For the first time, the heterodyned fitting analysis technique shows that the field profiles on the ab basal planes of single crystal Bi2212 are symmetric in all experimental fields 1.0--7.0 T and at all experimental temperatures 2.0-90.0 K. The muon spin relaxation rates due to the mixed state of Bi2212 were found to increase linearly from 0 mus-1 at the transition temperature, 90.0 K, to about 1.0 mus -1 at the lowest temperature, 2.0 K. The relaxation rates have much less field dependence than the temperature dependence and the field dependence of the relaxation rate is of opposite sign to that seen for YBCO, which is undoubtedly due to vortex lattice disorder caused by the weak coupling between the CuO planes. The scaled magnetic field penetration depths ll0 were found to be independent of magnetic field B in the temperature range 0--50.0 K. Fitting ll0 by currently available models was attempted. A proposed pancake vortex disorder model strongly suggests pancake disordering at all temperatures including 2.0 K, the lowest temperature reached in our experiment. Our experiments and the computer simulation from the pancake vortex disorder model showed that muSR data in this temperature and field range are attributed to the 2-D anisotropic vortex characteristics of Bi2212.

Electronic structure calculations using simulation cells for extended systems typically incorporate periodic boundary conditions as an attempt to mimic the real system with a practically infinite number of particles. Periodic boundary conditions introduce unphysical constraints that give rise to finite-size errors. In mean-field type calculations, the infinite size limit is achieved by simple quadrature in the Brillouin zone using a finite number of k-points. Many-body electronic structure calculations with explicit two-particle interactions cannot avail themselves of this simplification. Direct extrapolation is computationally costly while size correction with less accurate methods is frequently not sufficiently accurate. The Hartree-Fock method neglects the correlation energy, while the conventional density functional theory (DFT) uses the infinite-size limit of the exchange correlation function. Here we present a new finite-size exchange correlation function designed to be used in OFT calculations to give more accurate estimates of the finite-size errors. Applications of the method are presented, including the P2 molecule, fcc silicon, bcc sodium and BiScO3 perovskite. The method is shown to deliver rapidly convergent size-corrections.