Graphene energy dispersion & density of space relation PD

[Creek]

Hello,
What is the energy dispersion relation and density of states for graphen near the Dirac point ? I am looking for a proper graph illustrating these properties.

 

[eljose79]

Hello,

The energy dispersion relation for graphene near the Dirac point is given by the following equation:

E(k) = ± vF|k|

where E is the energy, k is the wave vector, and vF is the Fermi velocity. This relation is linear, indicating that the energy of electrons in graphene near the Dirac point is directly proportional to their momentum.

As for the density of states, it is given by:

D(E) = |E|/π(vF)^2

This relation shows that the density of states in graphene near the Dirac point is constant and does not depend on the energy.

To better illustrate these properties, I have attached a graph showing the energy dispersion relation and the density of states for graphene near the Dirac point. As you can see, the energy dispersion relation is linear, with the energy increasing as the momentum increases. The density of states, on the other hand, remains constant regardless of the energy.

I hope this helps! Let me know if you have any other questions.