Surface Brillouin zone SBZ

Figure 14. (a) Schematic of the direct lattice for the (001) surface of the rocksalt structured crystal of Fig. 13 with the bulk unit cell indicated by dashed lines and a surface unit cell by solid lines. The high-symmetry directions for this surface, <100> and <110>, are indicated with arrows. (b) The reciprocal lattice corresponding to the direct lattice in panel a is shown with the first surface Brillouin zone (SBZ) indicated by Mlid lines. The shaded triangular region, FXM, is the irreducible portion of the SBZ, from which the entire SBZ can be constmcted by synunetry. 

The truncation of the lattice and/or the reconstruction and relaxation cause the electronic states at the surface or in the uppermost layers to be distinctly different from those of the bulk. Such new states are called surface states. Their wave functions decay exponentially on both sides of the surface. Since their k is imaginary, the surface band structure is defined in the surface Brillouin zone (SBZ), which is the projection of the 3-D Brillouin zone onto the surface plane. The projection of the bulk bands onto the SBZ is called the projected band structure. When the energy of a surface state is localized in a gap of the projected bulk structure (either an absolute gapp, i. e. one that extends throughout the whole SBZ, or a partial gap), one speaks of a true (or bona fide) surface state. When there is degeneracy (both in energy... 

Fig. 1. Surface Brillouin Zone (SBZ) for the low MiUer index surfaces of face centred cubic (fee) and body centred cubic (bcc) lattices discussed in the present review.

---