Research On The Topological Semimetal Based On Cold Atomic Optical Lattice

We investigate the characterization of the topological semimetal and the topological invariants in two dimension systems, and discuss the mechanism of phase transition from topological semimetal to topological insulator. The paper is organized as follows: the first chapter, which is the introduction, introduced the mechanism of topological quantum state simply, the development process and characteristic of the semimetal. We also introduce the cold atoms and the present situation of research topological insulator in cold atoms.In the second chapter, we discuss the change of topological nature in the Kagome optical lattice with a periodically shaking field and an onsite interaction. We deduce the p-band model effect Hamiltonian of topological semimetal in two dimension Kagome optical lattice, and calculate the topological invariant i.e. the winding number which is the characterization of topological properties. We also studied how to utilize the mechanism of driving optical lattice in cold atoms to produce the phase transition from topological semimetal to topological insulator.In the third chapter, we discuss the change of topological nature in the Honeycomb optical lattice with a periodically shaking field and an onsite interaction. We deduce the p-band model effect Hamiltonian of topological semimetal in two dimension Honeycomb optical lattice, and present the phase diagram and band structure during the change of the parameters. We utilize the mechanism of driving optical lattice in cold atoms to produce the phase transition from topological semimetal to topological insulator.In the fourth chapter, we put forward a realization of f-band topological semimetal,and analyze the topological characteristics of p, d, and f-band in two dimension topological semimetal.