First-principles Studies of Lattice Vibration and Electron Topology

Abstract

Quantum theory stands as a cutting-edge theory for unravelling properties of matter in contemporary science. It furnishes a framework beyond classical physics, enabling us to describe the exotic behaviour of electrons, the fundamental particles that compose matter, and phonons, the elementary energy that constitutes vibration. More importantly, the integration of quantum theory into high-performance computing technology has given rise to the first-principles study, i.e. harnessing numerical algorithms and supercomputing power to solve the quantum equations governing the system of interest directly. This research paradigm liberates us from reliance on phenomenological models and empirical parameters, empowering the investigation of real-world materials from their microscopic origins with unprecedented precision. Based on the above background, this thesis presents a theoretical study of phonons and their coupling to electrons (main thread I), and topology in electronic structures (main thread II). In main thread I, a non-uniform phonon sampling scheme based on non-diagonal supercells is proposed for the first time, which minimises the computational cost of phonon calculations and provides higher momentum resolution. Through this approach, we demonstrate that an accurate description of phonons in heavy metal compounds In5Bi3 and CeH9 necessitates the incorporation of advanced electronic structure theories. The former requires considering the relativistic effect of electrons, while the latter needs to include electronic correlation exhaustively. In main thread II, we showcase the material realisations of Hamiltonians with non-trivial topology. We reveal the electronic structures of ReO3 and Cd2Re2O7 as ideal platforms for observing the Chern class and Euler class respectively. The former manifests itself as a series of high-chirality Weyl nodes protected by hexagonal screw symmetry, while the latter involves the braiding of Weyl nodes across the Brillouin zone through a phase transition. At the convergence of these two main threads, we explore the role of temperature on topological insulators, using the transition metal dichalcogenide monolayers MX2 (where M=W, Mo and X=S, Se) as examples. We find that electron-phonon coupling promotes the topologically non-trivial band gap while thermal expansion acts as a counteracting effect.