11.5 Occupation
If there aren’t any electron-electron interactions (free electron model) the probability of occupation is
given by the Fermi Dirac distribution. Now (including electron-electron interactions) this isn’t correct
anymore, which means that the probability now depends on thetemperatureandonthe other
occupied states. This means that at zero temperature the probability function may look similar to
the Fermi Dirac distribution for temperatureT > 0.
Fig. 82 (left) shows a High Temperature Superconductor likeY Ba 2 Cu 3 Ox. The x-axis presents the
doping (the doping ofOx;x...doping) the, y-axis presents the TemperatureT. The change of these
two variables changes the characteristic of this material completely. For instance high doping and low
temperature will be a Fermi liquid (like discussed above), less doping will lead to a mott insulator.
The right plot of fig. 82 showsCeCoIn 5 −xSnxwith different doping ofIn. The y-axis again presents
the temperatureT, the x-axis the magnetic fieldH. This material has three different phases with
different properties. These phases are:
SC ... Superconductor
NFL ... Non Fermi Liquid
FL ... Fermi Liquid
Figure 82: left: Probability of a High Temperature Superconductor likeY Ba 2 Cu 3 Ox; right: Differ-
ent phases ofCeCoIn 5 −xSnx. SC...Superconductor, NFL...Non Fermi Liquid, FL...Fermi
Liquid
A good way understanding certain materials is to analyze the resistanceρversus temperatureT as
shown in fig. 83. Important to understand is that above the Debye temperature all phonon modes
are excited and as a result the resistance increases linear with the temperature.
Also shown in fig. 83 is a specific resistance atρ= 150μΩcm. In this region it is possible to describe
Transition metals. Important to describe is the resistance at room temperature: