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Graphene energy dispersion.

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  1. Jan 6, 2014 #1
    Hi,
    1. The problem statement, all variables and given/known data
    I have two questions, in fact, both involving 2D graphene:
    (1) How may I determine the number of nearest neighbours in a primitive cell of graphene?
    (2) Given that graphene has linear energy dispersion near the fermi level and the dispersion is given by E=(hbar)vF|k|, I would like to determine the density of states. I think it is equal to g(E)=E/2π[itex](hbar)2vF2, but how may I show that?

    I'd appreciate your help.


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 7, 2014 #2
    I suppose I will aid in getting the ball rolling with this. There are a number of ways that you can approach this problem, however, it is rather difficult to help you without a gauge on your level of quantum mechanics.
     
  4. Jan 7, 2014 #3
    Hi,
    I believe I have managed through most of this. I have found the number of near neighbours to be 3. I even managed to nearly prove the required relation. However, what I am lacking is an explanation, or an algebraic proof, why N=total number of states=(A/2π)∗∫[between 0 and k(E)] dkk in the vicinity of the dirac points?
    Also, how may I show that the units of g(E) in the above expression (my first post) are number of states per area per energy?
     
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