Electron Wave Function at a Vicinal Surface: Switch from Terrace to Step Modulation

Abstract

The Cu(111) surface state has been mapped for vicinal surfaces with variable step densities by angleresolved photoemission. Using tunable synchrotron radiation to vary the k dependence perpendicular to the surface, as well as the k k dependence, we find a switch between two qualitatively different regimes at a miscut of 7 ± (17 Å terrace width). For larger miscut angles the step modulation of the wave function dominates, and for smaller miscut angles the terrace modulation dominates. These observations resolve an apparent inconsistency between prior photoemission and STM results.

One-dimensional versus two-dimensional electronic states in vicinal surfaces

“…In reality, the 1D or 2D nature appears unambiguously defined in surfaces with very large or very small d values, respectively. A less clear behaviour is found for intermediate d values [4,5], [11]- [14]. A number of different explanations have been given to explain this 1D-2D transition, and all of them lead to similar critical values around d c ∼ 20 Å for both Au(1 1 1) and Cu(1 1 1) vicinal surfaces.…”

“…By changing the miscut angle, the surface plane rotates and hence the band projection along the SBZ. At a small miscut, an effective bulk-surface overlap is also possible at the L point via 2π/d step lattice umklapp [4], as shown in figure 7(b). For larger miscuts, as the projected band gap shrinks, there is an increasing overlap of projected bulk states with surface state Fourier components from L to .…”

“…Probably the most interesting observation concerns the change in the dimensionality of the surface state as one varies the superlattice constant d of the step array, as schematically depicted in figure 1. For relatively small d, surface states display electron propagation across the steps, and hence 2D behaviour [4,5,7,8]. In contrast, step arrays with large d lead to weakly dispersing bands, i.e.…”

“…A number of different explanations have been given to explain this 1D-2D transition, and all of them lead to similar critical values around d c ∼ 20 Å for both Au(1 1 1) and Cu(1 1 1) vicinal surfaces. They include the finite coherence length of the surface state [4], the Fermi wavelength of surface electrons [13] and the onset of overlap with bulk states [4,5,7]. The latter is a consequence of the progressive formation of a surface resonance as the projected bulk band gap around the Fermi energy closes [11].…”

“…In the past few years, a number of works have been devoted to the study of surface states in step arrays of Au and Cu surfaces vicinal to the (1 1 1) plane using angle-resolved photoemission spectroscopy (ARPES) [4]- [13] and scanning tunnelling microscopy (STM) [14,15]. Probably the most interesting observation concerns the change in the dimensionality of the surface state as one varies the superlattice constant d of the step array, as schematically depicted in figure 1.…”