Energy Band Crossing Points in Multilayers of Graphene

The monolayer of carbon atoms in a hexagonal lattice is called graphene. It is a monoatomic layer of graphite. The stacking of hexagons one over the other creates a variety of layers. We can stack in such a way that the hexagons of the first layer coincide with the hexagons of the next layer or they may be displaced. In this way we are able to make three types of layer stacks of graphene. These are called A, B and C types. We have found that a single layer of graphene shows a small gap of 27.212 meV. In the two layers of the AA type also the crossing is avoided. The energy from the apparent crossing point towards higher energies is not equal to that towards lower energies. The energy levels are not symmetric with respect to the apparent crossing point. In the AB type stacking for two layers the energy gap is 4.8 meV. The energy gap for a variety of stacking of layers has been obtained from the non‐relativistic Schrodinger theory.