Topological Materials, and Realization of Fermion Set: Dirac, Majorana, and Weyl
The last decade has witnessed great advances in discovery of materials with unconventional band structures, forming a field named topological materials. The topological materials are characteristic of symmetry-protected boundary states such as the end state in one dimension, the edge states in two dimensions, and the surface states in three dimensions. These boundary states are the consequence of unconventional band structures of the bulk, instead of the boundary condition of systems. Up to now a series of topological materials have been discovered experimentally, such as topological insulators, quantum spin Hall system, and topological Weyl semimetals. As one of the applications these materials provide platform to realize the long sought elementary particles in high-energy physics, such as relativistic Dirac fermions, Weyl fermions, and even possible Majorana fermion. In this talk I shall start with a one-dimensional dimer model, and introduce the basic concepts and intuitive pictures of topological materials. Then I shall show how to generalize it from one dimension to three dimensions, and from insulators to superconductors, and even photonic crystals. Finally I demonstrate how to realize the fermion set as emergent quasiparticles in solid-state systems and photonic crystals.