Bulk‐Boundary Correspondence of Semimetal Ru ₃ Sn ₇ and Topological Surface States on Chemically Realistic Terminations

Abstract Ru ₃ Sn ₇ is experimentally demonstrated as an efficient catalyst, with potential utilization of topological surface states for hydrogen evolution reaction. Despite its promising catalytic performance, the topological nature of Ru ₃ Sn ₇ remains uncertain. Particularly, the bulk‐boundary correspondence has not yet been established, hence hindering a rigorous justification of its topologically‐protected surface states. In this work, the bulk topology of Ru ₃ Sn ₇ is detailed using first‐principles calculations and the topological quantum chemistry formalism. Ru ₃ Sn ₇ turns out to be an enforced semimetal possessing symmetry‐protected crossings within a set of bands near the Fermi level, which are enforced and prescribed by the violations of symmetry‐prescribed compatibility relations. Moreover, the surface states and the associated origin from the same set of entangled bands are identified, thereby establishing the bulk‐boundary correspondence. To evaluate the effects of chemical modifications, the response of topological surface states to various surface terminations, stoichiometry, and oxidation is examined. The surface structures are globally optimized, and the phase diagrams for various experimental conditions are built. It is shown that, due to changes in the local chemical environment, the original surface states are significantly altered. Modified surface bands can be observed near the Fermi level on surface terminations that preserve the C _{4 v} symmetry.