Crystal Symmetry Problem

Apr 2018
Hello guys!

I have to solve a problem about crystal symmetry, but I am very lost, so I wonder if anyone could guide me.

The problem is the following:

Using semiclassical transport theory the conductivity tensor can be defined as:


Where e is the electron charge, tau is a constant called relaxation time and vi the group velocity of an electron


Knowing that the system belongs to the P6mm group draw a band diagram for the system with at least 4 special points of the reciprocal cell and, based on it, discuss the components of the conductivity tensor, including the directions along which the system conducts best and worst.

I use a specific program to obtain the band diagram, so that the only thing I have to do (I guess) is to optimize the number of k-points and to enter the band path, in order to obtain the band diagram.

But then, I have a lot of questions. Is there any specific path to study the conductivity? How many bands should I obtain in the diagram? How can I relate the conductivity tensor and the diagram? How do I know the directions along which the system conducts best and worst?

Please, give me a hand :(

Thank you!!!!!