It has come to my attention that there is a common mistake by people calculating the dielectric constant.
The problem is that they find a weird scaling of the dielectric constant with respect to system size (as it should not scale with the system size in isotropic material), and I will here try to explain why this the case.
The OpticalSpectrum has two parameters for control the number of bands to include in the Kubo-Greenwood calculation, and by default these are both 4. For most semi-conductors this is very sufficient, however if the semi-conductor is repeated people have observed a different between the repeated and unrepeated system. This can easliy be fixed by increasing the number of bands to include.
I have created a small case study to create demonstration of the problem and the solution. The system being modeled is atomic carbon chain. In the first picture "unrepeated_singleband.png" you will see the imaginary part dielectric constant for this system plotted against the bandstructure for the same system. You will see a dramatic increase in the imaginary part of the dielectric constant at around 7 eV. When comparing this to the bandstructure it becomes clear that this optical process is related to the electrons in the gamma of the Brillouin zone. As the title of the file says we have only included one band of valence and conduction in the calculation.
The system is then doubled in size, and as excepted there is band folding, and if we only allow a single valence band and conduction band, then at the Gamma point there is energy difference between for the highest valence band and lowest conducting band around 3 eV, but this optical transition is prohibited due to the symmetry (It is the same band zone folded),
and therefore the imaginary part of the dielectric constant is zero for all energies.
This can be seen in "repeated_singleband.png".
If the number of bands in increased in this calculation to include more valence bands and conduction bands, we see that we get the exact same dielectric constant for the repeated/unrepeated system. This can be seen in "repeated_multiband.png"
I have attached a small script for generating these plots if you want to try to yourself.
