Deriving electrical conduction in 2d crystal

[steenreem]

Hey.

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

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

Thanks,
Remy.

 

[kanato]

Have you looked at the Boltzmann semi-classical theory of transport?

 

[steenreem]

Well I just did but it's a but too much for me. I just want a simple formula for 2D crystals like graphene.

 

[kanato]

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.

 

[steenreem]

Okay thanks. I'll try working it out on my own now.