Cyclotron resonance in graphene and Kohn's theorem

In 1961 Kohn has shown [1] that the cyclotron frequency is independent of the interaction. In the case of graphene there is some effort to suggest that the electron dispersion is linear in k, instead of (h/2$\pi $ )$^{2}$k$^{2}$/2m so that the Kohn theorem may not apply [2]. We find that the Kohn theorem does not use the dispersion relation and applies to graphene the same way as in some other material. We find that if e is replaced by e*=(1/2)ge, the Kohn theorem applies with the cyclotron frequency (h/2$\pi )\omega _{c}$= (1/2)geB/mc. Hence there is no interaction and all of the interaction is contained in g = (2j+1)/(2l+1) which is used only in the unperturbed Hamiltonian. The degeneracy of the levels is found to be related to the flux quantization. We have explained [3] the plateaus observed in the Hall effect resistivity of graphene without the use of interaction. Hence the Kohn's them applies to graphene. \\[4pt] [1] W. Kohn, Phys. Rev. 123, 1242-1244 (1961);\\[0pt] [2] E. A. Henriksen, et al., Phys. Rev. Lett. 104, 067404(2010). \\[0pt] [3] K. N. Shrivastava, AIP Conf. Proc. 1150, 59-67(2009); 1017,422-428(2008); Proc. SPIE 7155, 71552F(2008).