Possible High-Temperature Superconductivity in Multilayer Graphane: Can the Cuprates be Beaten?

We analyze a possible superconductivity in the hole-doped system of layered hydrogenized graphene by taking into account thermal fluctuations of the order parameter. In particular, we demonstrate that in the one-layer case the values of the high mean-field (MF) critical temperature T(c)(MF) similar to 80-90 K, predicted recently by Savini et al (Phys. Rev. Lett. 105:037002, 2010), do not alter significantly due to the fluctuations, and the Berezinskii-Kosterlitz-Thouless (BKT) critical temperature of the vortex superconductivity is almost the same as the MF temperature at doping 0.01-0.1. We show that in the case of multilayer system, when the coupling between the layers stabilizes the superconducting phase in the form of fluxon superconductivity, the critical temperature T(c) can increase dramatically to the values similar to 150 K, higher than the corresponding values in cuprates under ambient pressure.