1. a) Using the 2x2 matrix we derived in class on Wednesday, find the shape of the Fermi boundary, that is, the constant energy contours for E= 0.1 eV, 0.2 eV...
(You can reference all energies to \(E_{2pz}\) and use \(\gamma = 2 eV\).)
b) what bandwidth do you get with \(\gamma = 2 eV\) ?
2. At what values of k do you find the centers of Dirac cones to be?
3. Using the 2x2 matrix, and a gamma of 2 eV, what is the speed associated with dispersion near a dirac point. Please go ahead and post your results, thoughts, questions and comments here. Try this as a group effort and work on it right here in the comments.
PS. I think you can do this in closed form (without numerical methods), once you understand the "landscape".
PPS. Like c is the speed of light and w=ck is a dispersion relationship. What is the analogous thing for graphene?
Just a conceptual question: how do the Dirac points relate to non-reciprocal space? As in, where physically in the graphene lattice are the Dirac points?
ReplyDeleteAs I see it, there is no direct relationship. Reciprocal space is somewhat like momentum space.
Delete