Introduction to the tenfold classification of topological insulators and superconductors
The tenfold classification of topological insulators and superconductors can be understood in several different approaches, such as K-theory and nonlinear sigma model. It is known that nontrivial topological insulators and superconductors possess stable gapless boundary modes. In this talk, I will try to classify topological phases under time-reversal symmetry, particle-hole symmetry, or chiral symmetry by using the simplest approach, which is the stability of gapless boundary modes under symmetries. That is, we will write down gapless boundary Hamiltonians in the Dirac form and then study the existence of gap opening terms. The absence of the gap opening terms leads to nontrivial topology.
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