Topologically protected states in a 1D monoatomic insulator through s-p orbital hybridization*

Topological crystalline insulators (TCIs) require multiple degrees of freedom (DoF) in every unit cell to support the required band topology, and the typical approach is to realize these DoFs using spatially separated states. However, the definition of the unit cell in such realizations is susceptible to a translation ambiguity, and the topological protection is itself susceptible to the local breaking of the protective spatial symmetries due to inhomogeneity across the material. In this work, we show how both these issues can be overcome by collapsing the spatial DoFs across a unit cell into orbital DoFs at a single site. This approach forbids partial cuts of a unit cell, and the material is also more tolerant to disorder of the mode energies since the orbitals at each atomic site retain exact representations of the reflection symmetry. We support this concept by experimentally realizing the first mono-atomic orbital-based 1D TCI through a mechanical metamaterial approach, in which s and p orbital states are implemented using vibrational modes of a plate structure.