Novel Z(2) Topological Metals and Semimetals

We report two theoretical discoveries for Z(2) topological metals and semimetals. It is shown first that any dimensional Z(2) 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 so that the total topological charge is zero for all cases. Most remarkably, we find and prove an unconventional strong no-go theorem: all Z(2) Fermi points have the same topological charge ν(Z(2))=1 or 0 for periodic systems. Moreover, we also establish all six topological types of Z(2) models for realistic physical dimensions.