# Density of states of graphene per unit area

In summary, the aim is to obtain the density of states per unit area for monolayer/bilayer graphene using a sampling k grid and a gaussian function to obtain the DOS per energy. To obtain the DOS per area, the expression must be divided by the area of the Brillouin zone, which is related to the reciprocal lattice vectors.
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..

## The Attempt at a Solution

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)|.

## 1. What is the density of states of graphene per unit area?

The density of states of graphene per unit area refers to the number of electronic states per unit area in the energy spectrum of graphene. It is a measure of the available energy levels for electrons in graphene per unit area.

## 2. How is the density of states of graphene per unit area calculated?

The density of states of graphene per unit area can be calculated using the formula D(E) = (4 * pi * E) / (h^2 * v_F^2), where D(E) is the density of states, E is the energy, h is the Planck constant, and v_F is the Fermi velocity of graphene.

## 3. What factors affect the density of states of graphene per unit area?

The density of states of graphene per unit area is affected by the Fermi velocity, the size and shape of the graphene sheet, and any external factors that may alter the electronic structure of graphene such as doping or strain.

## 4. How does the density of states of graphene per unit area relate to its electronic properties?

The density of states of graphene per unit area is directly related to its electronic properties. A higher density of states means there are more available energy levels for electrons to occupy, which can affect the electrical conductivity and other electronic properties of graphene.

## 5. Can the density of states of graphene per unit area be modified?

Yes, the density of states of graphene per unit area can be modified through various methods such as doping, applying strain, or altering the size and shape of the graphene sheet. These modifications can change the electronic structure and therefore affect the density of states of graphene per unit area.

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