Classification of topological insulators and superconductors in three spatial dimensions

  title={Classification of topological insulators and superconductors in three spatial dimensions},
  author={Andreas P. Schnyder and Shinsei Ryu and Akira Furusaki and Andreas W. W. Ludwig},
  journal={Physical Review B},
We systematically study topological phases of insulators and superconductors (or superfluids) in three spatial dimensions. We find that there exist three-dimensional (3D) topologically nontrivial insulators or superconductors in five out of ten symmetry classes introduced in seminal work by Altland and Zirnbauer within the context of random matrix theory, more than a decade ago. One of these is the recently introduced ${\mathbb{Z}}_{2}$ topological insulator in the symplectic (or spin-orbit… 

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