Why is graphene the way it is ?

[michael71828]

Hello :)

I'm not at all a specialist in condensed matter, nor do I understand much of its basics. I'm nevertheless a 1st year physics student who has a summer project on some aspect of modes in graphene and I would like to understand why the mathematics I was using this summer was the one required. Here are the principal unawnsered questions I have, despite numerous readings I did :

Is there any theoretical evidence that electrons in graphene are seen as being massless Dirac fermions (that is, 1/2 spin with zero effective mass which exhibits relativistic behavior, and therefor describe by Dirac equation), or are the evidence only experimental ? Why is the effective mass zero and the behavior relativistic ?

I wasn't able to deduced the 2D dirac equation useful for graphene from the ''original'' 4-components-spinor one. How can I do this ?

I would really appreciate any (even partial) anwsers that make minimum use of ''obscur'' concepts of condensed matter (like fermi energy, Dirac point, Brillouin zone, etc.) without explaining it.

Thank you very much for your help.

 

[atyy]

Maybe try Pachos's http://arxiv.org/abs/arXiv:0812.1116" suggests.

 

[Physics Monkey]

The electronic properties of graphene were predicted long before they were observed experimentally, so yes, we have convincing theoretical arguments that the electrons in graphene behave like relativistic particles in 2+1 dimensions. The excitement for experiments is in part because of the surprises they bring i.e. how interactions and the other facts of life about real graphene modify the simplest theory picture.

Try taking a look at the pedagogical lectures "From pencil lead to relativistic quantum physics" located here http://www.physics.upenn.edu/~kane/