Topological Classification Table Implemented with Classical Passive Meta-Materials

TL;DR

This paper presents a universal method to realize all topological phases from the classification table using passive classical meta-materials, including novel topological superconducting phases in mechanical systems.

Contribution

It introduces a mapping technique to create classical analogs for all topological phases, expanding the scope to include previously unimplemented topological superconducting phases.

Findings

All strong topological phases in 2D are realized mechanically.

Classical analogs for three 3D topological classes are demonstrated.

Includes the first classical realization of topological superconducting phases.

Abstract

Topological condensed matter systems from class A and class AII of the classification table have received classical electromagnetic and mechanical analogs and protected wave-guiding with such systems has been demonstrated experimentally. Here we introduce a map which generates classical analogs for all entries of the classification table, using only passive elements. Physical mechanical models are provided for all strong topological phases in dimension 2, as well as for three classes in dimension 3. This includes topological super-conducting phases, which have never been attempted with classical systems.