The Kubo formula for conductivity is valid, independent of the number of layers [1] in multi-layer graphene. The point that in particular Hao et al. raise is not that the Kubo formula for conductivity were invalid, but that for N-layer graphene the conductivity (as calculated on the basis of the Kubo formula) is to a good approximation N times the conductivity of a single layer (again, as calculated on the basis of the Kubo formula) for N ≲ 5, and that this is no longer the case for N ≳ 5. Clearly, the latter observation is not about the Kubo formula, but about the conductivity of an N-layer graphene.

[1] There are some subtle issues with regard to the general validity of the linear-response theory, first raised by NG van Kampen, that I do not go into. For details, you may wish to consult e.g. this relevant publication: CM van Vliet, J. Stat. Phys. 53, 49 (1988).

Thanks Behnam Farid very much. But there is a new concern that is described in the attachment file.

Zhihong Li : My pleasure. There is no conceivable reason why the conductivity of a N-layer graphene should be N times that of a single-layer graphene (the layers interact, so that even for N ≲ 5 one does not have N independent conducting channels in parallel). From my perspective, there is no cause for any concern. To see how things develop as N is increased from 1 to beyond 5, one needs to do some electronic structures calculations. This will in particular clarify what happens for N around 5.

Thanks Behnam Farid very much.

Regards.

Zhihong Li : My pleasure.