Topological Insulators and Superconductors

Topological insulators and superconductors are new quantum states of matter that are characterized by nontrivial topological structures of the Hilbert space. Recently, they attract a lot of attention because of the appearance of exotic quasiparticles such as spin-momentum-locked Dirac fermions or Majorana fermions on their edge/surface, which hold promise for various novel applications. In particular, localized Majorana zero modes are expected to obey non-Abelian statistics and enable topological quantum computing. In this colloquium, I will introduce the basics of these materials and present some of the contributions we have made in this new frontier. In addition, I will discuss how one can conceive to build topological qubits based on Majorana zero modes and demonstrate the non-Abelian statistics.