Realistic Electronic Structure Calculations for Quantum Materials

Abstract

A complex arrangement of electronic states within materials can manifest exotic quantum-mechanical effects. These systems are often referred to as quantum materials. Increased understanding of quantum materials has historically lead to the development of new technologies. It is therefore extremely important to develop and test precise methods for calculating the behaviour of electronic states within a material.

For decades, the workhorse of electronic structure calculations has been density functional theory (DFT). DFT is often referred to as a first-principles method because it allows for the calculation of the distribution of electrons throughout a material with only specification of the lattice geometry and atomic components. From the results of a DFT calculation, it is possible to study the orbital character of electronic wavefunctions, topology of electronic band structure, and some aspects of superconductivity. This provides insight into many quantum properties of a system which may otherwise be difficult or impossible to ascertain from experiments. DFT is, however, sometimes limited by the approximations necessary for practical implementation. Further methods have been developed to systematically correct the limitations of DFT. In particular, the combination of DFT with dynamical mean-field theory (DFT+DMFT) is among the most widely accepted methods for correcting the inadequacy of DFT in handling strong electron-electron correlations. In this thesis, I use methods from DFT and DFT+DMFT to study the quantum properties of materials.