# Graphene energy dispersion.

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1. Jan 6, 2014

### peripatein

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?

2. Relevant equations

3. The attempt at a solution

2. Jan 7, 2014

### sandy.bridge

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.

3. Jan 7, 2014

### peripatein

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?