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Thread: Crystal Symmetry Problem, Conductivity tensor

  1. #1 Crystal Symmetry Problem, Conductivity tensor 
    Junior Member
    Join Date
    Apr 2018
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    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^2tv_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?

    Please, give me a hand

    Thank you!!!!!
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  2. #2  
    Senior Member
    Join Date
    Jan 2013
    Posts
    427
    Quote Originally Posted by Juanchotutata View Post
    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^2tv_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?

    Please, give me a hand

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

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