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Topological crystalline insulators (TCIs) are classified by topologicalinvariants defined with respect to the crystalline symmetries of their gappedbulk. The bulk-boundary correspondence then links the topological properties ofthe bulk to robust observables on the edges, e.g., the existence of robust edgemodes or fractional charge. In one dimension, TCIs protected by reflectionsymmetry have been realized in a variety of systems where each unit cell hasspatially distributed degrees of freedom (SDoF). However, these realizations ofTCIs face practical challenges stemming from the sensitivity of the resultingedge modes to variations in edge termination and to the local breaking of theprotective spatial symmetries by inhomogeneity. Here we demonstratetopologically protected edge states in a mono-atomic, orbital-based TCI thatmitigates both of these issues. By collapsing all SDoF within the unit cell toa singular point in space, we eliminate the ambiguity in unit cell definitionand hence remove a prominent source of boundary termination variability. Thetopological observables are also more tolerant to disorder in the orbitalenergies. To validate this concept, we experimentally realize a lattice ofmechanical resonators where each resonator acts as an "atom" that harbors twokey orbital degrees of freedom having opposite reflection parity. Ourmeasurements of this system provide direct visualization of the$sp$-hybridization between orbital modes that leads to a non-trivial bandinversion in the bulk. Furthermore, as the spatial width of the resonators istuned, one can drive a transition between a topological and trivial phase. Inthe future we expect our approach can be extended to realize orbital-basedobstructed atomic insulators and TCIs in higher dimensions.

A mono-atomic orbital-based 1D topological crystalline insulator