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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 theoritical 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.