Unveiling the Hidden Spin-Polarized Bi(110) Surface States by Spin-Resolved Photoemission.

The full three-dimensional spin texture of the Bi(110) surface states has been investigated by means of spin- and angle-resolved photoemission spectroscopy. The observed complex in-plane spin texture is in basic agreement with the prior reports and first-principles calculations, and the previously unreported out-of-plane spin polarization (P_{Z}) is observed to be substantial. More significantly, the P_{Z} texture exhibits an unexpected breaking of spin degeneracy at the Brillouin zone boundary, in contradiction to standard symmetry-based expectations. Our first-principles calculations reveal that the anticipated vanishing of P_{Z} arises from the quantum interference between two surface wave functions propagating with opposite out-of-plane spin polarizations. These findings strongly suggest that the photoemission process selectively probes one of them, exposing the hidden P_{Z} polarization of the surface wave function; i.e., the apparent spin vanishing is not due to an absence of polarization, but rather results from interference at the wave function level.