I have learned that for a meterial to be conductive, it must contain free charge carriers, in most cases electrons.
Graphite does conduct electricity parellel to its graphene layers, which is due to the $p_z$ orbital of the carbon atoms containing electrons which are not "used" for bonding with other carbon atoms (as it is the case with the elctrons in the $sp^2$ hybrid orbitals - these are used to form $\sigma$ bonds to other carbon atoms).
The $p_z$ orbitals of the carbon atoms interact and form $\pi$ bonds whith each other, which results in a conjugated pi system - the electrons are delocalized over the whole layer (one could say that there is one big hybrid orbital formed from the individual $p_z$ orbitals.
However, since these electrons are not localized, one cannot define some movement for it - as far as I've understood, the orbital only describes the probability of where you may find the electron if measuring its position. Until then, due to the wavelike behaviour of an electron, it cannot be said to be in one specific place.
So how can delocalized electrons transfer electricity if one cannot really say that they are "moving"? (I asked about graphite, but the same should apply to metals)