This paper states that the carbon atoms in a sheet of graphene form 3 $\sigma$ bonds with the neighbouring carbons and a $\pi$ bond that comes out of the plane (in the $z$ direction).
Unfortunately the paper doesn't go into detail about what this $\pi$ bond is exactly. I thought it could be a lone pair but carbon can't do that with 3 $\sigma$ bonds already in place.
What is the bond bonding the carbon to? How is this $\pi$ bond possible?
Best Answer
I want to answer my own question as I now understand how the $\pi$ bond forms.
As @YuzurihaInori said;
This image is what helped my understanding of it
The $\pi$ orbitals form together to make the "$\pi$-bands" the paper was talking about. It also helped me to understand why graphene is such a good conductor: due to delocalised electrons in the $\pi$ orbitals.