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   <subfield code="a">Possible High-Temperature Superconductivity in Multilayer Graphane: Can the Cuprates be Beaten?</subfield>
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   <subfield code="a">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 $T_{\mathrm{\mathrm{c}}}^{\mathrm{MF}}\sim 80$-90K, 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 ∼150K, higher than the corresponding values in cuprates under ambient pressure.</subfield>
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