# Wave function of graphene

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1. May 8, 2012

### Newstein

I have read many papers stating that the wave function of graphene has two components due to the fact that the unit cell of graphene consists of two carbon atoms (A and B atoms). However, I was confused about that. If the unit cell consist of more atoms, what will the wave function be? Does it has more component?
Do not deride me for my stupied question for I'm not majored in theory. Expecting someone's instruction.

2. May 9, 2012

### DrDu

The point is more that there are two basis functions (a p_z orbital on each carbon atom) in the tight binding approximation. For each k value, the Bloch states are linear combinations of these two orbitals, or, to be more precise, they are obtained by a unitary transformation from these two orbitals. Hence there will be as many Bloch states as there are basis functions. Inclusion of the p_x, p_y and s orbitals will lead to the appearance of more bands which are however either completely occupied or unoccupied and lie below or above the pi orbitals. Hence they are of little interest as far as the electronic properties are concerned (however they are important to explain e.g. the bond strength in graphene).