Title: Electronic structure and phase stability of strongly correlated electron materials
Description: In this thesis, we use first-principles methods to study a class of systems known as strongly correlated materials in which exceptionally strong electron-electron repulsion in the d or f electron shell can lead to intriguing physical properties. The focus is on transition metal oxide and phosphate intercalation materials such as LiₓCoO₂ and LiₓFePO₄, which are employed as the positive electrode in rechargeable Li ion batteries. We also study the transition metal dichalcogenide system VS₂ as a candidate for strong correlation physics with analogous features to the cuprate high-temperature superconductors. Density functional theory (DFT), the standard theory of materials science which can be viewed as an effective single-electron theory, often breaks down for strongly correlated materials. In this thesis, we augment DFT with a more sophisticated many-electron approach known as dynamical mean-field theory (DMFT). We use the resultant DFT+DMFT approach with the numerically exact continuous-time quantum Monte Carlo solver to explore the physics of the materials studied here and probe compositional phase stability and related observables within DFT+DMFT for the first time.

The elementary but efficient Hartree-Fock solver for the DMFT equations (i.e., DFT+U) is also utilized in order to cleanly separate the role of dynamical correlations and to better understand the respective methods. With these ab initio methods, we predict the compositional phase stability, average intercalation voltage, Li order-disorder transition temperature, structural phase stability, phonons, magnetic properties, and other important characteristics of strongly correlated materials. At the DFT+U level of theory, electronic correlations destabilize the intermediate-x compounds of cathode materials via enhanced ordering of the endmember d orbitals. DFT+U is qualitatively consistent with experiments for phase stable LixCoO₂, phase separating LiₓFePO₄, and phase stable LiₓCoPO₄. In Li₁/₂CoO₂, which is not charge ordered in experiments, the charge ordering predicted by DFT+U primarily stems from the approximate interaction, is necessary to qualitatively capture the phase stability, and erroneously predicts an insulating state and an overestimated Li order-disorder transition temperature.

DFT+DMFT calculations describe LiCoO₂ as a band insulator with appreciable correlations within the Eg states and CoO₂ as a moderately correlated Fermi liquid; for both these systems we find evidence for appreciable charge and spin fluctuations. Dynamical correlations substantially dampen changes in the number of d electrons per site and the total energy as compared to DFT+U, which alters the predicted battery voltage between the two methods. We find that our DFT+DMFT results underestimate the average intercalation voltage for LiₓCoO₂ and discuss possible reasons for the discrepancy. In monolayer VS₂, a combination of crystal field splitting and direct V-V hopping leads to an isolated low-energy band for the trigonal prismatic phase within non-spin-polarized DFT. Ferromagnetism spin splits this band within spin DFT and leads to a S=1/2 ferromagnetic Stoner insulator. DFT+U opens this gap and leads to Mott insulating behavior, though for sufficiently high U an octahedral phase becomes favored.

Using the known charge density wave of this octahedral phase, we assess the validity of DFT and DFT+U in this class of materials. If realized, trigonal prismatic VS₂ could be experimentally probed in an unprecedented fashion due to its monolayer nature.