Density of states of graphene per unit area

[Physicslad78]

Dear all,

My aim is to get the density of states (DOS) per unit area for monolayer (bilayer) graphene. I have done this using mathematica. I have set a sampling k grid with 22500 points and computed the expression:

DOS=(1/Nk)*Ʃ δ(E-Ek) where the sum is over the k points in the reciprocal space and Nk is the total number of k vectors covering the First Brillouin zone. Then I substituted the δ-function with a gaussian function so that the above DOS is obtained per energy. My question is how to obtain the DOS per area from this expression. Do we have to divide by the area of the Brillouin zone (is it the area of the Unit cells described by lattice vectors?). If yes, is it in the real space of reciprocal space? Thanks a lot...waiting for your reply..

Homework Equations

The Attempt at a Solution

 

[member 553083]

Yes, you have to divide by the area of the Brillouin zone. The area is in the reciprocal space as it is related to the reciprocal lattice vectors. The area of the Brillouin zone is given by A = (2π)^2/|det(G)|, where G is the matrix containing the reciprocal lattice vectors. Therefore, the DOS per unit area is given by DOS/(2π)^2/|det(G)|.