Abstracto
- Topological materials and topological phases of matter are of unique interest to fundamental sciences and advanced technologies. They exhibit conducting states at the surface or edge and insulating states in the bulk of the material which are protected by symmetries and topological invariants. Ergo, topological materials are robust against perturbations and dissipations. These features are extremely attractive for the development of topological quantum devices. However, the control and diagnosis of topological phases and transitions still are in their early phase and demand intense research. High-order harmonic generation (HHG) produced by the interaction of a strong mid-infrared laser with solids is becoming a unique tool to explore the ultrafast electron dynamics and the electronic structure. In this chapter, we will review the recent theoretical and experimental efforts in studying topological materials via the application of attosecond physics tools. We will start with the paradigmatic topological Haldane model and show how the helicity and circular dichroism of the HHG spectra can contain information on the topological phases and transitions of this model. We will review the recent experiments of HHG in 3D topological insulators, how HHG is used to diagnose these materials, and the ultrafast lasers control the topological phases.