Projected bulk band structure

In many cases there are electronic states with a strong weight in the surface layer, but which are not located in a gap of the projected bulk band structure. The electrons in these states can decay into bulk states much faster than those occupying pure surface states. These states are known as surface resonances. One of these cases occur in the Ru(0001) surface. 

The required 2D nearly free electron gas is realized in Shockley type surface states of close-packed surfaces of noble metals. These states are located in narrow band gaps in the center of the first Brillouin zone of the (lll)-projected bulk band structure. The fact that their occupied bands are entirely in bulk band gaps separates the electrons in the 2D surface state from those in the underlying bulk. Only at structural defects, such as steps or adsorbates, is there an overlap of the wave functions, opening a finite transmission between the 2D and the 3D system. The fact that the surface state band is narrow implies extremely small Fermi wave vectors and consequently the Friedel oscillations of the surface state have a significantly larger wave length than those of bulk states. 

Figure 14-7. Surface band structures for the configurations 1-1,1-2, F-l and F-2 at 0.125 ML. The shaded areas represent the projected bulk band structure, while surface states are shown as solid lines...

Where possible, a comparison with theoretical results and the projected bulk band structure has been presented. 

Fig. 5.2-39 Surface band structure of GaAs(l 10). Comparison between theoretical structure (continous brown line) and experimental determinations KRIPES filled and open circles), ARUPS dashed line), and two-step photoemission triangles). It can be noticed that the surface states nearly coincide with the band edges of the projected bulk band structure [2.63-67]...

The combination of photoemission and inverse photoemission provides a general picture of the 5d/6s gadolinium band structure along the F-A direction of bulk Brillouin zone, as is summarized in fig. 10. As previously pointed out, fig. 10 makes clear that the surface states fall into a gap of the projected bulk band structure. Note that while the... 

Figure 5.16 Projected bulk band structures (PBS) of Cu(OOl), Cu(llO), and Cu(lll) along hIgh-symmetry lines of the two-dimensional surface Brillouin zones. Gaps In the PBS are Indicated by white...

Figure 6.2 Projected bulk band structure (shaded areas) for the Cu(lll) and Cu(lOO) surfaces with intrinsic Shock-ley surface-state bands (n = 0) and image-potential bands (n > 1). Arrows indicate possible electron-electron (ee), electron-phonon (ep), and defect (def) scattering processes.

Figure 2.24 Surface-projected bulk band structure for a 12-layer Cu(lll) slab as computed from a plane-wave pseu-dopotentlal DFT calculation within the LDA (computed by the authors).

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