Graphene has a high electron mobility at ordinary room temperature. Experiments also has shown that the conductivity of electron and holes are almost the same. Between the temperature 10 to 100 k it is independent of temperature. At room temperature the resistivity is $10 ^{-6}$ ohmcm. There is a good wikipedia article for more information.
The minimum value for the energy is when both $\cos$ functions are 1 which gives an energy of $-3t$ which is the lowest occupied state. The highest occupied state is the Fermi level which in this case is $E_f = 0$. Thus the Fermi energy is $3t$.
The value of $t$ seems to be somewhere in the range of $2.5eV$ to $3eV$ (here with associated references) which would put the Fermi energy somewhere between $7.5eV$ to $9eV$.
I should point out that this value is not unique, but is by far the most commonly quoted result which stems from a tight-binding model that considers only nearest-neighbor interactions. You can also consider second nearest-neighbor interactions as well as many others (e.g. spin-orbit) which will change the result slightly.
Finally, I would add we are just considering the $\pi$ band and aren't considering any of the more tightly bound orbitals that come from the interplane bonding (the sp2 orbitals). I used to know the calculation for these energy levels as well but I seem to have misplaced my notes on the subject. Finding this energy would give you the most correct value of the Fermi energy, but since these states are rarely accessed they are typically ignored.
yeah it should do. as long as the material is conductive, it will induce a magnetic field. the problem is that you need exfoliated graphene which is hard to produce. once mass production of it starts, it will easily replace copper solenoids.
Best Answer
Graphene has a high electron mobility at ordinary room temperature. Experiments also has shown that the conductivity of electron and holes are almost the same. Between the temperature 10 to 100 k it is independent of temperature. At room temperature the resistivity is $10 ^{-6}$ ohmcm. There is a good wikipedia article for more information.