ABSTRACT
This chapter describes the construction of the bulk Hamiltonian for two-dimensional (2D) topological insulators (TI), as the forms the foundation for the understanding of the 3D TI and allows one to extrapolate to the construction of more complicated Hamiltonians containing additional symmetries. It focuses on the salient features associated with 2D TIs, including the formation of the metallic spin-polarized edge states and their topological protection. The chapter discusses some of the progress that has been achieved in the field of topological superconductivity within TIs, so as to realize the necessary components for topological quantum information processing. Subsequent to the work on TIs in both 2D and three-dimensional, the notion of topological protection was then extended to encompass topological phases of matter that are protected by symmetries beyond time-reversal. The helical edge states of 2D TIs are protected against elastic and time-reversal symmetry protecting single-particle perturbations.
