# Deriving electrical conduction in 2d crystal

1. Jun 27, 2009

### 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.

Last edited: Jun 27, 2009
2. Jun 27, 2009

### kanato

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

3. Jun 28, 2009

### 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.

4. Jun 29, 2009

### 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.

5. Jun 29, 2009

### steenreem

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