Advanced Solid State Physics

Figure 104: Dielectric response of an insulator. The dotted line represents the real part, the solid line
the imaginary part.

frequencies. As a resultan insulator reflects incoming waves at particular frequencies where
the dielectric constant is below 0.

With eqn. (214) and the static dielectric constantst = (ω = 0)we get

(ω) = ∞+

(st−∞)ω 02 (ω 02 −ω^2 +iωb)

(ω^20 −ω^2 )^2 +ω^2 b^2

(216)

Now it is possible to do some quantum calculations. There is a coupling between electromagnetic
waves and electron states. When light hits the crystal, absorption is possible, which means that an
electron of the filled state goes to an empty state. With Fermi’s golden rule it is possible to calculate
the transition rate of this process. The couplings of the initial state and the final state has to do
with the dipole moment, which means that the oscillator strength (eqn. (217)) is proportional to the
tunneling rate.

 = 1 +χ = 1 +

P

 0 E

= 1 +

ne^2

 0 m

∑

i,k

fik

ω^2 ik−ω^2

(217)

with the Oscillator strengthfik:

fij =

2 m

~

ωik|(rik)|^2

Fig. 105 shows an example of such calculations with two harmonic oscillators (2 frequencies). For real
materials it’s common that there are more than one residents.

Another example would be an infrared absorption of very thin materials, which is shown in fig. 106.
Every peak stands for a certain mode with a certain frequency. At theses frequencies there is a resident
and as a result an energy loss (absorption).