Design Of New Two-Dimensional Topological Insulators

Topological insulator has become a research focus of condensed matter physics and materials physics, due to the feature that its interior and surface present insulation state and conductor state respectively. Scientists believe that topological insulator has excellent prospects in many fields like new device design. In recent years, the research on special topology order of assumed material, like’Z2 number’, has become an important field of condensed matter theory and computational physics.The work in this dissertation is validation and design on a new type of topological insulator which has the topological invariants of Z2。First of all, I focused on the related algorithm solution of phonon spectrum by using Herman-Feynman force. In addition, I used the method of non-diagonal supercell extension to increase the calculation precision of the phonon spectrum for the hexagonal symmetry of the crystal material. The calculation of phonon provides a nice basis to test and verify existence and manufacturing feasibility of an assumed material. Secondly, I designed a new topological material called delta graphyne. The material has a lower energy when compared with other allotropes,and it shows stable state validated by phonon spectrum. We can use Z2 features number algorithms to verify its topological properties, as the material has space inversion symmetry, and it passed the verification. Finally, I use tight-bind model to analyze the influence on band by spin-orbit coupling, exploring its topological property further.The purpose of this work is to search for the topological properties of new materials with dynamical stability. From the work, not only a new model of topological material is provided, but also the theory on topological properties is studied.