Reza Hekmati
For calculating dielectric function of graphene (sheet), you must know its complex
conductivity. One way is using random phase approximation (RPA). At last, complex dielectric function should be consider as a function of graphene's complex conductivity. Another way is Lindhard formula.
For GNR you must writes their Hamiltonians and use formulas which published in journals. The following papers may help you:
[1] http://arxiv.org/abs/0904.4378
[2] http://arxiv.org/abs/0806.3663
[3] http://arxiv.org/abs/cond-mat/0610157
[4] http://arxiv.org/pdf/0803.1802.pdf
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