Strong Electron Confinement By Stacking-fault Induced Fractional Steps on Ag(111) Surfaces

The electron reflection amplitude $R$ at stacking-fault (SF) induced fractional steps is determined for Ag(111) surface states using a low temperature scanning tunneling microscope. Unexpectedly, $R$ remains as high as $0.6\sim 0.8$ as energy increases from 0 to 0.5 eV, which is in clear contrast to its rapidly decreasing behavior for monatomic (MA) steps [L. B{"u}rgi et al., Phys. Rev. Lett. $\mathbf{\text{81}}$, 5370 (1998)]. Tight-binding calculations based on {\em ab-initio} derived band structures confirm the experimental finding. Furthermore, the phase shifts at descending SF steps are found to be systematically larger than counterparts for ascending steps by $\approx 0.4 \pi$. These results indicate that the subsurface SF plane significantly contributes to the reflection of surface states.