Advanced Solid State Physics

For most metals this plasma frequency is up in the ultraviolet which means that in the visible spectrum
they look shiny but in a frequency range aboveωp they are transparent (see chapter 10). Plasma
waves can be quantized like any other waves and there is a quantum that equals~ωp. This quantum
is called plasmon, it describes oscillations of charges and can be measured with electron energy loss
spectroscopy. Fig. 80 shows the results of an EELS measurement. The peaks correspond to plasma

Figure 80: Results of an EELS measurement

waves with a certain frequency and the spacing between the peaks is the quantum~ωp. But there is a
smaller second peak which is caused by surface plasmons whereas the dominant peak comes from the
bulk plasmons.

11.3.5 Surface Plasmons

The charge could be non-uniform at the surface and electric fields then penetrate into the vacuum.
In general, surface plasmons are waves in the electron density at the boundary of two materials.

metal

vacuum

+

e.m. wave

(a)

metal

+

aptamer

molecule

(b)

Figure 81: a) Surface plasmons; b) Biosensor.

Specifically, waves that propagate along the surface of a metal are a combination of a charge wave in
the metal and an electromagnetic wave in the vacuum above (see fig. 81(a)). Due to that combination
the surface plasmons tend to have a different (lower) frequency than the bulk plasmons. For example,