Q:

Why are the electrons in graphene massless?

I was reading Tommy Ohlsson's book on Relativistic Quantum Mechanics where he goes to a little digression on electrons and holes in Graphene. He claims that electrons and holes in Graphene can be considered as relativistic massless fermions and hence can be described by Weyl equations. Does anyone have any idea whether this description is really viable? If yes, why?

A:

Yes, low energy electrons and holes in graphene can be thought of as massless because of the linear dispersion of the band structure near the K points.  This is an analogy to the relativistic energy dispersion $E^2=p^2c^2+m^2c^4$, which becomes linear in momentum for $m=0$. This linear dispersion has been confirmed countless times via optical and electrical means, and it is the source of many of the bizarre relativistic-like properties that made graphene famous (e.g. Klein tunneling and the half-integer quantum Hall effect).

