Fermi surfaces of the two-dimensional surface states on vicinal Cu(111)

The Shockley $(L$-gap) surface states on Cu(111) and the vicinal (332) and (221) surfaces have been mapped by angle-scanned ultraviolet photoelectron spectroscopy. We find two-dimensional (2D) surface states on both vicinal surfaces. An analysis of the photoemission line shape that includes the effects of the terrace width distribution indicates an isotropic reduction of the photohole lifetime on the vicinal surfaces and allows us to quantify the intrinsic initial-state dispersion. For the larger step-step separation of $12\hspace{0.5em}\AA$ on Cu(332), the Fermi contour shows the characteristic elliptical shape of a 2D Bloch state in a 1D lattice. On Cu(221) with $7.7\hspace{0.5em}\AA$ terraces we find an isotropic dispersion within the accuracy of the experiment. These findings are interpreted as a continuous surface state to surface resonance transition with decreasing terrace length. The effective step potential is estimated using a simple perturbation theory ansatz.