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Deriving electrical conduction in 2d crystal

  1. Jun 27, 2009 #1

    I want to derive the conductivity of graphene.
    I'm looking for a formula of the sort:

    [tex]J = \frac{e}{\hbar} n \frac{dE}{dk} D(E) \Delta E[/tex]
    [tex]\frac{1}{\hbar} \frac{dE}{dk}[/tex]
    is the electron velocity,
    [tex]D(E) = \frac{dN}{dE}[/tex]
    is the density of states,
    [tex]\Delta E[/tex]
    might be the applied voltage.
    is the free electron density,
    is the current density and
    [tex]e[/tex] is the electron charge.

    Last edited: Jun 27, 2009
  2. jcsd
  3. Jun 27, 2009 #2
    Have you looked at the Boltzmann semi-classical theory of transport?
  4. Jun 28, 2009 #3
    Well I just did but it's a but too much for me. I just want a simple formula for 2D crystals like graphene.
  5. Jun 29, 2009 #4
    Well, transport is a difficult topic. You could try working out the equivalent of the Drude formula for 2D, which shouldn't be hard, but you are going to need a value for the mean free path or time, which is not trivial to compute. And it may not work well for graphene.
  6. Jun 29, 2009 #5
    Okay thanks. I'll try working it out on my own now.
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