Translation-invariant topological superconductors on a lattice
Su-Peng Kou, Xiao-Gang Wen
DOI 10.1103/PhysRevB.82.144501 · Physical Review B
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Abstract
In this paper we introduce four Z2 topological indices ζk=0,1 at k=(0,0), (0,π), (π,0), and (π,π) characterizing 16 universal classes of two-dimensional superconducting states that have translation symmetry but may break any other symmetries. The 16 classes of superconducting states are distinguished by their even/odd numbers of fermions on even-by-even, even-by-odd, odd-by-even, and odd-by-odd lattices. As a result, the 16 classes topological superconducting states exist even for interacting systems. For noninteracting systems, we find that ζk is the number of electrons on k=(0,0), (0,π), (π,0), or (π,π) orbitals (mod 2) in the ground state. For three-dimensional superconducting states with only translation symmetry, topological indices give rise to 256 different types of topological superconductors.
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