  Study of the Weyl and Dirac topological materials (topological semimetals,
insulators, superfluids and superconductors) opens the route for the
investigation of the topological quantum vacua of relativistic fields. The
symmetric phase of the Standard Model (SM), where both electroweak and chiral
symmetry are not broken, represents the topological semimetal. The vacua of the
SM (and its extensions) in the phases with broken Electroweak symmetry
represent the topological insulators of different types. We discuss in details
the topological invariants in both symmetric and broken phases and establish
their relation to the stability of vacuum.
