| The discovery of exotic topological phenomenon in condensed matter has raised a perspective for enlarging the concept of order in quantum phase, and emerged in search-ing for the nontrivial materials called topological insulators, thus promoted the big de-velopment of physics in early years of 21st century. The concept of topology have became the most exotic feature in different fields of physics:topological photonics, topological semimetal, topological superconductor and so on.In chapter one, first we give a brief introduction to topological order and invariant concepts in condensed matter physics. Then, after a short summary of the development history of topological materials, we introduce the timely hot topics in topological ma-terials:the Dirac semimetal and Weyl semimetal. Finally, we discuss the calculations methods based on first-principles density functional theory.In chapter two, we propose two new kinds of 2D monolayer topological insulators. The first kind is based on rare-earth monopnictide (Sc, Y, La, Yb)-Bi rock-salt structure by first-principles calculations. Band structures with spin-orbit coupling show that there exist band inversions at f point, which reveals the non-trivial topological states. The SOC gap of this system could be as large as 0.38 eV for LaBi monolayer and 0.42 e V for ScBi monolayer, which is higher than room temperature, making the potential applica-tions in low dimensional nano-devices. The second kind is based on 1,4-phenylene di-isocyanide organic molecules and noble metal atoms (gold and silver), realizing the 2-D topological phase. Band structures with nontrivial flat bands and Dirac cones are pos-sible to achieve many exotic phenomenons. Due to its easy fabrication in experiments, our finding lights up a reliable way towards the material realization of the organometal-lic topological insulator.The third chapter is devided into two parts. In part one, we demonstrate the Dirac semimetal state and coexisting topological states in oxygen-deficient pyrochlore lead stannate SnPbO3. We show that SnPbO3 features Dirac points (DPs) at around 1.4 eV above the Fermi level, which can be tuned to the Fermi level by substituting Pb atoms with either Bi or Sb atoms. Based on group theoretical analysis, we also show that the symmetry breaking by the substitution partially opens the DPs, inducing nontriv-ial topological state characterized by a nonzero time-reversal Z2 topological invariant. The new insight from the present work suggests a feasible route to the first material re- alization of nonsymmorphic Dirac semimetals, illuminating the fundamental interplay between crystalline symmetry and topology. In part two, we propose a new family of 3-D Dirac semimetal based on ternary honeycomb XAuTe (X=K, Na, Rb) compounds by first principles calculations, which are proved to be topological Dirac semimetal in which the Dirac points are induced by band inversion. Dirac points with four-fold degeneracy that protected by C3 rotation symmetry locate on the F-A high symmetry path.In chapter four, we give a introduction to different types Weyl semimetals, and by breaking the spatial inversion symmetry, we propose a superlattice structure K(Au0.5 Hg0.5)(Te0.5As0.5) that formed by KHgAs and KAuTe compounds are proved to be a Weyl semimetal with the type II Weyl points, which connect electron-like and holelike bands, in contrast to the isolated Weyl points in type I Weyl semimetal. In this super-lattice structure the six pairs of Weyl nodes dis-tribute along high symmetry path K-F at kz=0 plane.In chapter five, we propose a series of new two-dimensional (2D) half metallic ma-terial based on metal-organic framework (MOF) with honeycomb structure. The MOF is composed by (1,3,5)-Benzenetricarbonitrile (TCB) molecules and noble metal atoms (Au, Cu, Ag). The molecules and the noble metal atoms are connected by cyano-groups (CNs), which not only stabilize the whole structure but also guarantee the electron trans-fer from the metal atoms to the molecules. The transferred electrons on the molecules form local magnetic moments which experience strong ferromagnetic coupling through the noble metal atoms and make the whole system to be half-metallic. |
PDF Full Text Request