Spin-polarized saddle points in the topological surface states of elemental bismuth revealed by pump-probe spin- and angle-resolved photoemission spectroscopy

We use pump-probe, spin- and angle-resolved photoemission spectroscopy (ARPES) with a 10.7 eV laser accessible up to the Brillouin zone edge, and reveal the entire band structure around the Fermi level, including the unoccupied side, for the elemental bismuth (Bi) with the spin-polarized surface states. Our data identify Bi as in a strong topological insulator phase (${Z}_{2}=1)$ against the prediction of most band calculations. We unveil that the unoccupied topological surface states possess spin-polarized saddle points yielding the van Hove singularity. The unique feature provides an excellent platform for the future development of optospintronics.