Question

How are the q-states in graphene spaced?

Answer 1

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Graphene production begins with a sheet of copper foil, held within a furnace filled with argon gas, designed to drive out oxygen in the air. Carbon atoms are then deposited onto the matrix, and a plastic coating is added to cover the sheet, which is then spun 3,000 times a minute.

Answer 2

We know that the energy is is given by Eq⃗ =ℏvF|q|, where ℏvF=3Aa/2, where A=2.8eV and a is the lattice spacing in graphene. (Note that this is the dispersion relation around the Dirac points, where it is appropriate to approximate it as a linear function.)

I am trying to find an expression for the number of q-states. Considering a Fermi circle of states (since we are in 2D), I have

Nq2=πq2(Δq)2,

where I divided by two to account for electron spin. This is analogous to doing

Nk2=πk2(Δk)2=πk2(2π/L)2