Optical and Electrical Properties Topological Materials

In this chapter, we present an overview of the structure, optical and electrical properties of materials that exhibit, or are predicted to exhibit, topological properties. We note that many of these materials consist of layers that are bonded by van der Waals forces and many have a local hexagonal structure. The materials are divided into those with a band gap and those without a band gap. We present the definitions of many of the key terms used in the topological description of materials as well as a description of the various types of topological materials such as topological insulators, Weyl semimetals, and Dirac semimetals. A useful and important part of this discussion is topological classification. For example, we describe the topological invariant Z₂. We present a brief overview of a tight binding, second quantization Hamiltonian that includes spin orbit and electron–electron interactions. Then we discuss materials with a band gap including the well-known tetradymites such as Bi₂Se₃ starting with a discussion of the crystal and electronic structure and resulting Z₂ classification. Next we present the optical and electrical properties of these materials. Whenever possible, experimental data for the dielectric functions are shown. Photoluminescence and Raman spectra are also shown, and the layer number dependence of the Raman spectra are discussed. This is followed by a similar discussion of gapped materials including Weyl semimetals, Dirac semimetals, and nodal line materials. When possible, experimental data is discussed in terms of whether or not topological properties are observed.