# Thread: Crystal Symmetry Problem, Conductivity tensor

1. 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:

σ(k)=e^2·t·v_a(k)·v_b(k)

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

vi=(1/h)(∂ε(k)/∂k_a)

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?

Thank you!!!!!

2. Originally Posted by Juanchotutata
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:

σ(k)=e^2·t·v_a(k)·v_b(k)

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

vi=(1/h)(∂ε(k)/∂k_a)

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?

Thank you!!!!!
Hint: Is there a relationship between band structure and effective mass? If so, how might you use it?