Microscopic study of quantum spin Hall effect : Time-reversal symmetry and topological invariants

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The spin Hall effect is a newly-discovered topological matter. The concenpt of topological matter has quite recently been gneneralized to topological insulators and superconductors, and attracting much current interest. In particular, I study the relationship between the defects and emergence of zero modes, using so-called index theorems. To be conctrete, I extend the index theorem to time-reversal invariant systems, and also apply the index theorem to superconductors of Dirac fermions with various kinds of defects.