Novel Z₂-topological metals and semimetals

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We report two theoretical discoveries for Z₂-topological metals and semimetals. It is shown first that any dimensional Z₂ Fermi surface is topologically equivalent to a Fermi point. Then the famous conventional no-go theorem, which was merely proven before for Z Fermi points in a periodic system without any discrete symmetry, is generalized to that the total topological charge is zero for all cases. Most remarkably, we find and prove an unconventional strong no-go theorem: all Z₂ Fermi points have the same topological charge νZ₂ =1 or 0 for periodic systems. Moreover, we also establish all six topological types of Z₂ models for realistic physical dimensions.