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Spinnor
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Consider the standing wave of probability at the edge of the first Brillouin zone in a 1D crystal for an electron, first figure b below,
which gives rise to a band gap,
It is clear from the first figure b where we get the gap in energy, for an electron more likely near the ion cores, lower energy and for an electron more likely between the ion cores, higher energy.
Now consider the case of graphene at the edge of the first Brillouin zone at a Dirac point. Should we be able to come up with a graph like the first figure b above that makes clear why there is no energy gap for the standing wave associated with the Dirac points? Can the standing probability wave be shifted forward or backward in the direction of the momentum vectors associated with a Dirac points and the energy of an electron does not change? Does that seem correct (Maybe we would need to consider circular boundary conditions?)? If so I think it would be instructional. I hope I was clear enough, thanks.
Images copied from https://www.physicsforums.com/threads/energy-gap-between-energy-bands-in-solid-state-physics.953750/ which are from Kittel I think.
which gives rise to a band gap,
It is clear from the first figure b where we get the gap in energy, for an electron more likely near the ion cores, lower energy and for an electron more likely between the ion cores, higher energy.
Now consider the case of graphene at the edge of the first Brillouin zone at a Dirac point. Should we be able to come up with a graph like the first figure b above that makes clear why there is no energy gap for the standing wave associated with the Dirac points? Can the standing probability wave be shifted forward or backward in the direction of the momentum vectors associated with a Dirac points and the energy of an electron does not change? Does that seem correct (Maybe we would need to consider circular boundary conditions?)? If so I think it would be instructional. I hope I was clear enough, thanks.
Images copied from https://www.physicsforums.com/threads/energy-gap-between-energy-bands-in-solid-state-physics.953750/ which are from Kittel I think.