Charge density wave metallic surfaces

Besides magnetic perturbations and electron-lattice interactions, there are other instabilities in solids which have to be considered. For example, one-dimensional solids cannot be metallic since a periodic lattice distortion (Peierls distortion) destroys the Fermi surface in such a system. The perturbation of the electron states results in charge-density waves (CDW), involving a periodicity in electron density in phase with the lattice distortion. Blue molybdenum bronzes, K0.3M0O3, show such features (see Section 4.9 for details). In two- or three-dimensional solids, however, one observes Fermi surface nesting due to the presence of parallel Fermi surface planes perturbed by periodic lattice distortions. Certain molybdenum bronzes exhibit this behaviour. 

In a metal, the superposition of many electron-hole pairs leads to a wave-like disturbance of the charge density at the surface. This disturbance is called the surface plasmon. Its frequency is related to the bulk plasma frequency co/, as co, = oj/,/V2. The existence of both surface and bulk plasma excitation was detected under conditions of electron-beam or photon excitation, and their corresponding energies are in the range of 5-20 eV (8-32 x 10 J). 

Plasmons exist in bulk metal, metal surfaces as well as in metal nanoparticles and are based on the coherent oscillations of (i)-electrons under the influence of an external photon field. In fhe case of a bulk metal a collective charge density wave in the electron gas is built up and its plasmon frequency lies in the range of UV light. Above this plasma frequency the radiation is partly absorbed or transmitted, since the electrons in the field cannof follow fhe incidenf field. Its frequency is simply to fast for the electrons to respond. Below the plasma frequency, the incoming field is screened by the electrons and oscillates. As a consequence, the incoming radiation is... 

The simplest of the simple metals, in many respects, are the alkali metals. Not only are the bands of nearly-free-electron form, but since there is only one electron per atom, this means that the first Brillouin zone is only half filled and all of the gaps in the band structure lie above the Fermi level, resulting in a relatively undistorted Fermi surface, as illustrated in Figure 17. Lee has recently reviewed both theory and experiment for the alkali metals (particularly Fermi surface data). He concludes that, with few exceptions, the experimental evidence is consistent with the straightforward NFE band picture, rather than the spin-density-wave or charge-density-wave models which have been advanced to explain supposed discrepancies. 

When the atom comes closer to the metal surface, the electron wave functions of the atom start to feel the charge density of the metal. The result is that the levels 1 and 2 broaden into so-called resonance levels, which have a Lorentzian shape. Strictly speaking, the broadened levels are no longer atomic states, but states of the combined system of atom plus metal, although they retain much of their atomic character. Figure A.9 illustrates the formation of broadened adsorbate... 

Fig. 2-10. Profile of electron density and electronic potential energy across a metal/vacuum interface calculated by using the jellium model of metals MS = jellium surface of metals Xf = Fermi wave length p. - average positive charge density P- s negative charge density V = electron exchange and correlation energy V, - kinetic energy of electrons. [From Lange-Kohn, 1970.]...

On surfaces of some d band metals, the 4= states dominated the surface Fermi-level LDOS. Therefore, the corrugation of charge density near the Fermi level is much higher than that of free-electron metals. This fact has been verified by helium-beam diffraction experiments and theoretical calculations (Drakova, Doyen, and Trentini, 1985). If the tip state is also a d state, the corrugation amplitude can be two orders of magnitude greater than the predictions of the 4-wave tip theory, Eq. (1.27) (Tersoff and Hamann, 1985). The maximum enhancement factor, when both the surface and the tip have d- states, can be calculated from the last row of Table 6.2. For Pt(lll), the lattice constant is 2.79 A, and b = 2.60 A . The value of the work function is c() w 4 cV, and k 1.02 A . From Eq. (6.54), y 3.31 A . The enhancement factor is... 

Theoretically, SPW is described as a charge density oscillation that goierates highly confined electromagnetic fields on the surfoce of a metal film (24, 26, 31-35). The criterion for the excitation of SPW is that the incident laser beam must be matched in both frequency and momentum with that of SPW. This can only occur, for example, if P wave (TM wave) is incident from the glass side at a specific angle of which the projection of k vector of the incident photon matches SPW s k vector (26, 36, 37). The dispersion relation for a semi-infinite metal plane surface of... 

---