Topological Classification Table Implemented with Classical Passive Meta-Materials

Topological condensed matter systems from class A and class AII of the classification table have received classical electromagnetic and mechanical analogs. They topological phases exhibit protected wave-guiding which has been demonstrated experimentally. In this talk, we introduce a map which generates classical analogs for all entries of the classification table, using only passive elements. Physical mechanical models can be realized for all strong topological phases in dimension 2, as well as for three classes in dimension 3. As an example, we will show how the Kitaev topological super-conducting chain and it's braiding properties can be realized in classical systems.