1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Graphene energy dispersion.

  1. Jan 6, 2014 #1
    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
    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted