How is it possible that graphene has Fermi energy equal to zero? And why is the Fermi energy located where the density of states is zero? Does it have something to do with the fact that the Sommerfeld model only treats free electrons and graphene can’t be treated as free electrons?
I think that’s because you can always shift the energy by any constant. In this case it’s convenient to shift the graph such that it is symmetric around \epsilon=0, which apparently is also the Fermi energy.
For me this graph of the DoS helped to understand the whole picture (source https://physics.stackexchange.com/questions/234587/density-of-states-for-graphene):
So we just approximated the behavior around \epsilon=\epsilon_F=0 as linear.
I don’t know why \epsilon_F=0 though, I think that’s just a given fact here for this problem
Let’s keep this question open and see if we can revisit it towards the end of the course 