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theses

In this thesis, we study the properties of topological materials using theoretical techniques such as first-principles calculations and tight-binding models. In the first part of the thesis, we deal with the phase transitions in 3D topological insulators. We first study the topological phase transitions in In- and Sb-doped Bi2Se3, where distinct behaviors are found. In the In-doped case, we find that the In 5s orbitals destroy the topological phase at low impurity compositions, and the phase transition is better described by a local percolation scenario. On the other hand, the Sb-doped Bi2Se3 is well described by a "linear-gap-closure" picture, where the phase transition is dominated by the gradual decrease of the effective spin-orbital coupling. We also discuss the Weyl semimetals emerging from noncentrosymmetric topological insulators. We first clarify the previous theory, and prove that an intermediate Weyl semimetal must show up through the phase transition from a 3D topological to normal insulator. Then we propose LaBi1−xSbxTe3, LuBi1−xSbxTe3 and pressurized BiTeI as possible candidates of Weyl semimetals. The second part of the thesis is focused on method development. We first propose a quantitative definition for the band inversions driven by spin-orbit coupling in insulators, known as the ``spin-orbit spillage". The spin-orbit spillage has been applied to various topological systems, which turns out to be a useful tool for the identification of topological characters in band theory. In the last chapter of the thesis, we develop a new method for calculating the Chern-Simons orbital magnetoelectric coupling in 3D insulators. The contributions from the gauge discontinuity and the "vortex loops" are taken into account in our method. The former is expressed as a 2D integral over a k plane across which the gauge of the occupied Bloch functions become discontinuous, while the latter is expressed as the Berry phases around 1D "vortex loops" lying in the gauge-discontinuity plane. Our method is successfully applied to the Fu-Kane-Mele model with the breaking of time-reversal symmetry.

ETD_6659

doi:10.7282/T3ZP4849

Ph.D.

Includes bibliographical references

by Jianpeng Liu

ETD doctoral

The author owns the copyright to this work.