I am looking for an explanation of the fact that although graphene is a very good conductor of electricity, at the Dirac point the conductivity of graphene is very low. Why? Keep in mind that at Dirac point the energy band gap becomes zero for graphene.
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The reason the conductivity is low at the Dirac point is that the density of states vanish. Thus, even though there is no energy penalty to excite the electrons and give them momentum, the available states to scatter into are so few that the net current is almost vanishing.
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$\begingroup$ can you send me any literature on this: " at the Dirac point is that the density of states vanish" $\endgroup$ Commented Sep 14, 2017 at 14:17
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$\begingroup$ @ArkaMukherjee - that is kind of the whole point of the 'Dirac point', that the density of states goes to zero? Wikipedia has some good coverage for graphene, with diagrams. $\endgroup$ Commented Sep 14, 2017 at 14:40