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The typical graphene band-structure is a double-cone (in opposite directions to each other) with Dirac point in the middle. I assume the bottom cone is like the valence band, while the top cone is like the conduction band, if we compare this to silicon band-structure for example. But in case of silicon, such arrangement would constitute one valley! If silicon has multiple valleys (all in conduction band) they are clearly visible as multiple minimas in the band-structure (you can google these images I'm in a hurry).

So where does the "double valley" in graphene come from?

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