Figure 94: Semiconductor at low temperature: P in Si.and become one big crystal and the conductivity gets better. If they are weakly coupled the electrons
get localized on the crystals as they are cooled down and the material becomes an insulator. In order
to understand the Mott transition, we start with the description of a tunnel junction.
12.3.2 Peierls Transition
The transition at low temperature from a metal state to an insulator state is called Peierls transition.
This Peierls transition gain from an electron-phonon interaction and happens inquasi-one dimen-
sional metals. Those materials are three dimensional crystals with a certain chain length structure
which have much better conductivity in one direction than in the other one.
One way to understand this theory is to consider a one dimensional lattice of atoms with a lattice
constantaas shown in fig. 97. Fig. 98 shows a periodic distortion of this one dimensional lattice with
a periodicity of 2 a(new lattice constant). This kind of distortion is calleddimerization.