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To change $v_F$ is to change the dispersion and density of states, which you generally expect to have an affect on every electronic and optoelectronic property. A particularly straightforward example: When you "gate" graphene (as you would a transistor), the fermi level moves, which you can measure most clearly by a cutting-off of IR absorption above a ...

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Well, I'm no expert on this, but a quick literature search suggests that you are sort of correct. Here's a paper on arXiv which is about this. You shouldn't trust everything you read on arXiv because it is not peer reviewed but this paper has subsequently been published in Phys. Rev. B as 1/N expansion in correlated graphene By: Kotov, Valeri N.; Uchoa, ...

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In the continuum limit the lattice spacing $a$ goes to zero, therefore the Brillouin zone grows to infinity. If the Fermi velocity shall remain constant, the hopping parameter has to be rescaled as $t \propto 1/a$ (remember that the bandwidth is on the scale of $t$ and $v_F = \nabla_k E(\vec k)$), therefore only the features close to the Dirac points remain ...

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