One-dimensional versus two-dimensional surface states on stepped $\mathrm{Au}\mathrm{}\left(111\right)\mathrm{}$

Surface states at vicinal Au(788) and Au(322) have been investigated with angle-resolved photoemission and synchrotron radiation. Both surfaces are characterized by highly regular one-dimensional step arrays with relatively wide (∼3.9 Å) or narrow (∼1.3 Å) terraces in Au(788) and Au(322), respectively. Depending on the terrace size we observe that surface electrons behave in a completely different way. In Au(788) terraces become one-dimensional, lateral quantum wells that confine surface electrons between adjacent steps. In Au(322) surface electrons propagate across the step array forming two-dimensional superlattice bands. By tuning photon energy and angle we probe fundamental properties of the electron wave functions in both cases.