Standard model as the topological material

The 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 detail the topological invariants in both the symmetric and broken phases and establish their relation to the stability of vacuum.