Multiple topological Dirac cones in a mixed-valent Kondo semimetal: g-SmS

We demonstrate theoretically that the golden phase of SmS ($g$-SmS), a correlated mixed-valent system, exhibits nontrivial surface states with diverse topology. It turns out that this material is an ideal playground to investigate different band topologies in different surface terminations. We have explored surface states on three different (001), (111), and (110) surface terminations. Topological signature in the (001) surface is not apparent due to a hidden Dirac cone inside the bulk-projected bands. In contrast, the (111) surface shows a clear gapless Dirac cone in the gap region, demonstrating the unambiguous topological Kondo nature of $g$-SmS. Most interestingly, the (110) surface exhibits both topological-insulator-type and topological-crystalline-insulator (TCI)-type surface states simultaneously. Two different types of double Dirac cones, Rashba-type and TCI-type, realized on the (001) and (110) surfaces, respectively, are analyzed with the mirror eigenvalues and mirror Chern numbers obtained from the model-independent \emph{ab initio} band calculations.