Question

Why are the electrons in graphene massless?

Answer 1

electrons velocity is near the velocity of light in here dirac points

Answer 2

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 E2=p2c2+m2c4E2=p2c2+m2c4, which becomes linear in momentum for m=0m=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).