  The Bi/Si(111) (sqrt{3} x sqrt{3})R30 trimer phase offers a prime example of
a giant spin-orbit splitting of the electronic states at the interface with a
semiconducting substrate. We have performed a detailed angle-resolved
photoemission (ARPES) study to clarify the complex topology of the hybrid
interface bands. The analysis of the ARPES data, guided by a model
tight-binding calculation, reveals a previously unexplored mechanism at the
origin of the giant spin-orbit splitting, which relies primarily on the
underlying band structure. We anticipate that other similar interfaces
characterized by trimer structures could also exhibit a large effect.
